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Friday, June 3, 2022

Robot

From Wikipedia, the free encyclopedia

ASIMO (2000) at the Expo 2005
 
Articulated welding robots used in a factory are a type of industrial robot
 
The quadrupedal military robot Cheetah, an evolution of BigDog (pictured), was clocked as the world's fastest legged robot in 2012, beating the record set by an MIT bipedal robot in 1989.

A robot is a machine—especially one programmable by a computer—capable of carrying out a complex series of actions automatically. A robot can be guided by an external control device, or the control may be embedded within. Robots may be constructed to evoke human form, but most robots are task-performing machines, designed with an emphasis on stark functionality, rather than expressive aesthetics.

Robots can be autonomous or semi-autonomous and range from humanoids such as Honda's Advanced Step in Innovative Mobility (ASIMO) and TOSY's TOSY Ping Pong Playing Robot (TOPIO) to industrial robots, medical operating robots, patient assist robots, dog therapy robots, collectively programmed swarm robots, UAV drones such as General Atomics MQ-1 Predator, and even microscopic nano robots. By mimicking a lifelike appearance or automating movements, a robot may convey a sense of intelligence or thought of its own. Autonomous things are expected to proliferate in the future, with home robotics and the autonomous car as some of the main drivers.

The branch of technology that deals with the design, construction, operation, and application of robots, as well as computer systems for their control, sensory feedback, and information processing is robotics. These technologies deal with automated machines that can take the place of humans in dangerous environments or manufacturing processes, or resemble humans in appearance, behavior, or cognition. Many of today's robots are inspired by nature contributing to the field of bio-inspired robotics. These robots have also created a newer branch of robotics: soft robotics.

From the time of ancient civilization, there have been many accounts of user-configurable automated devices and even automata resembling humans and other animals, designed primarily as entertainment. As mechanical techniques developed through the Industrial age, there appeared more practical applications such as automated machines, remote-control and wireless remote-control.

The term comes from a Slavic root, robot-, with meanings associated with labor. The word 'robot' was first used to denote a fictional humanoid in a 1920 Czech-language play R.U.R. (Rossumovi Univerzální Roboti – Rossum's Universal Robots) by Karel Čapek, though it was Karel's brother Josef Čapek who was the word's true inventor. Electronics evolved into the driving force of development with the advent of the first electronic autonomous robots created by William Grey Walter in Bristol, England in 1948, as well as Computer Numerical Control (CNC) machine tools in the late 1940s by John T. Parsons and Frank L. Stulen.

The first modern digital and programmable robot was invented by George Devol in 1954 and spawned his seminal robotics company, Unimation. The first Unimate was sold to General Motors in 1961 where it lifted pieces of hot metal from die casting machines at the Inland Fisher Guide Plant in the West Trenton section of Ewing Township, New Jersey.

Robots have replaced humans in performing repetitive and dangerous tasks which humans prefer not to do, or are unable to do because of size limitations, or which take place in extreme environments such as outer space or the bottom of the sea. There are concerns about the increasing use of robots and their role in society. Robots are blamed for rising technological unemployment as they replace workers in increasing numbers of functions. The use of robots in military combat raises ethical concerns. The possibilities of robot autonomy and potential repercussions have been addressed in fiction and may be a realistic concern in the future.

Summary

KITT (a fictional robot) is mentally anthropomorphic.
 
iCub is physically anthropomorphic.

The word robot can refer to both physical robots and virtual software agents, but the latter are usually referred to as bots. There is no consensus on which machines qualify as robots but there is general agreement among experts, and the public, that robots tend to possess some or all of the following abilities and functions: accept electronic programming, process data or physical perceptions electronically, operate autonomously to some degree, move around, operate physical parts of itself or physical processes, sense and manipulate their environment, and exhibit intelligent behavior, especially behavior which mimics humans or other animals. Closely related to the concept of a robot is the field of Synthetic Biology, which studies entities whose nature is more comparable to beings than to machines.

History

The idea of automata originates in the mythologies of many cultures around the world. Engineers and inventors from ancient civilizations, including Ancient China, Ancient Greece, and Ptolemaic Egypt, attempted to build self-operating machines, some resembling animals and humans. Early descriptions of automata include the artificial doves of Archytas, the artificial birds of Mozi and Lu Ban, a "speaking" automaton by Hero of Alexandria, a washstand automaton by Philo of Byzantium, and a human automaton described in the Lie Zi.

Early beginnings

Many ancient mythologies, and most modern religions include artificial people, such as the mechanical servants built by the Greek god Hephaestus (Vulcan to the Romans), the clay golems of Jewish legend and clay giants of Norse legend, and Galatea, the mythical statue of Pygmalion that came to life. Since circa 400 BC, myths of Crete include Talos, a man of bronze who guarded the island from pirates.

In ancient Greece, the Greek engineer Ctesibius (c. 270 BC) "applied a knowledge of pneumatics and hydraulics to produce the first organ and water clocks with moving figures." In the 4th century BC, the Greek mathematician Archytas of Tarentum postulated a mechanical steam-operated bird he called "The Pigeon". Hero of Alexandria (10–70 AD), a Greek mathematician and inventor, created numerous user-configurable automated devices, and described machines powered by air pressure, steam and water.

Al-Jazari – A Musical Toy

The 11th century Lokapannatti tells of how the Buddha's relics were protected by mechanical robots (bhuta vahana yanta), from the kingdom of Roma visaya (Rome); until they were disarmed by King Ashoka.

In ancient China, the 3rd-century text of the Lie Zi describes an account of humanoid automata, involving a much earlier encounter between Chinese emperor King Mu of Zhou and a mechanical engineer known as Yan Shi, an 'artificer'. Yan Shi proudly presented the king with a life-size, human-shaped figure of his mechanical 'handiwork' made of leather, wood, and artificial organs. There are also accounts of flying automata in the Han Fei Zi and other texts, which attributes the 5th century BC Mohist philosopher Mozi and his contemporary Lu Ban with the invention of artificial wooden birds (ma yuan) that could successfully fly.

Su Song's astronomical clock tower showing the mechanical figurines which chimed the hours.

In 1066, the Chinese inventor Su Song built a water clock in the form of a tower which featured mechanical figurines which chimed the hours. His mechanism had a programmable drum machine with pegs (cams) that bumped into little levers that operated percussion instruments. The drummer could be made to play different rhythms and different drum patterns by moving the pegs to different locations.

Samarangana Sutradhara, a Sanskrit treatise by Bhoja (11th century), includes a chapter about the construction of mechanical contrivances (automata), including mechanical bees and birds, fountains shaped like humans and animals, and male and female dolls that refilled oil lamps, danced, played instruments, and re-enacted scenes from Hindu mythology.

13th century Muslim Scientist Ismail al-Jazari created several automated devices. He built automated moving peacocks driven by hydropower. He also invented the earliest known automatic gates, which were driven by hydropower, created automatic doors as part of one of his elaborate water clocks. One of al-Jazari's humanoid automata was a waitress that could serve water, tea or drinks. The drink was stored in a tank with a reservoir from where the drink drips into a bucket and, after seven minutes, into a cup, after which the waitress appears out of an automatic door serving the drink. Al-Jazari invented a hand washing automaton incorporating a flush mechanism now used in modern flush toilets. It features a female humanoid automaton standing by a basin filled with water. When the user pulls the lever, the water drains and the female automaton refills the basin.

Mark E. Rosheim summarizes the advances in robotics made by Muslim engineers, especially al-Jazari, as follows:

Unlike the Greek designs, these Arab examples reveal an interest, not only in dramatic illusion, but in manipulating the environment for human comfort. Thus, the greatest contribution the Arabs made, besides preserving, disseminating and building on the work of the Greeks, was the concept of practical application. This was the key element that was missing in Greek robotic science.

Model of Leonardo's robot with inner workings. Possibly constructed by Leonardo da Vinci around 1495.

In Renaissance Italy, Leonardo da Vinci (1452–1519) sketched plans for a humanoid robot around 1495. Da Vinci's notebooks, rediscovered in the 1950s, contained detailed drawings of a mechanical knight now known as Leonardo's robot, able to sit up, wave its arms and move its head and jaw. The design was probably based on anatomical research recorded in his Vitruvian Man. It is not known whether he attempted to build it. According to Encyclopædia Britannica, Leonardo da Vinci may have been influenced by the classic automata of al-Jazari.

In Japan, complex animal and human automata were built between the 17th to 19th centuries, with many described in the 18th century Karakuri zui (Illustrated Machinery, 1796). One such automaton was the karakuri ningyō, a mechanized puppet. Different variations of the karakuri existed: the Butai karakuri, which were used in theatre, the Zashiki karakuri, which were small and used in homes, and the Dashi karakuri which were used in religious festivals, where the puppets were used to perform reenactments of traditional myths and legends.

In France, between 1738 and 1739, Jacques de Vaucanson exhibited several life-sized automatons: a flute player, a pipe player and a duck. The mechanical duck could flap its wings, crane its neck, and swallow food from the exhibitor's hand, and it gave the illusion of digesting its food by excreting matter stored in a hidden compartment.

Remote-controlled systems

The Brennan torpedo, one of the earliest 'guided missiles'

Remotely operated vehicles were demonstrated in the late 19th century in the form of several types of remotely controlled torpedoes. The early 1870s saw remotely controlled torpedoes by John Ericsson (pneumatic), John Louis Lay (electric wire guided), and Victor von Scheliha (electric wire guided).

The Brennan torpedo, invented by Louis Brennan in 1877, was powered by two contra-rotating propellers that were spun by rapidly pulling out wires from drums wound inside the torpedo. Differential speed on the wires connected to the shore station allowed the torpedo to be guided to its target, making it "the world's first practical guided missile". In 1897 the British inventor Ernest Wilson was granted a patent for a torpedo remotely controlled by "Hertzian" (radio) waves and in 1898 Nikola Tesla publicly demonstrated a wireless-controlled torpedo that he hoped to sell to the US Navy.

In 1903, the Spanish engineer Leonardo Torres y Quevedo demonstrated a radio control system called "Telekino", which he wanted to use to control an airship of his own design. Unlike the previous systems, which carried out actions of the 'on/off' type, Torres device was able to memorize the signals received to execute the operations on its own and could carry out to 19 different orders.

Archibald Low, known as the "father of radio guidance systems" for his pioneering work on guided rockets and planes during the First World War. In 1917, he demonstrated a remote controlled aircraft to the Royal Flying Corps and in the same year built the first wire-guided rocket.

Origin of the term 'robot'

'Robot' was first applied as a term for artificial automata in the 1920 play R.U.R. by the Czech writer, Karel Čapek. However, Josef Čapek was named by his brother Karel as the true inventor of the term robot. The word 'robot' itself was not new, having been in the Slavic language as robota (forced labor), a term applied to peasants obligated to compulsory service under the feudal system (see: Robot Patent). Čapek's fictional story postulated the technological creation of artificial human bodies without souls, and the old theme of the feudal robota class eloquently fit the imagination of a new class of manufactured, artificial workers.

English pronunciation of the word has evolved relatively quickly since its introduction. In the U.S. during the late '30s to early '40s the second syllable was pronounced with a long "O" like "row-boat." By the late '50s to early '60s, some were pronouncing it with a short "U" like "row-but" while others used a softer "O" like "row-bought." By the '70s, its current pronunciation "row-bot" had become predominant.

Early robots

W. H. Richards with "George", 1932

In 1928, one of the first humanoid robots, Eric, was exhibited at the annual exhibition of the Model Engineers Society in London, where it delivered a speech. Invented by W. H. Richards, the robot's frame consisted of an aluminium body of armour with eleven electromagnets and one motor powered by a twelve-volt power source. The robot could move its hands and head and could be controlled through remote control or voice control. Both Eric and his "brother" George toured the world.

Westinghouse Electric Corporation built Televox in 1926; it was a cardboard cutout connected to various devices which users could turn on and off. In 1939, the humanoid robot known as Elektro was debuted at the 1939 New York World's Fair. Seven feet tall (2.1 m) and weighing 265 pounds (120.2 kg), it could walk by voice command, speak about 700 words (using a 78-rpm record player), smoke cigarettes, blow up balloons, and move its head and arms. The body consisted of a steel gear, cam and motor skeleton covered by an aluminum skin. In 1928, Japan's first robot, Gakutensoku, was designed and constructed by biologist Makoto Nishimura.

Modern autonomous robots

The first electronic autonomous robots with complex behaviour were created by William Grey Walter of the Burden Neurological Institute at Bristol, England in 1948 and 1949. He wanted to prove that rich connections between a small number of brain cells could give rise to very complex behaviors – essentially that the secret of how the brain worked lay in how it was wired up. His first robots, named Elmer and Elsie, were constructed between 1948 and 1949 and were often described as tortoises due to their shape and slow rate of movement. The three-wheeled tortoise robots were capable of phototaxis, by which they could find their way to a recharging station when they ran low on battery power.

Walter stressed the importance of using purely analogue electronics to simulate brain processes at a time when his contemporaries such as Alan Turing and John von Neumann were all turning towards a view of mental processes in terms of digital computation. His work inspired subsequent generations of robotics researchers such as Rodney Brooks, Hans Moravec and Mark Tilden. Modern incarnations of Walter's turtles may be found in the form of BEAM robotics.

U.S. Patent 2,988,237, issued in 1961 to Devol.

The first digitally operated and programmable robot was invented by George Devol in 1954 and was ultimately called the Unimate. This ultimately laid the foundations of the modern robotics industry. Devol sold the first Unimate to General Motors in 1960, and it was installed in 1961 in a plant in Trenton, New Jersey to lift hot pieces of metal from a die casting machine and stack them. Devol's patent for the first digitally operated programmable robotic arm represents the foundation of the modern robotics industry.

The first palletizing robot was introduced in 1963 by the Fuji Yusoki Kogyo Company. In 1973, a robot with six electromechanically driven axes was patented by KUKA robotics in Germany, and the programmable universal manipulation arm was invented by Victor Scheinman in 1976, and the design was sold to Unimation.

Commercial and industrial robots are now in widespread use performing jobs more cheaply or with greater accuracy and reliability than humans. They are also employed for jobs which are too dirty, dangerous or dull to be suitable for humans. Robots are widely used in manufacturing, assembly and packing, transport, earth and space exploration, surgery, weaponry, laboratory research, and mass production of consumer and industrial goods.

Future development and trends

External video
video icon Atlas, The Next Generation

Various techniques have emerged to develop the science of robotics and robots. One method is evolutionary robotics, in which a number of differing robots are submitted to tests. Those which perform best are used as a model to create a subsequent "generation" of robots. Another method is developmental robotics, which tracks changes and development within a single robot in the areas of problem-solving and other functions. Another new type of robot is just recently introduced which acts both as a smartphone and robot and is named RoboHon.

As robots become more advanced, eventually there may be a standard computer operating system designed mainly for robots. Robot Operating System is an open-source set of programs being developed at Stanford University, the Massachusetts Institute of Technology and the Technical University of Munich, Germany, among others. ROS provides ways to program a robot's navigation and limbs regardless of the specific hardware involved. It also provides high-level commands for items like image recognition and even opening doors. When ROS boots up on a robot's computer, it would obtain data on attributes such as the length and movement of robots' limbs. It would relay this data to higher-level algorithms. Microsoft is also developing a "Windows for robots" system with its Robotics Developer Studio, which has been available since 2007.

Japan hopes to have full-scale commercialization of service robots by 2025. Much technological research in Japan is led by Japanese government agencies, particularly the Trade Ministry.

Many future applications of robotics seem obvious to people, even though they are well beyond the capabilities of robots available at the time of the prediction. As early as 1982 people were confident that someday robots would: 1. Clean parts by removing molding flash 2. Spray paint automobiles with absolutely no human presence 3. Pack things in boxes—for example, orient and nest chocolate candies in candy boxes 4. Make electrical cable harness 5. Load trucks with boxes—a packing problem 6. Handle soft goods, such as garments and shoes 7. Shear sheep 8. prosthesis 9. Cook fast food and work in other service industries 10. Household robot.

Generally such predictions are overly optimistic in timescale.

New functionalities and prototypes

In 2008, Caterpillar Inc. developed a dump truck which can drive itself without any human operator. Many analysts believe that self-driving trucks may eventually revolutionize logistics. By 2014, Caterpillar had a self-driving dump truck which is expected to greatly change the process of mining. In 2015, these Caterpillar trucks were actively used in mining operations in Australia by the mining company Rio Tinto Coal Australia. Some analysts believe that within the next few decades, most trucks will be self-driving.

A literate or 'reading robot' named Marge has intelligence that comes from software. She can read newspapers, find and correct misspelled words, learn about banks like Barclays, and understand that some restaurants are better places to eat than others.

Baxter is a new robot introduced in 2012 which learns by guidance. A worker could teach Baxter how to perform a task by moving its hands in the desired motion and having Baxter memorize them. Extra dials, buttons, and controls are available on Baxter's arm for more precision and features. Any regular worker could program Baxter and it only takes a matter of minutes, unlike usual industrial robots that take extensive programs and coding to be used. This means Baxter needs no programming to operate. No software engineers are needed. This also means Baxter can be taught to perform multiple, more complicated tasks. Sawyer was added in 2015 for smaller, more precise tasks.

Prototype cooking robots have been developed and could be programmed for autonomous, dynamic and adjustable preparation of discrete meals.

Etymology

A scene from Karel Čapek's 1920 play R.U.R. (Rossum's Universal Robots), showing three robots

The word robot was introduced to the public by the Czech interwar writer Karel Čapek in his play R.U.R. (Rossum's Universal Robots), published in 1920. The play begins in a factory that uses a chemical substitute for protoplasm to manufacture living, simplified people called robots. The play does not focus in detail on the technology behind the creation of these living creatures, but in their appearance they prefigure modern ideas of androids, creatures who can be mistaken for humans. These mass-produced workers are depicted as efficient but emotionless, incapable of original thinking and indifferent to self-preservation. At issue is whether the robots are being exploited and the consequences of human dependence upon commodified labor (especially after a number of specially-formulated robots achieve self-awareness and incite robots all around the world to rise up against the humans).

Karel Čapek himself did not coin the word. He wrote a short letter in reference to an etymology in the Oxford English Dictionary in which he named his brother, the painter and writer Josef Čapek, as its actual originator.

In an article in the Czech journal Lidové noviny in 1933, he explained that he had originally wanted to call the creatures laboři ("workers", from Latin labor). However, he did not like the word, and sought advice from his brother Josef, who suggested "roboti". The word robota means literally "corvée", "serf labor", and figuratively "drudgery" or "hard work" in Czech and also (more general) "work", "labor" in many Slavic languages (e.g.: Bulgarian, Russian, Serbian, Slovak, Polish, Macedonian, Ukrainian, archaic Czech, as well as robot in Hungarian). Traditionally the robota (Hungarian robot) was the work period a serf (corvée) had to give for his lord, typically 6 months of the year. The origin of the word is the Old Church Slavonic (Old Bulgarian) rabota "servitude" ("work" in contemporary Bulgarian and Russian), which in turn comes from the Proto-Indo-European root *orbh-. Robot is cognate with the German root Arbeit (work).

The word robotics, used to describe this field of study, was coined by the science fiction writer Isaac Asimov. Asimov created the "Three Laws of Robotics" which are a recurring theme in his books. These have since been used by many others to define laws used in fiction. (The three laws are pure fiction, and no technology yet created has the ability to understand or follow them, and in fact most robots serve military purposes, which run quite contrary to the first law and often the third law. "People think about Asimov's laws, but they were set up to point out how a simple ethical system doesn't work. If you read the short stories, every single one is about a failure, and they are totally impractical," said Dr. Joanna Bryson of the University of Bath.)

Modern robots

A laparoscopic robotic surgery machine

Mobile robot

Mobile robots have the capability to move around in their environment and are not fixed to one physical location. An example of a mobile robot that is in common use today is the automated guided vehicle or automatic guided vehicle (AGV). An AGV is a mobile robot that follows markers or wires in the floor, or uses vision or lasers. AGVs are discussed later in this article.

Mobile robots are also found in industry, military and security environments. They also appear as consumer products, for entertainment or to perform certain tasks like vacuum cleaning. Mobile robots are the focus of a great deal of current research and almost every major university has one or more labs that focus on mobile robot research.

Mobile robots are usually used in tightly controlled environments such as on assembly lines because they have difficulty responding to unexpected interference. Because of this most humans rarely encounter robots. However domestic robots for cleaning and maintenance are increasingly common in and around homes in developed countries. Robots can also be found in military applications.

Industrial robots (manipulating)

A pick and place robot in a factory

Industrial robots usually consist of a jointed arm (multi-linked manipulator) and an end effector that is attached to a fixed surface. One of the most common type of end effector is a gripper assembly.

The International Organization for Standardization gives a definition of a manipulating industrial robot in ISO 8373:

"an automatically controlled, reprogrammable, multipurpose, manipulator programmable in three or more axes, which may be either fixed in place or mobile for use in industrial automation applications."

This definition is used by the International Federation of Robotics, the European Robotics Research Network (EURON) and many national standards committees.

Service robot

Most commonly industrial robots are fixed robotic arms and manipulators used primarily for production and distribution of goods. The term "service robot" is less well-defined. The International Federation of Robotics has proposed a tentative definition, "A service robot is a robot which operates semi- or fully autonomously to perform services useful to the well-being of humans and equipment, excluding manufacturing operations."

Educational (interactive) robots

Robots are used as educational assistants to teachers. From the 1980s, robots such as turtles were used in schools and programmed using the Logo language.

There are robot kits like Lego Mindstorms, BIOLOID, OLLO from ROBOTIS, or BotBrain Educational Robots can help children to learn about mathematics, physics, programming, and electronics. Robotics have also been introduced into the lives of elementary and high school students in the form of robot competitions with the company FIRST (For Inspiration and Recognition of Science and Technology). The organization is the foundation for the FIRST Robotics Competition, FIRST Tech Challenge, FIRST Lego League Challenge and FIRST Lego League Explore competitions.

There have also been robots such as the teaching computer, Leachim (1974). Leachim was an early example of speech synthesis using the using the Diphone synthesis method. 2-XL (1976) was a robot shaped game / teaching toy based on branching between audible tracks on an 8-track tape player, both invented by Michael J. Freeman. Later, the 8-track was upgraded to tape cassettes and then to digital.

Modular robot

Modular robots are a new breed of robots that are designed to increase the use of robots by modularizing their architecture. The functionality and effectiveness of a modular robot is easier to increase compared to conventional robots. These robots are composed of a single type of identical, several different identical module types, or similarly shaped modules, which vary in size. Their architectural structure allows hyper-redundancy for modular robots, as they can be designed with more than 8 degrees of freedom (DOF). Creating the programming, inverse kinematics and dynamics for modular robots is more complex than with traditional robots. Modular robots may be composed of L-shaped modules, cubic modules, and U and H-shaped modules. ANAT technology, an early modular robotic technology patented by Robotics Design Inc., allows the creation of modular robots from U and H shaped modules that connect in a chain, and are used to form heterogeneous and homogenous modular robot systems. These "ANAT robots" can be designed with "n" DOF as each module is a complete motorized robotic system that folds relatively to the modules connected before and after it in its chain, and therefore a single module allows one degree of freedom. The more modules that are connected to one another, the more degrees of freedom it will have. L-shaped modules can also be designed in a chain, and must become increasingly smaller as the size of the chain increases, as payloads attached to the end of the chain place a greater strain on modules that are further from the base. ANAT H-shaped modules do not suffer from this problem, as their design allows a modular robot to distribute pressure and impacts evenly amongst other attached modules, and therefore payload-carrying capacity does not decrease as the length of the arm increases. Modular robots can be manually or self-reconfigured to form a different robot, that may perform different applications. Because modular robots of the same architecture type are composed of modules that compose different modular robots, a snake-arm robot can combine with another to form a dual or quadra-arm robot, or can split into several mobile robots, and mobile robots can split into multiple smaller ones, or combine with others into a larger or different one. This allows a single modular robot the ability to be fully specialized in a single task, as well as the capacity to be specialized to perform multiple different tasks.

Modular robotic technology is currently being applied in hybrid transportation, industrial automation, duct cleaning and handling. Many research centres and universities have also studied this technology, and have developed prototypes.

Collaborative robots

A collaborative robot or cobot is a robot that can safely and effectively interact with human workers while performing simple industrial tasks. However, end-effectors and other environmental conditions may create hazards, and as such risk assessments should be done before using any industrial motion-control application.

The collaborative robots most widely used in industries today are manufactured by Universal Robots in Denmark.

Rethink Robotics—founded by Rodney Brooks, previously with iRobot—introduced Baxter in September 2012; as an industrial robot designed to safely interact with neighboring human workers, and be programmable for performing simple tasks. Baxters stop if they detect a human in the way of their robotic arms and have prominent off switches. Intended for sale to small businesses, they are promoted as the robotic analogue of the personal computer. As of May 2014, 190 companies in the US have bought Baxters and they are being used commercially in the UK.

Robots in society

Roughly half of all the robots in the world are in Asia, 32% in Europe, and 16% in North America, 1% in Australasia and 1% in Africa. 40% of all the robots in the world are in Japan, making Japan the country with the highest number of robots.

Autonomy and ethical questions

An android, or robot designed to resemble a human, can appear comforting to some people and disturbing to others

As robots have become more advanced and sophisticated, experts and academics have increasingly explored the questions of what ethics might govern robots' behavior, and whether robots might be able to claim any kind of social, cultural, ethical or legal rights. One scientific team has said that it was possible that a robot brain would exist by 2019. Others predict robot intelligence breakthroughs by 2050. Recent advances have made robotic behavior more sophisticated. The social impact of intelligent robots is subject of a 2010 documentary film called Plug & Pray.

Vernor Vinge has suggested that a moment may come when computers and robots are smarter than humans. He calls this "the Singularity". He suggests that it may be somewhat or possibly very dangerous for humans. This is discussed by a philosophy called Singularitarianism.

In 2009, experts attended a conference hosted by the Association for the Advancement of Artificial Intelligence (AAAI) to discuss whether computers and robots might be able to acquire any autonomy, and how much these abilities might pose a threat or hazard. They noted that some robots have acquired various forms of semi-autonomy, including being able to find power sources on their own and being able to independently choose targets to attack with weapons. They also noted that some computer viruses can evade elimination and have achieved "cockroach intelligence." They noted that self-awareness as depicted in science-fiction is probably unlikely, but that there were other potential hazards and pitfalls. Various media sources and scientific groups have noted separate trends in differing areas which might together result in greater robotic functionalities and autonomy, and which pose some inherent concerns.

Military robots

Some experts and academics have questioned the use of robots for military combat, especially when such robots are given some degree of autonomous functions. There are also concerns about technology which might allow some armed robots to be controlled mainly by other robots. The US Navy has funded a report which indicates that, as military robots become more complex, there should be greater attention to implications of their ability to make autonomous decisions. One researcher states that autonomous robots might be more humane, as they could make decisions more effectively. However, other experts question this.

One robot in particular, the EATR, has generated public concerns over its fuel source, as it can continually refuel itself using organic substances. Although the engine for the EATR is designed to run on biomass and vegetation specifically selected by its sensors, which it can find on battlefields or other local environments, the project has stated that chicken fat can also be used.

Manuel De Landa has noted that "smart missiles" and autonomous bombs equipped with artificial perception can be considered robots, as they make some of their decisions autonomously. He believes this represents an important and dangerous trend in which humans are handing over important decisions to machines.

Relationship to unemployment

For centuries, people have predicted that machines would make workers obsolete and increase unemployment, although the causes of unemployment are usually thought to be due to social policy.

A recent example of human replacement involves Taiwanese technology company Foxconn who, in July 2011, announced a three-year plan to replace workers with more robots. At present the company uses ten thousand robots but will increase them to a million robots over a three-year period.

Lawyers have speculated that an increased prevalence of robots in the workplace could lead to the need to improve redundancy laws.

Kevin J. Delaney said "Robots are taking human jobs. But Bill Gates believes that governments should tax companies’ use of them, as a way to at least temporarily slow the spread of automation and to fund other types of employment." The robot tax would also help pay a guaranteed living wage to the displaced workers.

The World Bank's World Development Report 2019 puts forth evidence showing that while automation displaces workers, technological innovation creates more new industries and jobs on balance.

Contemporary uses

A general-purpose robot acts as a guide during the day and a security guard at night.
 

At present, there are two main types of robots, based on their use: general-purpose autonomous robots and dedicated robots.

Robots can be classified by their specificity of purpose. A robot might be designed to perform one particular task extremely well, or a range of tasks less well. All robots by their nature can be re-programmed to behave differently, but some are limited by their physical form. For example, a factory robot arm can perform jobs such as cutting, welding, gluing, or acting as a fairground ride, while a pick-and-place robot can only populate printed circuit boards.

General-purpose autonomous robots

General-purpose autonomous robots can perform a variety of functions independently. General-purpose autonomous robots typically can navigate independently in known spaces, handle their own re-charging needs, interface with electronic doors and elevators and perform other basic tasks. Like computers, general-purpose robots can link with networks, software and accessories that increase their usefulness. They may recognize people or objects, talk, provide companionship, monitor environmental quality, respond to alarms, pick up supplies and perform other useful tasks. General-purpose robots may perform a variety of functions simultaneously or they may take on different roles at different times of day. Some such robots try to mimic human beings and may even resemble people in appearance; this type of robot is called a humanoid robot. Humanoid robots are still in a very limited stage, as no humanoid robot can, as of yet, actually navigate around a room that it has never been in. Thus, humanoid robots are really quite limited, despite their intelligent behaviors in their well-known environments.

Factory robots

Car production

Over the last three decades, automobile factories have become dominated by robots. A typical factory contains hundreds of industrial robots working on fully automated production lines, with one robot for every ten human workers. On an automated production line, a vehicle chassis on a conveyor is welded, glued, painted and finally assembled at a sequence of robot stations.

Packaging

Industrial robots are also used extensively for palletizing and packaging of manufactured goods, for example for rapidly taking drink cartons from the end of a conveyor belt and placing them into boxes, or for loading and unloading machining centers.

Electronics

Mass-produced printed circuit boards (PCBs) are almost exclusively manufactured by pick-and-place robots, typically with SCARA manipulators, which remove tiny electronic components from strips or trays, and place them on to PCBs with great accuracy. Such robots can place hundreds of thousands of components per hour, far out-performing a human in speed, accuracy, and reliability.

Automated guided vehicles (AGVs)

An intelligent AGV drops-off goods without needing lines or beacons in the workspace.

Mobile robots, following markers or wires in the floor, or using vision or lasers, are used to transport goods around large facilities, such as warehouses, container ports, or hospitals.

Early AGV-style robots

Limited to tasks that could be accurately defined and had to be performed the same way every time. Very little feedback or intelligence was required, and the robots needed only the most basic exteroceptors (sensors). The limitations of these AGVs are that their paths are not easily altered and they cannot alter their paths if obstacles block them. If one AGV breaks down, it may stop the entire operation.

Interim AGV technologies

Developed to deploy triangulation from beacons or bar code grids for scanning on the floor or ceiling. In most factories, triangulation systems tend to require moderate to high maintenance, such as daily cleaning of all beacons or bar codes. Also, if a tall pallet or large vehicle blocks beacons or a bar code is marred, AGVs may become lost. Often such AGVs are designed to be used in human-free environments.

Intelligent AGVs (i-AGVs)

Such as SmartLoader, SpeciMinder, ADAM, Tug Eskorta, and MT 400 with Motivity are designed for people-friendly workspaces. They navigate by recognizing natural features. 3D scanners or other means of sensing the environment in two or three dimensions help to eliminate cumulative errors in dead-reckoning calculations of the AGV's current position. Some AGVs can create maps of their environment using scanning lasers with simultaneous localization and mapping (SLAM) and use those maps to navigate in real time with other path planning and obstacle avoidance algorithms. They are able to operate in complex environments and perform non-repetitive and non-sequential tasks such as transporting photomasks in a semiconductor lab, specimens in hospitals and goods in warehouses. For dynamic areas, such as warehouses full of pallets, AGVs require additional strategies using three-dimensional sensors such as time-of-flight or stereovision cameras.

Dirty, dangerous, dull, or inaccessible tasks

There are many jobs that humans would rather leave to robots. The job may be boring, such as domestic cleaning or sports field line marking, or dangerous, such as exploring inside a volcano. Other jobs are physically inaccessible, such as exploring another planet, cleaning the inside of a long pipe, or performing laparoscopic surgery.

Space probes

Almost every unmanned space probe ever launched was a robot. Some were launched in the 1960s with very limited abilities, but their ability to fly and land (in the case of Luna 9) is an indication of their status as a robot. This includes the Voyager probes and the Galileo probes, among others.

Telerobots

A U.S. Marine Corps technician prepares to use a telerobot to detonate a buried improvised explosive device near Camp Fallujah, Iraq.

Teleoperated robots, or telerobots, are devices remotely operated from a distance by a human operator rather than following a predetermined sequence of movements, but which has semi-autonomous behaviour. They are used when a human cannot be present on site to perform a job because it is dangerous, far away, or inaccessible. The robot may be in another room or another country, or may be on a very different scale to the operator. For instance, a laparoscopic surgery robot allows the surgeon to work inside a human patient on a relatively small scale compared to open surgery, significantly shortening recovery time. They can also be used to avoid exposing workers to the hazardous and tight spaces such as in duct cleaning. When disabling a bomb, the operator sends a small robot to disable it. Several authors have been using a device called the Longpen to sign books remotely. Teleoperated robot aircraft, like the Predator Unmanned Aerial Vehicle, are increasingly being used by the military. These pilotless drones can search terrain and fire on targets. Hundreds of robots such as iRobot's Packbot and the Foster-Miller TALON are being used in Iraq and Afghanistan by the U.S. military to defuse roadside bombs or improvised explosive devices (IEDs) in an activity known as explosive ordnance disposal (EOD).

Automated fruit harvesting machines

Robots are used to automate picking fruit on orchards at a cost lower than that of human pickers.

Domestic robots

The Roomba domestic vacuum cleaner robot does a single, menial job

Domestic robots are simple robots dedicated to a single task work in home use. They are used in simple but often disliked jobs, such as vacuum cleaning, floor washing, and lawn mowing. An example of a domestic robot is a Roomba.

Military robots

Military robots include the SWORDS robot which is currently used in ground-based combat. It can use a variety of weapons and there is some discussion of giving it some degree of autonomy in battleground situations.

Unmanned combat air vehicles (UCAVs), which are an upgraded form of UAVs, can do a wide variety of missions, including combat. UCAVs are being designed such as the BAE Systems Mantis which would have the ability to fly themselves, to pick their own course and target, and to make most decisions on their own. The BAE Taranis is a UCAV built by Great Britain which can fly across continents without a pilot and has new means to avoid detection. Flight trials are expected to begin in 2011.

The AAAI has studied this topic in depth and its president has commissioned a study to look at this issue.

Some have suggested a need to build "Friendly AI", meaning that the advances which are already occurring with AI should also include an effort to make AI intrinsically friendly and humane. Several such measures reportedly already exist, with robot-heavy countries such as Japan and South Korea having begun to pass regulations requiring robots to be equipped with safety systems, and possibly sets of 'laws' akin to Asimov's Three Laws of Robotics. An official report was issued in 2009 by the Japanese government's Robot Industry Policy Committee. Chinese officials and researchers have issued a report suggesting a set of ethical rules, and a set of new legal guidelines referred to as "Robot Legal Studies." Some concern has been expressed over a possible occurrence of robots telling apparent falsehoods.

Mining robots

Mining robots are designed to solve a number of problems currently facing the mining industry, including skills shortages, improving productivity from declining ore grades, and achieving environmental targets. Due to the hazardous nature of mining, in particular underground mining, the prevalence of autonomous, semi-autonomous, and tele-operated robots has greatly increased in recent times. A number of vehicle manufacturers provide autonomous trains, trucks and loaders that will load material, transport it on the mine site to its destination, and unload without requiring human intervention. One of the world's largest mining corporations, Rio Tinto, has recently expanded its autonomous truck fleet to the world's largest, consisting of 150 autonomous Komatsu trucks, operating in Western Australia. Similarly, BHP has announced the expansion of its autonomous drill fleet to the world's largest, 21 autonomous Atlas Copco drills.

Drilling, longwall and rockbreaking machines are now also available as autonomous robots. The Atlas Copco Rig Control System can autonomously execute a drilling plan on a drilling rig, moving the rig into position using GPS, set up the drill rig and drill down to specified depths. Similarly, the Transmin Rocklogic system can automatically plan a path to position a rockbreaker at a selected destination. These systems greatly enhance the safety and efficiency of mining operations.

Healthcare

Robots in healthcare have two main functions. Those which assist an individual, such as a sufferer of a disease like Multiple Sclerosis, and those which aid in the overall systems such as pharmacies and hospitals.

Home automation for the elderly and disabled

The Care-Providing Robot FRIEND

Robots used in home automation have developed over time from simple basic robotic assistants, such as the Handy 1, through to semi-autonomous robots, such as FRIEND which can assist the elderly and disabled with common tasks.

The population is aging in many countries, especially Japan, meaning that there are increasing numbers of elderly people to care for, but relatively fewer young people to care for them. Humans make the best carers, but where they are unavailable, robots are gradually being introduced.

FRIEND is a semi-autonomous robot designed to support disabled and elderly people in their daily life activities, like preparing and serving a meal. FRIEND make it possible for patients who are paraplegic, have muscle diseases or serious paralysis (due to strokes etc.), to perform tasks without help from other people like therapists or nursing staff.

Pharmacies

Script Pro manufactures a robot designed to help pharmacies fill prescriptions that consist of oral solids or medications in pill form. The pharmacist or pharmacy technician enters the prescription information into its information system. The system, upon determining whether or not the drug is in the robot, will send the information to the robot for filling. The robot has 3 different size vials to fill determined by the size of the pill. The robot technician, user, or pharmacist determines the needed size of the vial based on the tablet when the robot is stocked. Once the vial is filled it is brought up to a conveyor belt that delivers it to a holder that spins the vial and attaches the patient label. Afterwards it is set on another conveyor that delivers the patient's medication vial to a slot labeled with the patient's name on an LED read out. The pharmacist or technician then checks the contents of the vial to ensure it's the correct drug for the correct patient and then seals the vials and sends it out front to be picked up.

McKesson's Robot RX is another healthcare robotics product that helps pharmacies dispense thousands of medications daily with little or no errors. The robot can be ten feet wide and thirty feet long and can hold hundreds of different kinds of medications and thousands of doses. The pharmacy saves many resources like staff members that are otherwise unavailable in a resource scarce industry. It uses an electromechanical head coupled with a pneumatic system to capture each dose and deliver it to either its stocked or dispensed location. The head moves along a single axis while it rotates 180 degrees to pull the medications. During this process it uses barcode technology to verify it's pulling the correct drug. It then delivers the drug to a patient specific bin on a conveyor belt. Once the bin is filled with all of the drugs that a particular patient needs and that the robot stocks, the bin is then released and returned out on the conveyor belt to a technician waiting to load it into a cart for delivery to the floor.

Research robots

While most robots today are installed in factories or homes, performing labour or life saving jobs, many new types of robot are being developed in laboratories around the world. Much of the research in robotics focuses not on specific industrial tasks, but on investigations into new types of robot, alternative ways to think about or design robots, and new ways to manufacture them. It is expected that these new types of robot will be able to solve real world problems when they are finally realized.

Bionic and biomimetic robots

One approach to designing robots is to base them on animals. BionicKangaroo was designed and engineered by studying and applying the physiology and methods of locomotion of a kangaroo.

Nanorobots

Nanorobotics is the emerging technology field of creating machines or robots whose components are at or close to the microscopic scale of a nanometer (10−9 meters). Also known as "nanobots" or "nanites", they would be constructed from molecular machines. So far, researchers have mostly produced only parts of these complex systems, such as bearings, sensors, and synthetic molecular motors, but functioning robots have also been made such as the entrants to the Nanobot Robocup contest. Researchers also hope to be able to create entire robots as small as viruses or bacteria, which could perform tasks on a tiny scale. Possible applications include micro surgery (on the level of individual cells), utility fog, manufacturing, weaponry and cleaning. Some people have suggested that if there were nanobots which could reproduce, the earth would turn into "grey goo", while others argue that this hypothetical outcome is nonsense.

Reconfigurable robots

A few researchers have investigated the possibility of creating robots which can alter their physical form to suit a particular task, like the fictional T-1000. Real robots are nowhere near that sophisticated however, and mostly consist of a small number of cube shaped units, which can move relative to their neighbours. Algorithms have been designed in case any such robots become a reality.

Robotic, mobile laboratory operators

In July 2020 scientists reported the development of a mobile robot chemist and demonstrate that it can assist in experimental searches. According to the scientists their strategy was automating the researcher rather than the instruments – freeing up time for the human researchers to think creatively – and could identify photocatalyst mixtures for hydrogen production from water that were six times more active than initial formulations. The modular robot can operate laboratory instruments, work nearly around the clock, and autonomously make decisions on his next actions depending on experimental results.

Soft-bodied robots

Robots with silicone bodies and flexible actuators (air muscles, electroactive polymers, and ferrofluids) look and feel different from robots with rigid skeletons, and can have different behaviors. Soft, flexible (and sometimes even squishy) robots are often designed to mimic the biomechanics of animals and other things found in nature, which is leading to new applications in medicine, care giving, search and rescue, food handling and manufacturing, and scientific exploration.

Swarm robots

Inspired by colonies of insects such as ants and bees, researchers are modeling the behavior of swarms of thousands of tiny robots which together perform a useful task, such as finding something hidden, cleaning, or spying. Each robot is quite simple, but the emergent behavior of the swarm is more complex. The whole set of robots can be considered as one single distributed system, in the same way an ant colony can be considered a superorganism, exhibiting swarm intelligence. The largest swarms so far created include the iRobot swarm, the SRI/MobileRobots CentiBots project and the Open-source Micro-robotic Project swarm, which are being used to research collective behaviors. Swarms are also more resistant to failure. Whereas one large robot may fail and ruin a mission, a swarm can continue even if several robots fail. This could make them attractive for space exploration missions, where failure is normally extremely costly.

Haptic interface robots

Robotics also has application in the design of virtual reality interfaces. Specialized robots are in widespread use in the haptic research community. These robots, called "haptic interfaces", allow touch-enabled user interaction with real and virtual environments. Robotic forces allow simulating the mechanical properties of "virtual" objects, which users can experience through their sense of touch.

Contemporary art and sculpture

Robots are used by contemporary artists to create works that include mechanical automation. There are many branches of robotic art, one of which is robotic installation art, a type of installation art that is programmed to respond to viewer interactions, by means of computers, sensors and actuators. The future behavior of such installations can therefore be altered by input from either the artist or the participant, which differentiates these artworks from other types of kinetic art.

Le Grand Palais in Paris organized an exhibition "Artists & Robots", featuring artworks created by more than forty artists with the help of robots in 2018.

Robots in popular culture

Toy robots on display at the Museo del Objeto del Objeto in Mexico City.
 

Literature

Robotic characters, androids (artificial men/women) or gynoids (artificial women), and cyborgs (also "bionic men/women", or humans with significant mechanical enhancements) have become a staple of science fiction.

The first reference in Western literature to mechanical servants appears in Homer's Iliad. In Book XVIII, Hephaestus, god of fire, creates new armor for the hero Achilles, assisted by robots. According to the Rieu translation, "Golden maidservants hastened to help their master. They looked like real women and could not only speak and use their limbs but were endowed with intelligence and trained in handwork by the immortal gods." The words "robot" or "android" are not used to describe them, but they are nevertheless mechanical devices human in appearance. "The first use of the word Robot was in Karel Čapek's play R.U.R. (Rossum's Universal Robots) (written in 1920)". Writer Karel Čapek was born in Czechoslovakia (Czech Republic).

Possibly the most prolific author of the twentieth century was Isaac Asimov (1920–1992) who published over five-hundred books. Asimov is probably best remembered for his science-fiction stories and especially those about robots, where he placed robots and their interaction with society at the center of many of his works. Asimov carefully considered the problem of the ideal set of instructions robots might be given to lower the risk to humans, and arrived at his Three Laws of Robotics: a robot may not injure a human being or, through inaction, allow a human being to come to harm; a robot must obey orders given it by human beings, except where such orders would conflict with the First Law; and a robot must protect its own existence as long as such protection does not conflict with the First or Second Law. These were introduced in his 1942 short story "Runaround", although foreshadowed in a few earlier stories. Later, Asimov added the Zeroth Law: "A robot may not harm humanity, or, by inaction, allow humanity to come to harm"; the rest of the laws are modified sequentially to acknowledge this.

According to the Oxford English Dictionary, the first passage in Asimov's short story "Liar!" (1941) that mentions the First Law is the earliest recorded use of the word robotics. Asimov was not initially aware of this; he assumed the word already existed by analogy with mechanics, hydraulics, and other similar terms denoting branches of applied knowledge.

Films

Robots appear in many films. Most of the robots in cinema are fictional. Two of the most famous are R2-D2 and C-3PO from the Star Wars franchise.

Sex robots

The concept of humanoid sex robots has drawn public attention and elicited debate regarding their supposed benefits and potential effects on society. Opponents argue that the introduction of such devices would be socially harmful, and demeaning to women and children, while proponents cite their potential therapeutical benefits, particularly in aiding people with dementia or depression.

Problems depicted in popular culture

Italian movie The Mechanical Man (1921), the first film to have shown a battle between robots.

Fears and concerns about robots have been repeatedly expressed in a wide range of books and films. A common theme is the development of a master race of conscious and highly intelligent robots, motivated to take over or destroy the human race. Frankenstein (1818), often called the first science fiction novel, has become synonymous with the theme of a robot or android advancing beyond its creator.

Other works with similar themes include The Mechanical Man, The Terminator, Runaway, RoboCop, the Replicators in Stargate, the Cylons in Battlestar Galactica, the Cybermen and Daleks in Doctor Who, The Matrix, Enthiran and I, Robot. Some fictional robots are programmed to kill and destroy; others gain superhuman intelligence and abilities by upgrading their own software and hardware. Examples of popular media where the robot becomes evil are 2001: A Space Odyssey, Red Planet and Enthiran.

The 2017 game Horizon Zero Dawn explores themes of robotics in warfare, robot ethics, and the AI control problem, as well as the positive or negative impact such technologies could have on the environment.

Another common theme is the reaction, sometimes called the "uncanny valley", of unease and even revulsion at the sight of robots that mimic humans too closely.

More recently, fictional representations of artificially intelligent robots in films such as A.I. Artificial Intelligence and Ex Machina and the 2016 TV adaptation of Westworld have engaged audience sympathy for the robots themselves.

Thursday, June 2, 2022

Arrow's impossibility theorem

From Wikipedia, the free encyclopedia

In social choice theory, Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem stating that when voters have three or more distinct alternatives (options), no ranked voting electoral system can convert the ranked preferences of individuals into a community-wide (complete and transitive) ranking while also meeting a specified set of criteria: unrestricted domain, non-dictatorship, Pareto efficiency, and independence of irrelevant alternatives. The theorem is often cited in discussions of voting theory as it is further interpreted by the Gibbard–Satterthwaite theorem. The theorem is named after economist and Nobel laureate Kenneth Arrow, who demonstrated the theorem in his doctoral thesis and popularized it in his 1951 book Social Choice and Individual Values. The original paper was titled "A Difficulty in the Concept of Social Welfare".

In short, the theorem states that no rank-order electoral system can be designed that always satisfies these three "fairness" criteria:

  • If every voter prefers alternative X over alternative Y, then the group prefers X over Y.
  • If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged (even if voters' preferences between other pairs like X and Z, Y and Z, or Z and W change).
  • There is no "dictator": no single voter possesses the power to always determine the group's preference.

Cardinal voting electoral systems are not covered by the theorem, as they convey more information than rank orders. However, Gibbard's theorem shows that strategic voting remains a problem.

The axiomatic approach Arrow adopted can treat all conceivable rules (that are based on preferences) within one unified framework. In that sense, the approach is qualitatively different from the earlier one in voting theory, in which rules were investigated one by one. One can therefore say that the contemporary paradigm of social choice theory started from this theorem.

The practical consequences of the theorem are debatable: Arrow has said "Most systems are not going to work badly all of the time. All I proved is that all can work badly at times."

Statement

The need to aggregate preferences occurs in many disciplines: in welfare economics, where one attempts to find an economic outcome which would be acceptable and stable; in decision theory, where a person has to make a rational choice based on several criteria; and most naturally in electoral systems, which are mechanisms for extracting a governance-related decision from a multitude of voters' preferences.

The framework for Arrow's theorem assumes that we need to extract a preference order on a given set of options (outcomes). Each individual in the society (or equivalently, each decision criterion) gives a particular order of preferences on the set of outcomes. We are searching for a ranked voting electoral system, called a social welfare function (preference aggregation rule), which transforms the set of preferences (profile of preferences) into a single global societal preference order. Arrow's theorem says that if the decision-making body has at least two members and at least three options to decide among, then it is impossible to design a social welfare function that satisfies all these conditions (assumed to be a reasonable requirement of a fair electoral system) at once:

Non-dictatorship
The social welfare function should account for the wishes of multiple voters. It cannot simply mimic the preferences of a single voter.
Unrestricted domain, or universality
For any set of individual voter preferences, the social welfare function should yield a unique and complete ranking of societal choices. Thus:
  • It must do so in a manner that results in a complete ranking of preferences for society.
  • It must deterministically provide the same ranking each time voters' preferences are presented the same way.
Independence of irrelevant alternatives (IIA)
The social preference between x and y should depend only on the individual preferences between x and y (pairwise independence). More generally, changes in individuals' rankings of irrelevant alternatives (ones outside a certain subset) should have no impact on the societal ranking of the subset. For example, if candidate x ranks socially before candidate y, then x should rank socially before y even if a third candidate z is removed from participation. (See Remarks below.)
Monotonicity, or positive association of social and individual values
If any individual modifies his or her preference order by promoting a certain option, then the societal preference order should respond only by promoting that same option or not changing, never by placing it lower than before. An individual should not be able to hurt an option by ranking it higher.
Non-imposition, or citizen sovereignty
Every possible societal preference order should be achievable by some set of individual preference orders. This means that the social welfare function is surjective: It has an unrestricted target space.

A later (1963) version of Arrow's theorem replaced the monotonicity and non-imposition criteria with:

Pareto efficiency, or unanimity
If every individual prefers a certain option to another, then so must the resulting societal preference order. This, again, is a demand that the social welfare function will be minimally sensitive to the preference profile.

This later version is more general, having weaker conditions. The axioms of monotonicity, non-imposition, and IIA together imply Pareto efficiency, whereas Pareto efficiency (itself implying non-imposition) and IIA together do not imply monotonicity.

Independence of irrelevant alternatives (IIA)

The IIA condition has three purposes (or effects):

Normative
Irrelevant alternatives should not matter.
Practical
Use of minimal information.
Strategic
Providing the right incentives for the truthful revelation of individual preferences. Though the strategic property is conceptually different from IIA, it is closely related.

Arrow's death-of-a-candidate example (1963, page 26) suggests that the agenda (the set of feasible alternatives) shrinks from, say, X = {a, b, c} to S = {a, b} because of the death of candidate c. This example is misleading since it can give the reader an impression that IIA is a condition involving two agenda and one profile. The fact is that IIA involves just one agendum ({x, y} in case of pairwise independence) but two profiles. If the condition is applied to this confusing example, it requires this: Suppose an aggregation rule satisfying IIA chooses b from the agenda {a, b} when the profile is given by (cab, cba), that is, individual 1 prefers c to a to b, 2 prefers c to b to a. Then, it must still choose b from {a, b} if the profile were, say: (abc, bac); (acb, bca); (acb, cba); or (abc, cba).

In different words, Arrow defines IIA as saying that the social preferences between alternatives x and y depend only on the individual preferences between x and y (not on those involving other candidates).

Formal statement of the theorem

Let A be a set of outcomes, N a number of voters or decision criteria. We shall denote the set of all full linear orderings of A by L(A).

A (strict) social welfare function (preference aggregation rule) is a function

which aggregates voters' preferences into a single preference order on A.

An N-tuple (R1, …, RN) ∈ L(A)N of voters' preferences is called a preference profile. In its strongest and simplest form, Arrow's impossibility theorem states that whenever the set A of possible alternatives has more than 2 elements, then the following three conditions become incompatible:

Unanimity, or weak Pareto efficiency
If alternative a is ranked strictly higher than b for all orderings R1 , …, RN, then a is ranked strictly higher than b by F(R1, R2, …, RN). (Unanimity implies non-imposition.)
Non-dictatorship
There is no individual, i whose strict preferences always prevail. That is, there is no i ∈ {1, …, N} such that for all (R1, …, RN) ∈ L(A)N and all a and b, when a is ranked strictly higher than b by Ri then a is ranked strictly higher than b by F(R1, R2, …, RN).
Independence of irrelevant alternatives
For two preference profiles (R1, …, RN) and (S1, …, SN) such that for all individuals i, alternatives a and b have the same order in Ri as in Si, alternatives a and b have the same order in F(R1, …, RN) as in F(S1, …, SN).

Informal proof

Based on two proofs appearing in Economic Theory. For simplicity we have presented all rankings as if ties are impossible. A complete proof taking possible ties into account is not essentially different from the one given here, except that one ought to say "not above" instead of "below" or "not below" instead of "above" in some cases. Full details are given in the original articles.

We will prove that any social choice system respecting unrestricted domain, unanimity, and independence of irrelevant alternatives (IIA) is a dictatorship. The key idea is to identify a pivotal voter whose ballot swings the societal outcome. We then prove that this voter is a partial dictator (in a specific technical sense, described below). Finally we conclude by showing that all of the partial dictators are the same person, hence this voter is a dictator.

Part one: There is a "pivotal" voter for B over A

Part one: Successively move B from the bottom to the top of voters' ballots. The voter whose change results in B being ranked over A is the pivotal voter for B over A.

Say there are three choices for society, call them A, B, and C. Suppose first that everyone prefers option B the least: everyone prefers A to B, and everyone prefers C to B. By unanimity, society must also prefer both A and C to B. Call this situation profile 0.

On the other hand, if everyone preferred B to everything else, then society would have to prefer B to everything else by unanimity. Now arrange all the voters in some arbitrary but fixed order, and for each i let profile i be the same as profile 0, but move B to the top of the ballots for voters 1 through i. So profile 1 has B at the top of the ballot for voter 1, but not for any of the others. Profile 2 has B at the top for voters 1 and 2, but no others, and so on.

Since B eventually moves to the top of the societal preference, there must be some profile, number k, for which B moves above A in the societal rank. We call the voter whose ballot change causes this to happen the pivotal voter for B over A. Note that the pivotal voter for B over A is not, a priori, the same as the pivotal voter for A over B. In part three of the proof we will show that these do turn out to be the same.

Also note that by IIA the same argument applies if profile 0 is any profile in which A is ranked above B by every voter, and the pivotal voter for B over A will still be voter k. We will use this observation below.

Part two: The pivotal voter for B over A is a dictator for B over C

In this part of the argument we refer to voter k, the pivotal voter for B over A, as the pivotal voter for simplicity. We will show that the pivotal voter dictates society's decision for B over C. That is, we show that no matter how the rest of society votes, if Pivotal Voter ranks B over C, then that is the societal outcome. Note again that the dictator for B over C is not a priori the same as that for C over B. In part three of the proof we will see that these turn out to be the same too.

Part two: Switching A and B on the ballot of voter k causes the same switch to the societal outcome, by part one of the argument. Making any or all of the indicated switches to the other ballots has no effect on the outcome.

In the following, we call voters 1 through k − 1, segment one, and voters k + 1 through N, segment two. To begin, suppose that the ballots are as follows:

  • Every voter in segment one ranks B above C and C above A.
  • Pivotal voter ranks A above B and B above C.
  • Every voter in segment two ranks A above B and B above C.

Then by the argument in part one (and the last observation in that part), the societal outcome must rank A above B. This is because, except for a repositioning of C, this profile is the same as profile k − 1 from part one. Furthermore, by unanimity the societal outcome must rank B above C. Therefore, we know the outcome in this case completely.

Now suppose that pivotal voter moves B above A, but keeps C in the same position and imagine that any number (even all!) of the other voters change their ballots to move B below C, without changing the position of A. Then aside from a repositioning of C this is the same as profile k from part one and hence the societal outcome ranks B above A. Furthermore, by IIA the societal outcome must rank A above C, as in the previous case. In particular, the societal outcome ranks B above C, even though Pivotal Voter may have been the only voter to rank B above C. By IIA, this conclusion holds independently of how A is positioned on the ballots, so pivotal voter is a dictator for B over C.

Part three: There exists a dictator

Part three: Since voter k is the dictator for B over C, the pivotal voter for B over C must appear among the first k voters. That is, outside of segment two. Likewise, the pivotal voter for C over B must appear among voters k through N. That is, outside of Segment One.

In this part of the argument we refer back to the original ordering of voters, and compare the positions of the different pivotal voters (identified by applying parts one and two to the other pairs of candidates). First, the pivotal voter for B over C must appear earlier (or at the same position) in the line than the dictator for B over C: As we consider the argument of part one applied to B and C, successively moving B to the top of voters' ballots, the pivot point where society ranks B above C must come at or before we reach the dictator for B over C. Likewise, reversing the roles of B and C, the pivotal voter for C over B must be at or later in line than the dictator for B over C. In short, if kX/Y denotes the position of the pivotal voter for X over Y (for any two candidates X and Y), then we have shown

kB/C ≤ kB/AkC/B.

Now repeating the entire argument above with B and C switched, we also have

kC/BkB/C.

Therefore, we have

kB/C = kB/A = kC/B

and the same argument for other pairs shows that all the pivotal voters (and hence all the dictators) occur at the same position in the list of voters. This voter is the dictator for the whole election.

Interpretations

Although Arrow's theorem is a mathematical result, it is often expressed in a non-mathematical way with a statement such as no voting method is fair, every ranked voting method is flawed, or the only voting method that isn't flawed is a dictatorship. These statements are simplifications of Arrow's result which are not universally considered to be true. What Arrow's theorem does state is that a deterministic preferential voting mechanism—that is, one where a preference order is the only information in a vote, and any possible set of votes gives a unique result—cannot comply with all of the conditions given above simultaneously.

Various theorists have suggested weakening the IIA criterion as a way out of the paradox. Proponents of ranked voting methods contend that the IIA is an unreasonably strong criterion. It is the one breached in most useful electoral systems. Advocates of this position point out that failure of the standard IIA criterion is trivially implied by the possibility of cyclic preferences. If voters cast ballots as follows:

  • 1 vote for A > B > C
  • 1 vote for B > C > A
  • 1 vote for C > A > B

then the pairwise majority preference of the group is that A wins over B, B wins over C, and C wins over A: these yield rock-paper-scissors preferences for any pairwise comparison. In this circumstance, any aggregation rule that satisfies the very basic majoritarian requirement that a candidate who receives a majority of votes must win the election, will fail the IIA criterion, if social preference is required to be transitive (or acyclic). To see this, suppose that such a rule satisfies IIA. Since majority preferences are respected, the society prefers A to B (two votes for A > B and one for B > A), B to C, and C to A. Thus a cycle is generated, which contradicts the assumption that social preference is transitive.

So, what Arrow's theorem really shows is that any majority-wins electoral system is a non-trivial game, and that game theory should be used to predict the outcome of most voting mechanisms. This could be seen as a discouraging result, because a game need not have efficient equilibria; e.g., a ballot could result in an alternative nobody really wanted in the first place, yet everybody voted for.

Remark: Scalar rankings from a vector of attributes and the IIA property

The IIA property might not be satisfied in human decision-making of realistic complexity because the scalar preference ranking is effectively derived from the weighting—not usually explicit—of a vector of attributes (one book dealing with the Arrow theorem invites the reader to consider the related problem of creating a scalar measure for the track and field decathlon event—e.g. how does one make scoring 600 points in the discus event "commensurable" with scoring 600 points in the 1500 m race) and this scalar ranking can depend sensitively on the weighting of different attributes, with the tacit weighting itself affected by the context and contrast created by apparently "irrelevant" choices. Edward MacNeal discusses this sensitivity problem with respect to the ranking of "most livable city" in the chapter "Surveys" of his book MathSemantics: making numbers talk sense (1994).

Alternatives based on functions of preference profiles

In an attempt to escape from the negative conclusion of Arrow's theorem, social choice theorists have investigated various possibilities ("ways out"). This section includes approaches that deal with

  • aggregation rules (functions that map each preference profile into a social preference), and
  • other functions, such as functions that map each preference profile into an alternative.

Since these two approaches often overlap, we discuss them at the same time. What is characteristic of these approaches is that they investigate various possibilities by eliminating or weakening or replacing one or more conditions (criteria) that Arrow imposed.

Infinitely many individuals

Several theorists (e.g., Fishburn and Kirman and Sondermann) point out that when one drops the assumption that there are only finitely many individuals, one can find aggregation rules that satisfy all of Arrow's other conditions.

However, such aggregation rules are practically of limited interest, since they are based on ultrafilters, highly non-constructive mathematical objects. In particular, Kirman and Sondermann argue that there is an "invisible dictator" behind such a rule. Mihara shows that such a rule violates algorithmic computability. These results can be seen to establish the robustness of Arrow's theorem.

On the other hand, the ultrafilters (indeed, constructing them in an infinite model relies on the axiom of choice) are inherent in finite models as well (with no need of the axiom of choice). They can be interpreted as decisive hierarchies, with the only difference that the hierarchy's top level - Arrow's dictator - always exists in a finite model but can be unattainable (= missing) in an infinite hierarchy. In the latter case, the "invisible dictator" is nothing else but the infinite decisive hierarchy itself. If desired, it can be complemented with a limit point, which then becomes a "visible dictator". Since dictators are inseparable from decisive hierarchies, the Dictatorship prohibition automatically prohibits decisive hierarchies, which is much less self-evident than the Dictatorship prohibition. See also paragraph "Relaxing the Dictatorship prohibition".

Limiting the number of alternatives

When there are only two alternatives to choose from, May's theorem shows that only simple majority rule satisfies a certain set of criteria (e.g., equal treatment of individuals and of alternatives; increased support for a winning alternative should not make it into a losing one). On the other hand, when there are at least three alternatives, Arrow's theorem points out the difficulty of collective decision making. Why is there such a sharp difference between the case of less than three alternatives and that of at least three alternatives?

Nakamura's theorem (about the core of simple games) gives an answer more generally. It establishes that if the number of alternatives is less than a certain integer called the Nakamura number, then the rule in question will identify "best" alternatives without any problem; if the number of alternatives is greater or equal to the Nakamura number, then the rule will not always work, since for some profile a voting paradox (a cycle such as alternative A socially preferred to alternative B, B to C, and C to A) will arise. Since the Nakamura number of majority rule is 3 (except the case of four individuals), one can conclude from Nakamura's theorem that majority rule can deal with up to two alternatives rationally. Some super-majority rules (such as those requiring 2/3 of the votes) can have a Nakamura number greater than 3, but such rules violate other conditions given by Arrow.

Pairwise voting

A common way "around" Arrow's paradox is limiting the alternative set to two alternatives. Thus, whenever more than two alternatives should be put to the test, it seems very tempting to use a mechanism that pairs them and votes by pairs. As tempting as this mechanism seems at first glance, it is generally far from satisfying even Pareto efficiency, not to mention IIA. The specific order by which the pairs are decided strongly influences the outcome. This is not necessarily a bad feature of the mechanism. Many sports use the tournament mechanism—essentially a pairing mechanism—to choose a winner. This gives considerable opportunity for weaker teams to win, thus adding interest and tension throughout the tournament. This means that the person controlling the order by which the choices are paired (the agenda maker) has great control over the outcome. In any case, when viewing the entire voting process as one game, Arrow's theorem still applies.

Domain restrictions

Another approach is relaxing the universality condition, which means restricting the domain of aggregation rules. The best-known result along this line assumes "single peaked" preferences.

Duncan Black has shown that if there is only one dimension on which every individual has a "single-peaked" preference, then all of Arrow's conditions are met by majority rule. Suppose that there is some predetermined linear ordering of the alternative set. An individual's preference is single-peaked with respect to this ordering if he has some special place that he likes best along that line, and his dislike for an alternative grows larger as the alternative goes further away from that spot (i.e., the graph of his utility function has a single peak if alternatives are placed according to the linear ordering on the horizontal axis). For example, if voters were voting on where to set the volume for music, it would be reasonable to assume that each voter had their own ideal volume preference and that as the volume got progressively too loud or too quiet they would be increasingly dissatisfied. If the domain is restricted to profiles in which every individual has a single peaked preference with respect to the linear ordering, then simple aggregation rules, which include majority rule, have an acyclic (defined below) social preference, hence "best" alternative. In particular, when there are odd number of individuals, then the social preference becomes transitive, and the socially "best" alternative is equal to the median of all the peaks of the individuals (Black's median voter theorem). Under single-peaked preferences, the majority rule is in some respects the most natural voting mechanism.

One can define the notion of "single-peaked" preferences on higher-dimensional sets of alternatives. However, one can identify the "median" of the peaks only in exceptional cases. Instead, we typically have the destructive situation suggested by McKelvey's Chaos Theorem: for any x and y, one can find a sequence of alternatives such that x is beaten by x1 by a majority, x1 by x2, up to xk by y.

Relaxing transitivity

By relaxing the transitivity of social preferences, we can find aggregation rules that satisfy Arrow's other conditions. If we impose neutrality (equal treatment of alternatives) on such rules, however, there exists an individual who has a "veto". So the possibility provided by this approach is also very limited.

First, suppose that a social preference is quasi-transitive (instead of transitive); this means that the strict preference ("better than") is transitive: if and , then . Then, there do exist non-dictatorial aggregation rules satisfying Arrow's conditions, but such rules are oligarchic. This means that there exists a coalition L such that L is decisive (if every member in L prefers x to y, then the society prefers x to y), and each member in L has a veto (if she prefers x to y, then the society cannot prefer y to x).

Second, suppose that a social preference is acyclic (instead of transitive): there do not exist alternatives that form a cycle (). Then, provided that there are at least as many alternatives as individuals, an aggregation rule satisfying Arrow's other conditions is collegial. This means that there are individuals who belong to the intersection ("collegium") of all decisive coalitions. If there is someone who has a veto, then he belongs to the collegium. If the rule is assumed to be neutral, then it does have someone who has a veto.

Finally, Brown's theorem left open the case of acyclic social preferences where the number of alternatives is less than the number of individuals. One can give a definite answer for that case using the Nakamura number. See limiting the number of alternatives.

Relaxing assumption IIA

There are numerous examples of aggregation rules satisfying Arrow's conditions except IIA. The Borda rule is one of them. These rules, however, are susceptible to strategic manipulation by individuals.

See also Interpretations of the theorem above.

Relaxing the Pareto criterion

Wilson (1972) shows that if an aggregation rule is non-imposed and non-null, then there is either a dictator or an inverse dictator, provided that Arrow's conditions other than Pareto are also satisfied. Here, an inverse dictator is an individual i such that whenever i prefers x to y, then the society prefers y to x.

Amartya Sen offered both relaxation of transitivity and removal of the Pareto principle. He demonstrated another interesting impossibility result, known as the "impossibility of the Paretian Liberal" (see liberal paradox for details). Sen went on to argue that this demonstrates the futility of demanding Pareto optimality in relation to voting mechanisms.

Relaxing the Dictatorship prohibition

Andranik Tangian (2010) introduced measures of dictator's "representativeness", for instance, the "popularity index" defined as the average size of the social group whose pairwise preferences are shared (= represented) by the dictator, averaged over all pairs of alternatives and all preference profiles. It was shown that there always exist "good" Arrow's dictators who on the average represent a majority. Since they are rather representatives of the society - like democratically elected presidents - there are no self-evident reasons to prohibit them. Restricting the notion of dictator to "bad" ones only, i.e. those who on the average represent a minority, Arrow's axioms were proven to be consistent.

Social choice instead of social preference

In social decision making, to rank all alternatives is not usually a goal. It often suffices to find some alternative. The approach focusing on choosing an alternative investigates either social choice functions (functions that map each preference profile into an alternative) or social choice rules (functions that map each preference profile into a subset of alternatives).

As for social choice functions, the Gibbard–Satterthwaite theorem is well-known, which states that if a social choice function whose range contains at least three alternatives is strategy-proof, then it is dictatorial.

As for social choice rules, we should assume there is a social preference behind them. That is, we should regard a rule as choosing the maximal elements ("best" alternatives) of some social preference. The set of maximal elements of a social preference is called the core. Conditions for existence of an alternative in the core have been investigated in two approaches. The first approach assumes that preferences are at least acyclic (which is necessary and sufficient for the preferences to have a maximal element on any finite subset). For this reason, it is closely related to relaxing transitivity. The second approach drops the assumption of acyclic preferences. Kumabe and Mihara adopt this approach. They make a more direct assumption that individual preferences have maximal elements, and examine conditions for the social preference to have a maximal element. See Nakamura number for details of these two approaches.

Other alternatives

Arrow originally rejected cardinal utility as a meaningful tool for expressing social welfare, and so focused his theorem on preference rankings, but later stated that a cardinal score system with three or four classes "is probably the best".

Arrow's framework assumes that individual and social preferences are "orderings" (i.e., satisfy completeness and transitivity) on the set of alternatives. This means that if the preferences are represented by a utility function, its value is an ordinal utility in the sense that it is meaningful so far as the greater value indicates the better alternative. For instance, having ordinal utilities of 4, 3, 2, 1 for alternatives a, b, c, d, respectively, is the same as having 1000, 100.01, 100, 0, which in turn is the same as having 99, 98, 1, .997. They all represent the ordering in which a is preferred to b to c to d. The assumption of ordinal preferences, which precludes interpersonal comparisons of utility, is an integral part of Arrow's theorem.

For various reasons, an approach based on cardinal utility, where the utility has a meaning beyond just giving a ranking of alternatives, is not common in contemporary economics. However, once one adopts that approach, one can take intensities of preferences into consideration, or one can compare (i) gains and losses of utility or (ii) levels of utility, across different individuals. In particular, Harsanyi (1955) gives a justification of utilitarianism (which evaluates alternatives in terms of the sum of individual utilities), originating from Jeremy Bentham. Hammond (1976) gives a justification of the maximin principle (which evaluates alternatives in terms of the utility of the worst-off individual), originating from John Rawls.

Not all voting methods use, as input, only an ordering of all candidates. Methods which don't, often called "rated" or "cardinal" (as opposed to "ranked", "ordinal", or "preferential") electoral system, can be viewed as using information that only cardinal utility can convey. In that case, it is not surprising if some of them satisfy all of Arrow's conditions that are reformulated. Range voting is such a method. Whether such a claim is correct depends on how each condition is reformulated. Other rated electoral system which pass certain generalizations of Arrow's criteria include approval voting and majority judgment. Note that Arrow's theorem does not apply to single-winner methods such as these, but Gibbard's theorem still does: no non-defective electoral system is fully strategy-free, so the informal dictum that "no electoral system is perfect" still has a mathematical basis.

Finally, though not an approach investigating some kind of rules, there is a criticism by James M. Buchanan, Charles Plott, and others. It argues that it is silly to think that there might be social preferences that are analogous to individual preferences. Arrow (1963, Chapter 8) answers this sort of criticism seen in the early period, which come at least partly from misunderstanding.

Operator (computer programming)

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