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Saturday, September 19, 2020

Economic bubble

From Wikipedia, the free encyclopedia

An economic bubble or asset bubble (sometimes also referred to as a speculative bubble, a market bubble, a price bubble, a financial bubble, a speculative mania, or a balloon) is a situation in which asset prices appear to be based on implausible or inconsistent views about the future. It could also be described as trade in an asset at a price or price range that strongly exceeds the asset's intrinsic value.

While some economists deny that bubbles occur, the causes of bubbles remain disputed by those who are convinced that asset prices often deviate strongly from intrinsic values.

Many explanations have been suggested, and research has recently shown that bubbles may appear even without uncertainty, speculation, or bounded rationality, in which case they can be called non-speculative bubbles or sunspot equilibria. In such cases, the bubbles may be argued to be rational, where investors at every point are fully compensated for the possibility that the bubble might collapse by higher returns. These approaches require that the timing of the bubble collapse can only be forecast probabilistically and the bubble process is often modelled using a Markov switching model. Similar explanations suggest that bubbles might ultimately be caused by processes of price coordination.

More recent theories of asset bubble formation suggest that these events are sociologically driven. For instance, explanations have focused on emerging social norms and the role that culturally-situated stories or narratives play in these events.

Because it is often difficult to observe intrinsic values in real-life markets, bubbles are often conclusively identified only in retrospect, once a sudden drop in prices has occurred. Such a drop is known as a crash or a bubble burst. In an economic bubble, prices can fluctuate erratically and become impossible to predict from supply and demand alone.

Asset bubbles are now widely regarded as a recurrent feature of modern economic history dating back as far as the 1600s. The Dutch Golden Age's Tulipmania (in the mid-1630s) is often considered the first recorded economic bubble in history.

Both the boom and the bust phases of the bubble are examples of a positive feedback mechanism (in contrast to the negative feedback mechanism that determines the equilibrium price under normal market circumstances).

History and origin of term

Jan Brueghel the Younger's A Satire of Tulip Mania (ca. 1640) depicts speculators as brainless monkeys in contemporary upper-class dress. The Tulip Mania (also known as Tulipmania or Tulipomania), of the 1630s, is generally considered the first recorded speculative bubble (or asset bubble) in history.
 
A card from the South Sea Bubble

The term "bubble", in reference to financial crisis, originated in the 1711–1720 British South Sea Bubble, and originally referred to the companies themselves, and their inflated stock, rather than to the crisis itself. This was one of the earliest modern financial crises; other episodes were referred to as "manias", as in the Dutch tulip mania. The metaphor indicated that the prices of the stock were inflated and fragile – expanded based on nothing but air, and vulnerable to a sudden burst, as in fact occurred.

Some later commentators have extended the metaphor to emphasize the suddenness, suggesting that economic bubbles end "All at once, and nothing first, / Just as bubbles do when they burst," though theories of financial crises such as debt deflation and the Financial Instability Hypothesis suggest instead that bubbles burst progressively, with the most vulnerable (most highly-leveraged) assets failing first, and then the collapse spreading throughout the economy.

Types of bubbles

There are different types of bubbles, with economists primarily interested in two major types of bubbles:

1. Equity bubble

An equity bubble is characterised by tangible investments and the unsustainable desire to satisfy a legitimate market in high demand. These kind of bubbles are characterised by easy liquidity, tangible and real assets, and an actual innovation that boosts confidence. Two instances of an equity bubble are the Tulip Mania and the dot-com bubble.

2. Debt bubble

A debt bubble is characterised by intangible or credit based investments with little ability to satisfy growing demand in a non-existent market. These bubbles are not backed by real assets and are characterized by frivolous lending in the hopes of returning a profit or security. These bubbles usually end in debt deflation causing bank runs or a currency crisis when the government can no longer maintain the fiat currency. Examples include the Roaring Twenties stock market bubble (which caused the Great Depression) and the United States housing bubble (which caused the Great Recession). The corporate debt bubble that caused the COVID-19 recession is an example of a combined debt and equity bubble.

Impact

The impact of economic bubbles is debated within and between schools of economic thought; they are not generally considered beneficial, but it is debated how harmful their formation and bursting is.

Within mainstream economics, many believe that bubbles cannot be identified in advance, cannot be prevented from forming, that attempts to "prick" the bubble may cause financial crisis, and that instead authorities should wait for bubbles to burst of their own accord, dealing with the aftermath via monetary policy and fiscal policy.

Political economist Robert E. Wright argues that bubbles can be identified before the fact with high confidence.

In addition, the crash which usually follows an economic bubble can destroy a large amount of wealth and cause continuing economic malaise; this view is particularly associated with the debt-deflation theory of Irving Fisher, and elaborated within Post-Keynesian economics.

A protracted period of low risk premiums can simply prolong the downturn in asset price deflation as was the case of the Great Depression in the 1930s for much of the world and the 1990s for Japan. Not only can the aftermath of a crash devastate the economy of a nation, but its effects can also reverberate beyond its borders.

Effect upon spending

Another important aspect of economic bubbles is their impact on spending habits. Market participants with overvalued assets tend to spend more because they "feel" richer (the wealth effect). Many observers quote the housing market in the United Kingdom, Australia, New Zealand, Spain and parts of the United States in recent times, as an example of this effect. When the bubble inevitably bursts, those who hold on to these overvalued assets usually experience a feeling of reduced wealth and tend to cut discretionary spending at the same time, hindering economic growth or, worse, exacerbating the economic slowdown.

In an economy with a central bank, the bank may therefore attempt to keep an eye on asset price appreciation and take measures to curb high levels of speculative activity in financial assets. This is usually done by increasing the interest rate (that is, the cost of borrowing money). Historically, this is not the only approach taken by central banks. It has been argued that they should stay out of it and let the bubble, if it is one, take its course.

Possible causes

In the 1970s, excess monetary expansion after the U.S. came off the gold standard (August 1971) created massive commodities bubbles. These bubbles only ended when the U.S. Central Bank (Federal Reserve) finally reined in the excess money, raising federal funds interest rates to over 14%. The commodities bubble popped and prices of oil and gold, for instance, came down to their proper levels. Similarly, low interest rate policies by the U.S. Federal Reserve in the 2001–2004 are believed to have exacerbated housing and commodities bubbles. The housing bubble popped as subprime mortgages began to default at much higher rates than expected, which also coincided with the rising of the fed funds rate.

It has also been variously suggested that bubbles may be rational, intrinsic, and contagious. To date, there is no widely accepted theory to explain their occurrence. Recent computer-generated agency models suggest excessive leverage could be a key factor in causing financial bubbles.

Puzzlingly for some, bubbles occur even in highly predictable experimental markets, where uncertainty is eliminated and market participants should be able to calculate the intrinsic value of the assets simply by examining the expected stream of dividends. Nevertheless, bubbles have been observed repeatedly in experimental markets, even with participants such as business students, managers, and professional traders. Experimental bubbles have proven robust to a variety of conditions, including short-selling, margin buying, and insider trading.

While there is no clear agreement on what causes bubbles, there is evidence to suggest that they are not caused by bounded rationality or assumptions about the irrationality of others, as assumed by greater fool theory. It has also been shown that bubbles appear even when market participants are well-capable of pricing assets correctly. Further, it has been shown that bubbles appear even when speculation is not possible or when over-confidence is absent.

More recent theories of asset bubble formation suggest that they are likely sociologically-driven events, thus explanations that merely involve fundamental factors or snippets of human behavior are incomplete at best. For instance, qualitative researchers Preston Teeter and Jorgen Sandberg argue that market speculation is driven by culturally-situated narratives that are deeply embedded in and supported by the prevailing institutions of the time. They cite factors such as bubbles forming during periods of innovation, easy credit, loose regulations, and internationalized investment as reasons why narratives play such an influential role in the growth of asset bubbles.

Liquidity

One possible cause of bubbles is excessive monetary liquidity in the financial system, inducing lax or inappropriate lending standards by the banks, which makes markets vulnerable to volatile asset price inflation caused by short-term, leveraged speculation. For example, Axel A. Weber, the former president of the Deutsche Bundesbank, has argued that "The past has shown that an overly generous provision of liquidity in global financial markets in connection with a very low level of interest rates promotes the formation of asset-price bubbles."

According to the explanation, excessive monetary liquidity (easy credit, large disposable incomes) potentially occurs while fractional reserve banks are implementing expansionary monetary policy (i.e. lowering of interest rates and flushing the financial system with money supply); this explanation may differ in certain details according to economic philosophy. Those who believe the money supply is controlled exogenously by a central bank may attribute an 'expansionary monetary policy' to said bank and (should one exist) a governing body or institution; others who believe that the money supply is created endogenously by the banking sector may attribute such a 'policy' with the behavior of the financial sector itself, and view the state as a passive or reactive factor. This may determine how central or relatively minor/inconsequential policies like fractional reserve banking and the central bank's efforts to raise or lower short-term interest rates are to one's view on the creation, inflation and ultimate implosion of an economic bubble. Explanations focusing on interest rates tend to take on a common form, however: When interest rates are set excessively low, (regardless of the mechanism by which it is accomplished) investors tend to avoid putting their capital into savings accounts. Instead, investors tend to leverage their capital by borrowing from banks and invest the leveraged capital in financial assets such as stocks and real estate. Risky leveraged behavior like speculation and Ponzi schemes can lead to an increasingly fragile economy, and may also be part of what pushes asset prices artificially upward until the bubble pops.

But these [ongoing economic crises] aren’t just a series of unrelated accidents. Instead, what we’re seeing is what happens when too much money is chasing too few investment opportunities.

Paul Krugman

Simply put, economic bubbles often occur when too much money is chasing too few assets, causing both good assets and bad assets to appreciate excessively beyond their fundamentals to an unsustainable level. Once the bubble bursts, the fall in prices causes the collapse of unsustainable investment schemes (especially speculative and/or Ponzi investments, but not exclusively so), which leads to a crisis of consumer (and investor) confidence that may result in a financial panic and/or financial crisis; if there is monetary authority like a central bank, it may be forced to take a number of measures in order to soak up the liquidity in the financial system or risk a collapse of its currency. This may involve actions like bailouts of the financial system, but also others that reverse the trend of monetary accommodation, commonly termed forms of 'contractionary monetary policy'.

Some of these measures may include raising interest rates, which tends to make investors become more risk averse and thus avoid leveraged capital because the costs of borrowing may become too expensive. Others may be countermeasures taken pre-emptively during periods of strong economic growth, such as increasing capital reserve requirements and implementing regulation that checks and/or prevents processes leading to over-expansion and excessive leveraging of debt. Ideally, such countermeasures lessen the impact of a downturn by strengthening financial institutions while the economy is strong.

Advocates of perspectives stressing the role of credit money in an economy often refer to (such) bubbles as "credit bubbles", and look at such measures of financial leverage as debt-to-GDP ratios to identify bubbles. Typically the collapse of any economic bubble results in an economic contraction termed (if less severe) a recession or (if more severe) a depression; what economic policies to follow in reaction to such a contraction is a hotly debated perennial topic of political economy.

The importance of liquidity was derived in a mathematical setting and in an experimental setting.

Social psychology factors

Greater fool theory

Greater fool theory states that bubbles are driven by the behavior of perennially optimistic market participants (the fools) who buy overvalued assets in anticipation of selling it to other speculators (the greater fools) at a much higher price. According to this explanation, the bubbles continue as long as the fools can find greater fools to pay up for the overvalued asset. The bubbles will end only when the greater fool becomes the greatest fool who pays the top price for the overvalued asset and can no longer find another buyer to pay for it at a higher price. This theory is popular among laity but has not yet been fully confirmed by empirical research.

Extrapolation

The term "bubble" should indicate a price that no reasonable future outcome can justify.

Clifford Asness

Extrapolation is projecting historical data into the future on the same basis; if prices have risen at a certain rate in the past, they will continue to rise at that rate forever. The argument is that investors tend to extrapolate past extraordinary returns on investment of certain assets into the future, causing them to overbid those risky assets in order to attempt to continue to capture those same rates of return.

Overbidding on certain assets will at some point result in uneconomic rates of return for investors; only then the asset price deflation will begin. When investors feel that they are no longer well compensated for holding those risky assets, they will start to demand higher rates of return on their investments.

Herding

Another related explanation used in behavioral finance lies in herd behavior, the fact that investors tend to buy or sell in the direction of the market trend. This is sometimes helped by technical analysis that tries precisely to detect those trends and follow them, which creates a self-fulfilling prophecy.

Investment managers, such as stock mutual fund managers, are compensated and retained in part due to their performance relative to peers. Taking a conservative or contrarian position as a bubble builds results in performance unfavorable to peers. This may cause customers to go elsewhere and can affect the investment manager's own employment or compensation. The typical short-term focus of U.S. equity markets exacerbates the risk for investment managers that do not participate during the building phase of a bubble, particularly one that builds over a longer period of time. In attempting to maximize returns for clients and maintain their employment, they may rationally participate in a bubble they believe to be forming, as the risks of not doing so outweigh the benefits.

Moral hazard

Moral hazard is the prospect that a party insulated from risk may behave differently from the way it would behave if it were fully exposed to the risk. A person's belief that they are responsible for the consequences of their own actions is an essential aspect of rational behavior. An investor must balance the possibility of making a return on their investment with the risk of making a loss – the risk-return relationship. A moral hazard can occur when this relationship is interfered with, often via government policy.

A recent example is the Troubled Asset Relief Program (TARP), signed into law by U.S. President George W. Bush on 3 October 2008 to provide a Government bailout for many financial and non-financial institutions who speculated in high-risk financial instruments during the housing boom condemned by a 2005 story in The Economist titled "The worldwide rise in house prices is the biggest bubble in history". A historical example was intervention by the Dutch Parliament during the great Tulip Mania of 1637.

Other causes of perceived insulation from risk may derive from a given entity's predominance in a market relative to other players, and not from state intervention or market regulation. A firm – or several large firms acting in concert (see cartel, oligopoly and collusion) – with very large holdings and capital reserves could instigate a market bubble by investing heavily in a given asset, creating a relative scarcity which drives up that asset's price. Because of the signaling power of the large firm or group of colluding firms, the firm's smaller competitors will follow suit, similarly investing in the asset due to its price gains.

However, in relation to the party instigating the bubble, these smaller competitors are insufficiently leveraged to withstand a similarly rapid decline in the asset's price. When the large firm, cartel or de facto collusive body perceives a maximal peak has been reached in the traded asset's price, it can then proceed to rapidly sell or "dump" its holdings of this asset on the market, precipitating a price decline that forces its competitors into insolvency, bankruptcy or foreclosure.

The large firm or cartel – which has intentionally leveraged itself to withstand the price decline it engineered – can then acquire the capital of its failing or devalued competitors at a low price as well as capture a greater market share (e.g., via a merger or acquisition which expands the dominant firm's distribution chain). If the bubble-instigating party is itself a lending institution, it can combine its knowledge of its borrowers’ leveraging positions with publicly available information on their stock holdings, and strategically shield or expose them to default.

Other possible causes

Some regard bubbles as related to inflation and thus believe that the causes of inflation are also the causes of bubbles. Others take the view that there is a "fundamental value" to an asset, and that bubbles represent a rise over that fundamental value, which must eventually return to that fundamental value. There are chaotic theories of bubbles which assert that bubbles come from particular "critical" states in the market based on the communication of economic factors. Finally, others regard bubbles as necessary consequences of irrationally valuing assets solely based upon their returns in the recent past without resorting to a rigorous analysis based on their underlying "fundamentals".

Experimental and mathematical economics

Bubbles in financial markets have been studied not only through historical evidence, but also through experiments, mathematical and statistical works. Smith, Suchanek and Williams designed a set of experiments in which an asset that gave a dividend with expected value 24 cents at the end of each of 15 periods (and were subsequently worthless) was traded through a computer network. Classical economics would predict that the asset would start trading near $3.60 (15 times $0.24) and decline by 24 cents each period. They found instead that prices started well below this fundamental value and rose far above the expected return in dividends. The bubble subsequently crashed before the end of the experiment. This laboratory bubble has been repeated hundreds of times in many economics laboratories in the world, with similar results.

The existence of bubbles and crashes in such a simple context was unsettling for the economics community that tried to resolve the paradox on various features of the experiments. To address these issues Porter and Smith and others performed a series of experiments in which short selling, margin trading, professional traders all led to bubbles a fortiori.

Much of the puzzle has been resolved through mathematical modeling and additional experiments. In particular, starting in 1989, Gunduz Caginalp and collaborators modeled the trading with two concepts that are generally missing in classical economics and finance. First, they assumed that supply and demand of an asset depended not only on valuation, but on factors such as the price trend. Second, they assumed that the available cash and asset are finite (as they are in the laboratory). This is contrary to the "infinite arbitrage" that is generally assumed to exist, and to eliminate deviations from fundamental value. Utilizing these assumptions together with differential equations, they predicted the following: (a) The bubble would be larger if there was initial undervaluation. Initially, "value-based" traders would buy the undervalued asset creating an uptrend, which would then attract the "momentum" traders and a bubble would be created. (b) When the initial ratio of cash to asset value in a given experiment was increased, they predicted that the bubble would be larger.

An epistemological difference between most microeconomic modeling and these works is that the latter offer an opportunity to test implications of their theory in a quantitative manner. This opens up the possibility of comparison between experiments and world markets.

These predictions were confirmed in experiments that showed the importance of "excess cash" (also called liquidity, though this term has other meanings), and trend-based investing in creating bubbles. When price collars were used to keep prices low in the initial time periods, the bubble became larger. In experiments in which L= (total cash)/(total initial value of asset) were doubled, the price at the peak of the bubble nearly doubled. This provided valuable evidence for the argument that "cheap money fuels markets."

Caginalp's asset flow differential equations provide a link between the laboratory experiments and world market data. Since the parameters can be calibrated with either market, one can compare the lab data with the world market data.

The asset flow equations stipulate that price trend is a factor in the supply and demand for an asset that is a key ingredient in the formation of a bubble. While many studies of market data have shown a rather minimal trend effect, the work of Caginalp and DeSantis on large scale data adjusts for changes in valuation, thereby illuminating a strong role for trend, and providing the empirical justification for the modeling.

The asset flow equations have been used to study the formation of bubbles from a different standpoint in where it was shown that a stable equilibrium could become unstable with the influx of additional cash or the change to a shorter time scale on the part of the momentum investors. Thus a stable equilibrium could be pushed into an unstable one, leading to a trajectory in price that exhibits a large "excursion" from either the initial stable point or the final stable point. This phenomenon on a short time scale may be the explanation for flash crashes.

Stages of an economic bubble

According to the economist Charles P. Kindleberger, the basic structure of a speculative bubble can be divided into 5 phases:

  • Substitution: increase in the value of an asset
  • Takeoff: speculative purchases (buy now to sell in the future at a higher price and obtain a profit)
  • Exuberance: a state of unsustainable euphoria.
  • Critical stage: begin to shorten the buyers, some begin to sell.
  • Pop (crash): prices plummet

Identifying asset bubbles

CAPE based on data from economist Robert Shiller's website, as of 8/4/2015. The 26.45 measure was 93rd percentile, meaning 93% of the time investors paid less for stocks overall relative to earnings.

Economic or asset price bubbles are often characterized by one or more of the following:

  1. Unusual changes in single measures, or relationships among measures (e.g., ratios) relative to their historical levels. For example, in the housing bubble of the 2000s, the housing prices were unusually high relative to income. For stocks, the price to earnings ratio provides a measure of stock prices relative to corporate earnings; higher readings indicate investors are paying more for each dollar of earnings.
  2. Elevated usage of debt (leverage) to purchase assets, such as purchasing stocks on margin or homes with a lower down payment.
  3. Higher risk lending and borrowing behavior, such as originating loans to borrowers with lower credit quality scores (e.g., subprime borrowers), combined with adjustable rate mortgages and "interest only" loans.
  4. Rationalizing borrowing, lending and purchase decisions based on expected future price increases rather than the ability of the borrower to repay.
  5. Rationalizing asset prices by increasingly weaker arguments, such as "this time it's different" or "housing prices only go up."
  6. A high presence of marketing or media coverage related to the asset.
  7. Incentives that place the consequences of bad behavior by one economic actor upon another, such as the origination of mortgages to those with limited ability to repay because the mortgage could be sold or securitized, moving the consequences from the originator to the investor.
  8. International trade (current account) imbalances, resulting in an excess of savings over investments, increasing the volatility of capital flow among countries. For example, the flow of savings from Asia to the U.S. was one of the drivers of the 2000s housing bubble.
  9. A lower interest rate environment, which encourages lending and borrowing.

Examples of asset bubbles

  • Tipper and See-Saw Time (1621)
  • Tulip mania (Holland) (1634–1637)
  • South Sea Company (British) (1720)
  • Mississippi Company (France) (1720)
  • Canal Mania (UK) (1790s–1810s)
  • Panic of 1819 (US) (1815–1818) Prices of US land in the south and west, cotton (US main export at the time), wheat, corn and tobacco grew into a bubble following the end of the Napoleonic Wars in 1815 as the European economy was beginning to recover from wars and demand was high for agricultural goods from America. The Second Bank of the US called in loans for specie beginning in August 1818 popped the speculative land bubble. Prices of agricultural commodities declined by almost -50% during 1819–1821 post bubble. A credit contraction caused by a financial crisis in England drained specie out of the U.S. The Bank of the United States also contracted its lending.
  • Panic of 1837 (1834–1837) (US) Prices of US land, cotton, and slaves grew into bubbles with easy bank credit by the mid-1830s. Ended in financial crisis starting with the Specie Circular of 1836. Five year recession followed along with currency in the United States contracting by about 34% with prices falling by 33%. The magnitude of this contraction is only matched by the Great Depression.
  • Railway Mania (UK) (1840s)
  • Panic of 1857 Land and railroad boom in US following discovery of gold in California in 1849. Resulted in large expansion of US money supply. Railroads boomed as people moved west. Railroad stocks peaks in July 1857. The failure of Ohio Life in August 1857 brought attention to the financial state of the railroad industry and land markets, thereby causing the financial panic to become a more public issue. Since banks had financed the railroads and land purchases, they began to feel the pressures of the falling value of railroad securities and many went bankrupt. Ended in worldwide crisis.
  • Melbourne Australia land and real estate bubble (1883–1889, crash in 1890–91)
  • Encilhamento ("Mounting") (Brazil) (1886–1892)
  • US farm bubble and crisis (1914–1918, crash 1919–1920) prices rapidly escalated during WWI and crash after war's end.
  • Roaring Twenties stock-market bubble (US) (1921–1929)
  • Florida speculative building bubble (US)(1922–1926)
  • Poseidon bubble (Australia) (1969–1970)
  • Gold and Silver bubble (1976–1980)
  • The dot-com bubble (US) (1995–2000)
  • Japanese asset price bubble (1986–1991) Japan real estate and stock market boom
  • 1997 Asian financial crisis (1997)
  • United States housing bubble (US) (2002–2006)
  • China stock and property bubble (China) (2003–2007)
  • The 2000s commodity bubbles (2002–2008)

Other goods which have produced bubbles include: postage stamps and coin collecting.

Examples of aftermaths of bubbles

Herd behavior

From Wikipedia, the free encyclopedia

Herd behavior is the behavior of individuals in a group acting collectively without centralized direction. Herd behavior occurs in animals in herds, packs, bird flocks, fish schools and so on, as well as in humans. Demonstrations, riots, general strikes, sporting events, religious gatherings, everyday decision-making, judgement and opinion-forming, are all forms of human based herd behavior.

Raafat, Chater and Frith proposed an integrated approach to herding, describing two key issues, the mechanisms of transmission of thoughts or behavior between individuals and the patterns of connections between them. They suggested that bringing together diverse theoretical approaches of herding behavior illuminates the applicability of the concept to many domains, ranging from cognitive neuroscience to economics.

In animals

Shimmering behaviour of Apis dorsata (giant honeybees)

A group of animals fleeing from a predator shows the nature of herd behavior. In 1971, in the oft cited article "Geometry For The Selfish Herd", evolutionary biologist W. D. Hamilton asserted that each individual group member reduces the danger to itself by moving as close as possible to the center of the fleeing group. Thus the herd appears as a unit in moving together, but its function emerges from the uncoordinated behavior of self-serving individuals.

Symmetry-breaking

Asymmetric aggregation of animals under panic conditions has been observed in many species, including humans, mice, and ants. Theoretical models have demonstrated symmetry-breaking similar to observations in empirical studies. For example, when panicked individuals are confined to a room with two equal and equidistant exits, a majority will favor one exit while the minority will favor the other.

Possible mechanisms for this behavior include Hamilton’s selfish herd theory, neighbor copying, or the byproduct of communication by social animals or runaway positive feedback.

Characteristics of escape panic include:

  • Individuals attempt to move faster than normal.
  • Interactions between individuals become physical.
  • Exits become arched and clogged.
  • Escape is slowed by fallen individuals serving as obstacles.
  • Individuals display a tendency towards mass or copied behavior.
  • Alternative or less used exits are overlooked.

In human societies: Early research

The philosophers Søren Kierkegaard and Friedrich Nietzsche were among the first to criticize what they referred to as "the crowd" (Kierkegaard) and "herd morality" and the "herd instinct" (Nietzsche) in human society. Modern psychological and economic research has identified herd behavior in humans to explain the phenomenon of large numbers of people acting in the same way at the same time. The British surgeon Wilfred Trotter popularized the "herd behavior" phrase in his book, Instincts of the Herd in Peace and War (1914). In The Theory of the Leisure Class, Thorstein Veblen explained economic behavior in terms of social influences such as "emulation," where some members of a group mimic other members of higher status. In "The Metropolis and Mental Life" (1903), early sociologist George Simmel referred to the "impulse to sociability in man", and sought to describe "the forms of association by which a mere sum of separate individuals are made into a 'society' ". Other social scientists explored behaviors related to herding, such as Sigmund Freud (crowd psychology), Carl Jung (collective unconscious), Everett Dean Martin (Behavior of Crowds) and Gustave Le Bon (the popular mind).

Swarm theory observed in non-human societies is a related concept and is being explored as it occurs in human society. Scottish journalist Charles Mackay identifies multiple facets of herd behaviour in his 1841 work, Extraordinary Popular Delusions and the Madness of Crowds.

In markets and economic situations

Currency crises

Currency crises tend to display herding behavior when foreign and domestic investors convert a government's currency into physical assets (like gold) or foreign currencies when they realize the government is unable to repay its debts. This is called a speculative attack and it will tend to cause moderate inflation in the short term. When consumers realize that the inflation of needed commodities is increasing, they will begin to stockpile and hoard goods, which will accelerate the rate of inflation even faster. This will ultimately crash the currency and likely lead to civil unrest.

Stock market bubbles

Large stock market trends often begin and end with periods of frenzied buying (bubbles) or selling (crashes). Many observers cite these episodes as clear examples of herding behavior that is irrational and driven by emotion—greed in the bubbles, fear in the crashes. Individual investors join the crowd of others in a rush to get in or out of the market.

Some followers of the technical analysis school of investing see the herding behavior of investors as an example of extreme market sentiment. The academic study of behavioral finance has identified herding in the collective irrationality of investors, particularly the work of Nobel laureates Vernon L. Smith, Amos Tversky, Daniel Kahneman, and Robert Shiller. Hey and Morone (2004) analyzed a model of herd behavior in a market context.

Some empirical works on methods for detecting and measuring the extent of herding include Christie and Huang (1995) and Chang, Cheng and Khorana (2000). These results refer to a market with a well-defined fundamental value. A notable incident of possible herding is the 2007 Uranium bubble, which started with flooding of the Cigar Lake Mine in Saskatchewan, during the year 2006.

Economic theory of herding

There are two strands of work in economic theory that consider why herding occurs and provide frameworks for examining its causes and consequences.

The first of these strands is that on herd behavior in a non-market context. The seminal references are Banerjee (1992) and Bikhchandani, Hirshleifer and Welch (1992), both of which showed that herd behavior may result from private information not publicly shared. More specifically, both of these papers showed that individuals, acting sequentially on the basis of private information and public knowledge about the behavior of others, may end up choosing the socially undesirable option. A large subsequent literature has examined the causes and consequences of such "herds" and information cascades, as surveyed by Golub and Sadler (2016).

The second strands concerns information aggregation in market contexts. A very early reference is the classic paper by Grossman and Stiglitz (1976) that showed that uninformed traders in a market context can become informed through the price in such a way that private information is aggregated correctly and efficiently. Subsequent work has shown that markets may systematically overweight public information; it has also studied the role of strategic trading as an obstacle to efficient information aggregation.

Herd behavior in social and political contexts

In crowds

Crowds that gather on behalf of a grievance can involve herding behavior that turns violent, particularly when confronted by an opposing ethnic or racial group. The Los Angeles riots of 1992, New York Draft Riots and Tulsa Race Riot are notorious in U.S. history. The idea of a "group mind" or "mob behavior" was put forward by the French social psychologists Gabriel Tarde and Gustave Le Bon.

Sheeple

Sheeple (/ˈʃpəl/; a portmanteau of "sheep" and "people") is a derogatory term that highlights the passive herd behavior of people easily controlled by a governing power or market fads which likens them to sheep, a herd animal that is easily led about. The term is used to describe those who voluntarily acquiesce to a suggestion without any significant critical analysis or research, in large part due to the majority of a population having a similar mindset. Word Spy defines it as "people who are meek, easily persuaded, and tend to follow the crowd (sheep + people)". Merriam-Webster defines the term as "people who are docile, compliant, or easily influenced: people likened to sheep". The word is pluralia tantum, which means it does not have a singular form.

While its origins are unclear, the word was used by W. R. Anderson in his column Round About Radio, published in London 1945, where he wrote:

The simple truth is that you can get away with anything, in government. That covers almost all the evils of the time. Once in, nobody, apparently, can turn you out. The People, as ever (I spell it "Sheeple"), will stand anything.

Another early use was from Ernest Rogers, whose 1949 book The Old Hokum Bucket contained a chapter entitled "We the Sheeple". The Wall Street Journal first reported the label in print in 1984; the reporter heard the word used by the proprietor of the American Opinion bookstore. The term was first popularized in the late 1980s and early 1990s by conspiracy theorist and broadcaster Bill Cooper on his radio program The Hour of the Time which was broadcast internationally via shortwave radio stations. The program gained a small, yet dedicated following, inspiring many individuals who would later broadcast their own radio programs critical of the United States government. This then led to its regular use on the radio program Coast to Coast AM by Art Bell throughout the 1990s and early 2000s. These combined factors significantly increased the popularity of the word and led to its widespread use.

The term can also be used for those who seem inordinately tolerant, or welcoming, of widespread policies. In a column entitled "A Nation of Sheeple", columnist Walter E. Williams writes, "Americans sheepishly accepted all sorts of Transportation Security Administration nonsense. In the name of security, we've allowed fingernail clippers, eyeglass screwdrivers, and toy soldiers to be taken from us prior to boarding a plane."

Everyday decision-making

"Benign" herding behaviors may occur frequently in everyday decisions based on learning from the information of others, as when a person on the street decides which of two restaurants to dine in. Suppose that both look appealing, but both are empty because it is early evening; so at random, this person chooses restaurant A. Soon a couple walks down the same street in search of a place to eat. They see that restaurant A has customers while B is empty, and choose A on the assumption that having customers makes it the better choice. Because other passersby do the same thing into the evening, restaurant A does more business that night than B. This phenomenon is also referred as an information cascade.

In marketing

Herd behavior is often a useful tool in marketing and, if used properly, can lead to increases in sales and changes to the structure of society. Whilst it has been shown that financial incentives cause action in large numbers of people, herd mentality often wins out in a case of "Keeping up with the Joneses".

In brand and product success

Communications technologies have contributed to the proliferation to consumer choice and "the power of crowds", Consumers increasingly have more access to opinions and information from both opinion leaders and formers on platforms that have largely user-generated content, and thus have more tools with which to complete any decision-making process. Popularity is seen as an indication of better quality, and consumers will use the opinions of others posted on these platforms as a powerful compass to guide them towards products and brands that align with their preconceptions and the decisions of others in their peer groups. Taking into account differences in needs and their position in the socialization process, Lessig & Park examined groups of students and housewives and the influence that these reference groups have on one another. By way of herd mentality, students tended to encourage each other towards beer, hamburger and cigarettes, whilst housewives tended to encourage each other towards furniture and detergent. Whilst this particular study was done in 1977, one cannot discount its findings in today's society. A study done by Burke, Leykin, Li and Zhang in 2014 on the social influence on shopper behavior shows that shoppers are influenced by direct interactions with companions, and as a group size grows, herd behaviour becomes more apparent. Discussions that create excitement and interest have greater impact on touch frequency and purchase likelihood grows with greater involvement caused by a large group. Shoppers in this Midwestern American shopping outlet were monitored and their purchases noted, and it was found up to a point, potential customers preferred to be in stores which had moderate levels of traffic. The other people in the store not only served as company, but also provided an inference point on which potential customers could model their behavior and make purchase decisions, as with any reference group or community.

Social media can also be a powerful tool in perpetuating herd behaviour. Its immeasurable amount of user-generated content serves as a platform for opinion leaders to take the stage and influence purchase decisions, and recommendations from peers and evidence of positive online experience all serve to help consumers make purchasing decisions. Gunawan and Huarng's 2015 study concluded that social influence is essential in framing attitudes towards brands, which in turn leads to purchase intention. Influencers form norms which their peers are found to follow, and targeting extroverted personalities increases chances of purchase even further. This is because the stronger personalities tend to be more engaged on consumer platforms and thus spread word of mouth information more efficiently. Many brands have begun to realise the importance of brand ambassadors and influencers, and it is being shown more clearly that herd behaviour can be used to drive sales and profits exponentially in favour of any brand through examination of these instances.

In social marketing

Marketing can easily transcend beyond commercial roots, in that it can be used to encourage action to do with health, environmentalism and general society. Herd mentality often takes a front seat when it comes to social marketing, paving the way for campaigns such as Earth Day, and the variety of anti-smoking and anti-obesity campaigns seen in every country. Within cultures and communities, marketers must aim to influence opinion leaders who in turn influence each other, as it is the herd mentality of any group of people that ensures a social campaign's success. A campaign run by Som la Pera in Spain to combat teenage obesity found that campaigns run in schools are more effective due to influence of teachers and peers, and students' high visibility, and their interaction with one another. Opinion leaders in schools created the logo and branding for the campaign, built content for social media and led in-school presentations to engage audience interaction. It was thus concluded that the success of the campaign was rooted in the fact that its means of communication was the audience itself, giving the target audience a sense of ownership and empowerment. As mentioned previously, students exert a high level of influence over one another, and by encouraging stronger personalities to lead opinions, the organizers of the campaign were able to secure the attention of other students who identified with the reference group.

Herd behaviour not only applies to students in schools where they are highly visible, but also amongst communities where perceived action plays a strong role. Between 2003 and 2004, California State University carried out a study to measure household conservation of energy, and motivations for doing so. It was found that factors like saving the environment, saving money or social responsibility did not have as great an impact on each household as the perceived behaviour of their neighbours did. Although the financial incentives of saving money, closely followed by moral incentives of protecting the environment, are often thought of as being a community's greatest guiding compass, more households responded to the encouragement to save energy when they were told that 77% of their neighbours were using fans instead of air conditioning, proving that communities are more likely to engage in a behaviour if they think that everyone else is already taking part.

Herd behaviours shown in the two examples exemplify that it can be a powerful tool in social marketing, and if harnessed correctly, has the potential to achieve great change. It is clear that opinion leaders and their influence achieve huge reach among their reference groups and thus can be used as the loudest voices to encourage others in any collective direction.

Crowd psychology

From Wikipedia, the free encyclopedia
 
A crowd

Crowd psychology, also known as mob psychology, is a branch of social psychology. Social psychologists have developed several theories for explaining the ways in which the psychology of a crowd differs from and interacts with that of the individuals within it. Major theorists in crowd psychology include Gustave Le Bon, Gabriel Tarde, Sigmund Freud, and Steve Reicher. This field relates to the behaviors and thought processes of both the individual crowd members and the crowd as an entity. Crowd behavior is heavily influenced by the loss of responsibility of the individual and the impression of universality of behavior, both of which increase with crowd size.

Origins

The psychological study of crowd phenomena was documented decades prior to 1900, as European culture was imbued with thoughts of the fin de siècle. This "modern" urban culture perceived that they were living in a new and different age. They witnessed marvelous new inventions and experienced life in new ways. The population, now living in densely packed, industrialized cities, such as Milan and Paris, witnessed the development of the light bulb, radio, photography, moving-picture shows, the telegraph, the bicycle, the telephone, and the railroad system. They experienced a faster pace of life and viewed human life as segmented, so they designated each of these phases of life with a new name. They created new concepts like "the adolescent", "kindergarten", "the vacation", "camping in nature", "the 5-minute segment", and "travel for the sake of pleasure" as a leisure class to describe these new ways of life.

Likewise, the abstract concept of "the crowd" grew as a new phenomenon simultaneously in Paris, France, and Milan, the largest city in the Kingdom of Italy. Legal reformers motivated by Darwin's evolutionary theory, particularly in the Kingdom of Italy, argued that the social and legal systems of Europe had been founded on antiquated notions of natural reason, or Christian morality, and ignored the irrevocable biology laws of human nature. Their goal was to bring social laws into harmony with biological laws. In pursuit of this goal, they developed the social science of criminal anthropology, which is tasked with the mission of changing the emphasis from one of the study of legal procedures to one of studying the criminal.

"Criminal anthropology", writes Giuseppe Sergi, "studies the delinquent in his natural place, that is to say, in the field of biology and pathology". The Italian Cesare Lombroso, professor of forensic medicine and hygiene in Turin, greatly advanced their agenda in 1878, when he published L'uomo delinquente, a highly influential book, which went through five editions. The book, published in English in 1900 under the title Criminal Man, solidified the links between social evolutionary theories and the fear of crowds with its concept of the "born" criminal as the savage in the midst of civilized society. The book influenced both European and American legal experts interested in assigning responsibility to individuals performing dubious behavior while engaged within a crowd.

The first debate in crowd psychology began in Rome at the first International Congress of Criminal Anthropology on 16 November 1885. The meeting was dominated by Cesare Lombroso and his fellow Italians, who emphasized the biological determinates.

"Lombroso detailed before the first congress his theories of the physical anomalies of criminals and his classification of criminals as 'born criminals', or criminals by occasion and mattoids. Ferri expressed his view of crime as degeneration more profound than insanity, for in most insane persons the primitive moral sense has survived the wreck of their intelligence. Along similar lines were the remarks of Benedickt, Sergi and Marro."

A weak response was offered by the French, who put forward an environmental theory of human psychology.

"M. Anguilli called attention to the importance of the influence of the social environment upon crime. Professor Alexandre Lacassagne thought that the atavistic and degenerative theories as held by the Italian school were exaggerations and false interpretations of the facts, and that the important factor was the social environment."

In Paris during 10–17 August 1889, the Italian school received a stronger rebuke of their biological theories during the 2nd International Congress of Criminal Anthropology. A radical divergence in the views between the Italian and the French schools was reflected in the proceedings.

"Professor Lombroso laid stress upon epilepsy in connection with his theory of the 'born criminal'. Professor Léonce Pierre Manouvrier characterized Lombroso's theory as nothing but the exploded science of phrenology. The anomalies observed by Lombroso were met with in honest men as well as criminals, Manouvrier claimed, and there is no physical difference between them. Baron Raffaele Garofalo, Drill, Alexandre Lacassagne and Benedikt opposed Lombroso's theories in whole or in part. Pugliese found the cause of crime in the failure of the criminal to adapt himself to his social surroundings, and Benedikt, with whom Tarde agreed, held that physical defects were not marks of the criminal qua criminal." It is in this context that you have a debate between Scipio Sighele, an Italian lawyer and Gabriel Tarde, a French magistrate on how to determine criminal responsibility in the crowd and hence who to arrest. (Sighele, 1892; Tarde, 1890, 1892, 1901)

Literature on crowds and crowd behavior appeared as early as 1841, with the publication of Charles Mackay's book Extraordinary Popular Delusions and the Madness of Crowds. The attitude towards crowds underwent an adjustment with the publication of Hippolyte Taine's six-volume The Origins of Contemporary France (1875). In particular Taine's work helped to change the opinions of his contemporaries on the actions taken by the crowds during the 1789 Revolution. Many Europeans held him in great esteem. While it is difficult to directly link his works to crowd behavior, it may be said that his thoughts stimulated further study of crowd behavior. However, it was not until the latter half of the 19th century that scientific interest in the field gained momentum. French physician and anthropologist Gustave Le Bon became its most-influential theorist.

Types of crowds

There is limited research into the types of crowd and crowd membership and there is no consensus as to the classification of types of crowds. Two recent scholars, Momboisse (1967) and Berlonghi (1995) focused upon purpose of existence to differentiate among crowds. Momboisse developed a system of four types: casual, conventional, expressive, and aggressive. Berlonghi classified crowds as spectator, demonstrator, or escaping, to correlate to the purpose for gathering.

Another approach to classifying crowds is sociologist Herbert Blumer's system of emotional intensity. He distinguishes four types of crowds: casual, conventional, expressive, and acting. His system is dynamic in nature. That is, a crowd changes its level of emotional intensity over time, and therefore, can be classed in any one of the four types.

Generally, researchers in crowd psychology have focused on the negative aspects of crowds, but not all crowds are volatile or negative in nature. For example, in the beginning of the socialist movement crowds were asked to put on their Sunday dress and march silently down the street. A more-modern example involves the sit-ins during the Civil Rights Movement. Crowds can reflect and challenge the held ideologies of their sociocultural environment. They can also serve integrative social functions, creating temporary communities.

Crowds can be active (mobs) or passive (audiences). Active crowds can be further divided into aggressive, escapist, acquisitive, or expressive mobs. Aggressive mobs are often violent and outwardly focused. Examples are football riots and the L.A. Riots of 1992. Escapist mobs are characterized by a large number of panicked people trying to get out of a dangerous situation. Acquisitive mobs occur when large numbers of people are fighting for limited resources. An expressive mob is any other large group of people gathering for an active purpose. Civil disobedience, rock concerts, and religious revivals all fall under this category.

Theoretical perspectives

Gustave Le Bon

Le Bon held that crowds existed in three stages: submergence, contagion, and suggestion. During submergence, the individuals in the crowd lose their sense of individual self and personal responsibility. This is quite heavily induced by the anonymity of the crowd. Contagion refers to the propensity for individuals in a crowd to unquestioningly follow the predominant ideas and emotions of the crowd. In Le Bon's view, this effect is capable of spreading between "submerged" individuals much like a disease. Suggestion refers to the period in which the ideas and emotions of the crowd are primarily drawn from a shared racial unconscious. This behavior comes from an archaic shared unconscious and is therefore uncivilized in nature. It is limited by the moral and cognitive abilities of the least capable members. Le Bon believed that crowds could be a powerful force only for destruction. Additionally, Le Bon and others have indicated that crowd members feel a lessened sense of legal culpability, due to the difficulty in prosecuting individual members of a mob.

Le Bon's idea that crowds foster anonymity and generate emotion has been contested by some critics. Clark McPhail points out studies which show that "the madding crowd" does not take on a life of its own, apart from the thoughts and intentions of members. Norris Johnson, after investigating a panic at a 1979 The Who concert concluded that the crowd was composed of many small groups of people mostly trying to help each other. Additionally, Le Bon's theory ignores the socio-cultural context of the crowd, which some theorists argue can disempower social change. R. Brown disputes the assumption that crowds are homogenous, suggesting instead that participants exist on a continuum, differing in their ability to deviate from social norms.

Freudian theory

Sigmund Freud's crowd behavior theory primarily consists of the idea that becoming a member of a crowd serves to unlock the unconscious mind. This occurs because the super-ego, or moral center of consciousness, is displaced by the larger crowd, to be replaced by a charismatic crowd leader. McDougall argues similarly to Freud, saying that simplistic emotions are widespread, and complex emotions are rarer. In a crowd, the overall shared emotional experience reverts to the least common denominator (LCD), leading to primitive levels of emotional expression. This organizational structure is that of the "primal horde" – pre-civilized society - and Freud states that one must rebel against the leader (re-instate the individual morality) in order to escape from it. Moscovici expanded on this idea, discussing how dictators such as Mao Zedong and Joseph Stalin have used mass psychology to place themselves in this "horde leader" position.

Theodor Adorno criticized the belief in a spontaneity of the masses: according to him, the masses were an artificial product of "administrated" modern life. The Ego of the bourgeois subject dissolved itself, giving way to the Id and the "de-psychologized" subject. Furthermore, Adorno stated the bond linking the masses to the leader through the spectacle is feigned:

"When the leaders become conscious of mass psychology and take it into their own hands, it ceases to exist in a certain sense. ... Just as little as people believe in the depth of their hearts that the Jews are the devil, do they completely believe in their leader. They do not really identify themselves with him but act this identification, perform their own enthusiasm, and thus participate in their leader's performance. ... It is probably the suspicion of this fictitiousness of their own 'group psychology' which makes fascist crowds so merciless and unapproachable. If they would stop to reason for a second, the whole performance would go to pieces, and they would be left to panic."

Deindividuation theory

Deindividuation theory argues that in typical crowd situations, factors such as anonymity, group unity, and arousal can weaken personal controls (e.g. guilt, shame, self-evaluating behavior) by distancing people from their personal identities and reducing their concern for social evaluation. This lack of restraint increases individual sensitivity to the environment and lessens rational forethought, which can lead to antisocial behavior. More recent theories have stated that deindividuation hinges upon a person being unable, due to situation, to have strong awareness of their self as an object of attention. This lack of attention frees the individual from the necessity of normal social behavior.

American social psychologist Leon Festinger and colleagues first elaborated the concept of deindividuation in 1952. It was further refined by American psychologist Philip Zimbardo, who detailed why mental input and output became blurred by such factors as anonymity, lack of social constraints, and sensory overload. Zimbardo's famous Stanford Prison Experiment is a strong argument for the power of deindividuation. Further experimentation has had mixed results when it comes to aggressive behaviors, and has instead shown that the normative expectations surrounding the situations of deindividuation influence behavior (i.e. if one is deindividuated as a KKK member, aggression increases, but if it is as a nurse, aggression does not increase).

A further distinction has been proposed between public and private deindividuation. When private aspects of self are weakened, one becomes more subject to crowd impulses, but not necessarily in a negative way. It is when one no longer attends to the public reaction and judgement of individual behavior that antisocial behavior is elicited.

Convergence theory

Convergence theory holds that crowd behavior is not a product of the crowd, but rather the crowd is a product of the coming together of like-minded individuals. Floyd Allport argued that "An individual in a crowd behaves just as he would behave alone, only more so." Convergence theory holds that crowds form from people of similar dispositions, whose actions are then reinforced and intensified by the crowd.

Convergence theory claims that crowd behavior is not irrational; rather, people in crowds express existing beliefs and values so that the mob reaction is the rational product of widespread popular feeling. However, this theory is questioned by certain research which found that people involved in the 1970s riots were less likely than nonparticipant peers to have previous convictions.

Critics of this theory report that it still excludes the social determination of self and action, in that it argues that all actions of the crowd are born from the individuals' intents.

Emergent norm theory

Ralph Turner and Lewis Killian put forth the idea that norms emerge from within the crowd. Emergent norm theory states that crowds have little unity at their outset, but during a period of milling about, key members suggest appropriate actions, and following members fall in line, forming the basis for the crowd's norms.

Key members are identified through distinctive personalities or behaviors. These garner attention, and the lack of negative response elicited from the crowd as a whole stands as tacit agreement to their legitimacy. The followers form the majority of the mob, as people tend to be creatures of conformity who are heavily influenced by the opinions of others. This has been shown in the conformity studies conducted by Sherif and Asch. Crowd members are further convinced by the universality phenomenon, described by Allport as the persuasive tendency of the idea that if everyone in the mob is acting in such-and-such a way, then it cannot be wrong.

Emergent norm theory allows for both positive and negative mob types, as the distinctive characteristics and behaviors of key figures can be positive or negative in nature. An antisocial leader can incite violent action, but an influential voice of non-violence in a crowd can lead to a mass sit-in. When a crowd described as above targets an individual, anti-social behaviors may emerge within its members.

A major criticism of this theory is that the formation and following of new norms indicates a level of self-awareness that is often missing in the individuals in crowds (as evidenced by the study of deindividuation). Another criticism is that the idea of emergent norms fails to take into account the presence of existent sociocultural norms. Additionally, the theory fails to explain why certain suggestions or individuals rise to normative status while others do not.

Social identity theory

The social identity theory posits that the self is a complex system made up primarily of the concept of membership or non-membership in various social groups. These groups have various moral and behavioral values and norms, and the individual's actions depend on which group membership (or non-membership) is most personally salient at the time of action.

This influence is evidenced by findings that when the stated purpose and values of a group changes, the values and motives of its members also change.

Crowds are an amalgam of individuals, all of whom belong to various overlapping groups. However, if the crowd is primarily related to some identifiable group (such as Christians or Hindus or Muslims or civil-rights activists), then the values of that group will dictate the crowd's action.

In crowds which are more ambiguous, individuals will assume a new social identity as a member of the crowd. This group membership is made more salient by confrontation with other groups - a relatively common occurrence for crowds.

The group identity serves to create a set of standards for behavior; for certain groups violence is legitimate, for others it is unacceptable. This standard is formed from stated values, but also from the actions of others in the crowd, and sometimes from a few in leadership-type positions.

A concern with this theory is that while it explains how crowds reflect social ideas and prevailing attitudes, it does not explain the mechanisms by which crowds enact to drive social change.

Lie group

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Lie_group In mathematics , a Lie gro...