Crowds Prof. Dr. Dirk Helbing and Team Zurich November 2, 2008 1 / 62

Mathematical , Agent-Based Modeling and Artificial

Prof. Dr. Dirk Helbing and Team

Chair of Sociology, in particular of Modeling and Simulation

November 2, 2008

Chair of Sociology, in particular of Modeling and Simulation http://www.soms.ethz.ch/ Crowds Prof. Dr. Dirk Helbing and Team Zurich November 2, 2008 1 / 62

Crowds

Anders Johansson www.soms.ethz.ch [email protected]

Chair of Sociology, in particular of Modeling and Simulation http://www.soms.ethz.ch/ Crowds Prof. Dr. Dirk Helbing and Team Zurich November 2, 2008 2 / 62 Overview

Overview

1 Introduction

2 Opinions and Decision Making in Crowds 3 Stampedes and Modeling of Crowds 4 Escape Panics 5 Collective Behavior

6 Contagion 7 Critical Mass

8 References

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Crowd Behavior

Often, calm demonstrations are transformed into riots by singular events followed by an outburst of violence. There are different theories for explaining the crowd behavior: 1 Contagion Theory 2 Convergence Theory 3 Emergent-Norm Theory

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Crowd Behavior: Contagion Theory

Le Bon’s (1895) contagion theory talks about hypnotic influence from the crowd over its members. Shielded by the anonymity in large crowds, individuals forget about their personal responsibilities. By this view, the crowd has its own life where emotions are stirred up and driving people to violence. Evidence that speaks for the contagion theory is: Crowds sometimes do things that the individuals do not have courage to carry out alone.

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Crowd Behavior: Convergence Theory

Convergence Theory on the other hand, is assuming that different people with similar opinions are creating crowds. Opposite from contagion theory which claims that the crowd makes people behave in the same way, convergence theory claims that individuals who want to act in a certain way come together to form a crowd. Evidence that speaks for the convergence theory is: Crowds can intensify an emotion by creating a critical mass of similar-minded people.

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Crowd Behavior: Emergent-Norm Theory Turner and Killan (1993) developed the emergent-norm theory, which is found in between the contagion theory and the convergence theory. This theory states that the crowd behavior is a result both of desires of the participants as well as emerged norms. The theory states that when similar-minded individuals come together, distinctive patterns of behavior may emerge. However, crowds are initially formed by people with mixed interests and motives. Evidence that speaks for the convergence theory is: People in a crowd take different roles. Some become leaders of the crowd and others follows. It is pointed out that decision making is of great importance in crowds.

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The Wisdom of Crowds

When polling for a certain opinion and averaging over the group, the average answer is under certain circumstances very close to the true value (Surowiecki, 2004). Knowledge is dispersed over a group. Examples: Wikipedia, Open Source Software, “Who wants to be a millionaire?”. Properaties of successful crowds: decentralized, diversity of opinions, independence, loose connections, possible to aggregate individual opinions.

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Condorcet’s Jury Theorem

(Marquis de Condorcet, 1785): 1 A number of people N can p=55% 0.8 vote between options A and p=51% B, and the average probability p=49% 0.6 p=45% that a certain person knows the “true” answer is p. Then, 0.4 the probability P that the

Probability that jury is right 0.2 majority vote gives the right

0 answer is limN→∞ P = 1 for all 0 2000 4000 6000 8000 10000 Jury size (N) p > 1/2 (and limN→∞ P = 0 for all p < 1/2)

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Condorcet’s Jury Theorem (II)

Condorcet’s jury theorem is sometimes used as a an argument why democracy is a good system. However, the theorem is only valid if the following assumptions hold: The number of options should be exactly 2. A clear definition of what answer is true must exist. Votes should be independent.

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Deliberating Groups

One example where votes are not independent is when the votes are a result of a deliberating group. In fact, for such groups, it is very likely that the deliberation process will create biases which polarizes the group. The people of the group have little incentive to “speak out”, since it provides benefit to others while possible facing high personal costs.

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Deliberating Groups (II)

According to Sunstein (2006): “Deliberating groups typically suffer from four problems. 1 They amplify the errors of their members 2 They do not elicit the information that their members have. 3 They are subject to cascading effects, producing a situation in which the blind lead the blind. 4 They show a tendency towards group polarization”.

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Prediction Markets

A possible solution to get rid of the problem of deliberating groups, is to use prediction markets. This can be implemented either by letting people vote anonymously (which lower their personal cost), or by introducing monetary incentives (the more certain a person is on his/her opinion, the higher amount of money he/she will bet).

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Policy Analysis Market

The United States’ Defense Advanced Research Projects (DARPA) started a project called Policy Analysis Market with the aim of aggregating dispersed information and predict certain aspects of the development in the middle east.

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Stampedes

Stampedes can occur as a result of panic. Stampedes can be triggered by fires, bombs or other dangers, but it can also be triggered by rumours of something dangerous, so called phantom panics.

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Stampede: Al A‘imma Bridge

In Baghdad, Iraq at the Al A‘imma Bridge there was a stampede in 2005, with more than one thousand fatalities. The reason for the stampede was phantom panic after rumours of an imminent suicide bomber. Most people died by drowning after jumping into the Tigris river in desperation to escape the crowded bridge. Others where stamped to death.

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Modeling of Pedestrian Crowds Modeling of pedestrian crowds can be done in various ways.

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Modeling of Pedestrian Crowds (II) Space and time can be either discrete or continuous:

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Social-Force Model The social-force model (Helbing et al.) is a microscopic model which is continuous both in space and time. Each pedestrian α is influenced by a number of forces, e.g. repulsive forces from other pedestrians β, repulsive forces from borders and a driving force towards the desired direction of motion.

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Social-Force Model

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Social-Force Model

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Social-Force Model

Let us start with only the first force component, i.e. the adaptation of the actual velocity to a desired velocity. 0 If we assume that the desired velocity vαe~α is known, the remaining parameter is τα.

[VIDEO]

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Social-Force Model

Next, we look at the second component, which reflects the forces from other pedestrians β.

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Social-Force Model

[VIDEO]

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Social-Force Model

~ Finally, forces from boundaries fαi are needed to prevent the pedestrians from penetrating walls and obstacles.

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Social-Force Model To prevent pedestrians from penetrating boundaries, we specify the force on the form:

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Social-Force Model Let us have a look at how the model can be solved numerically. The simplest way to solve the differential equations of the social-force model numerically is to use the 1st order Euler’s method:

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Social-Force Model

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Escape Panics

In an experiment by Mintz in 1951, a number of cones were put in a bottle and a string was attached to each of the cones. The ends of the strings were given to the participants. Water entered the bottle from below. A participant got rewarded if his/her cone came out dry, and got increasingly fined when there was water in the cone. The outcome was that there was always jamming and Mintz explained this by an unstable reward strategy. (from Fig. 3.3 in D. L. Miller)

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Escape Panics (II)

Brown (1965) puts Mintz’s experiment in a prisoner’s dilemma game with two players. Each player has the options rush or take turns. Paradoxically, the only rational action is to rush!

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Escape Panics III

The game can be reinterpreted as an evacuation from a building, where the two players, A1 and A2 each has the options: Transfer: Begin by walking, and run contingent to other’s running. Run: Begin by running, and run independently of other’s action.

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Panic

Often, rushing to the exit can be considered to be rational behavior. It is frequently reported that even though there is rushing to the exit, social order and social norms still remains, There is no evidence of family members abandoning each others in emergency situations. It has been reported that people did not overtake very slow or disabled evacuees from the WTC evacuation. Johnson (1988): “The evidence suggests that selfish individualistic crowd behavior, unregulated by social constraints, is likely to be extremely rare”. Evacuation: [VIDEO]experiment, [VIDEO]simulation [VIDEO]Hotel evacuation simulation

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Jonathan Sime, Crowd psychology and engineering: Designing for people or ballbearings

A crowd should not be seen as physical objects but as the crowd members who think, and behave. Crowd psychology: “the study of the mind and the behavior of masses and crowds, and of the experience of individuals in such crowds.” Total evacuation time = time before moving + time to move through the facility through the exit. “Disasters are characterized by poor communications before prior to, during, and and in the aftermatch of an accident, in which it is very often the victims, rather than the designers and managers of crowd settings, who are blamed.”

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Simulations of Escape Panics

Learning from Sime, Johnson and others, evacuations do not always break down to irrational “panic” behavior. With a modification of the social-force model, we can simulate both panic-like behavior where everybody tries to force their way out through the main exit, as compared to the case when each person tries to locate and use the fastest escape route. 1 The naive approach (shortest path) [VIDEO] 2 The fastest path [VIDEO]

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Pre-Movement Time From a series of evacuation experiments of a metro station, different alarm systems have been compared to each other:

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World Trade Center Questionnaires and interviews of the evacuees from the World Trade Center evacuation have made it possible to reconstruct the pre-movement time distributions (Averill et al., 2007):

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Unilateral Transfer of Control One observed behavior, especially in times of uncertainty, is unilateral transfer of control of actions to others: One day in church, in the middle of the sermon, we heard a fire engine drive into the church parking lot, next to the sanctuary. There was an uncertain feeling - were we in danger? The obvious impulse to get out of the place was countered by the obviously inappropriate character of any such behavior in the sacred setting of the church. I found myself looking to left and to right to see whether other people looked frightened, to see whether anyone was doing anything about the situation. [...] What I saw was a lot of other people also looking about, presumably in the same way I was! (Turner and Killian, 1957)

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Collective Behavior

The term collective behavior was first used by Robert Ezra Park, an American urban sociologist at the Chicago School of sociology, which he also co-founded. What is collective behavior? Social processes and events which do not reflect existing , but rather emerge in a spontaneous way. In between conformity and . Sets in when there are no norms, or the existing norms are not clear enough or there are norms that contradict each other.

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Collective Behavior People within collective behavior are described as: excitable, emotional, suggestive, and they exhibit contagion, they are subject to hypnotic effects of the crowd. They are irrational, disorderly, unpredictable, and spontaneous. Unilateral transfer of control does not always lead to mob-like behavior. Rather, depending on the actions of the people who initially act individually, the crowd can behave in very different ways. Coleman (1990): “A strong basis of knowledge about such phenomena [collective behavior] is important but has not been developed [...] Thus, the general area of collective behavior holds potentially great rewards for theory development and empirical research”.

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Examples of Collective Behavior

There is a broad range of examples, fitting into the classification of collective behavior. Among these: Escape panics. Behavioral fads, influencing a population of children (The Yo-yo toy, skateboarding, etc.). Stock-speculation manias. Riots and hostile unorganized demonstrations. The spread of clothing fashions. Religious frenzies.

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Revolts and Revolutions Revolts and revolutions can be understood by many instances of collective behavior. Both Le Bon (1895) and Brown (1965) point out that the collective behavior can not be explained by the average of the actions that the individuals would take individually. Rather, it is something that emerges.

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Emergence

Let us return to the social-force model. It turns out, that by local interactions on the microscopic scale, various patterns emerge on the macroscopic scale:

Lane formation [VIDEO] Bottleneck oscillations [VIDEO]

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Contagion

J. Breaux suggests in his Factors affecting social contagion in crowds (1975) a “sociological approach” where not every activity will spread through the crowd, since the crowd is a heterogeneous composition of individuals who are connected in a .

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Contagious Beliefs

Believing in flying saucers, ghosts and other strange but widely accepted phenomena is called contagious beliefs. The behavior involves a transform of control over belief. Sherif (1936) made an experiment where a participant was placed in a dark room, without any visual cues or spatial reference. A pinpoint of light was visible in the other end of the room. Even though the location of the light was fixed, the participant was tricked to believe that the light was moving. This phenomenon was termed the auto-kinetic effect. Cults often arise in times when the is undergoing a rapid and there is a breakdown of the traditional structure of authority.

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Paul McCartney is Dead!

In 1969, there was a rumour that Paul McCartney of The Beatles was dead. It started as an anonymous phone call to a radio station and when more and more “evidence“ in form of hidden messages was found in the songs and album covers of The Beatles, the rumour that Paul McCartney was dead (and being secretly replaced) grew very strong.

In the late 1960s many young people had distrust in media and other authorities. Therefore, rumours like the one of Paul McCartney’s death could spread like a disease.

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Kermack-McKendrick Model

The Kermack-McKendrick model was proposed for explaining the spreading of diseases like the plague and cholera. The model assumes: A constant population size. A zero incubation period. The duration of infectivity is as long as the duration of the clinical disease.

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Kermack-McKendrick Model (II)

The Kermack-McKendrick model is specified as: S: Susceptible persons. I: Infected persons. R: Removed (immune) persons. β: Infection rate. γ: Immunity rate.

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Kermack-McKendrick Model (III)

Putting it into equations we get:

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Kermack-McKendrick Model (VI)

The result from a simulation:

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Le Bon on Crowds

Le Bon: ”[...] in the aggregate which constitutes the a crowd there is in no sort a summing up of or an average struck between its elements. What really takes place is a combination followed by the creation of new characteristics just as in chemistry certain elements when brought into contact - bases and acids for example - combine to form a new body possessing properties quite different from those of the bodies that have served to form it.”

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Chemistry of Belief Adamatzky (2001) proposes a similar model as the Kermack-McKendrick model, but instead of contagious diseases, he explains contagious beliefs. Let p be a preposition, i be and individual, β a “belief” operator, defined as, βip : “Individual i believes that p is true”. λip means “p is true within the local vicinity of i.”

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Chemistry of Belief (II)

Adamatzky’s equations can also be written as chemical reactions:

Chemistry of anxious believers.

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Chemistry of Belief (III)

Adamatzky’s equations can be written as a set of differential equations:

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Chemistry of Belief (IV) Result of simulation of anxious believers:

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Chemistry of Belief (V) With a modified set of reactions:

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Chemistry of Belief (VI) With a further modified set of reactions:

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Critical Mass

The critical mass can be specified as the threshold, s, of how large fraction of a population must have joined an event, before the individual wants to join.

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An Example of Critical Mass A group of pedestrians are waiting at a red light. After a while, one pedestrian may get restless and pass the crosswalk, even though the light is still red. Then, another pedestrians are following and after a while the whole group of pedestrians is passing the crosswalk.

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La Ola

La Ola, or The Mexican Wave is a collective phenomenon, occurring within a crowd of excited soccer supporters. If a critical mass of people is jumping on their feet in excitation, they trigger their neighbor to do the same, and the result is a wave, propagating among the supporters. Video: La Ola [VIDEO]

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References J. Surowiecki, The Wisdom of Crowds, 2004. J. Breaux, Factors affecting social contagion in crowds, D. Phil, , 1975 J. Sime, Crowd psychology and engineering: Designing for people or ballbearings, in R. A. Smith and J. F. Dickie (eds): Engineering for Crowd Safety, 1993. M. de Condorcet, Essai sur l’ application de l’ analyse a´ la probabilite´ des decisions´ rendues a´ la pluralite´ des voix, 1785. J. S. Coleman, Foundations of Social Theory, Press, London, England, 1990. N. R. Johnson, Fire in a crowded theater: A descriptive investigation of the emergence of panic, International Journal of Mass Emergencies and Disasters, 6 (1), 7–26, 1988.

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References H. Esser, Soziologie, Band 4, Campus Verlag, Frankfurt/Main, Germany, 2000. T. C. Schelling, Choice and Consequence, Harward University Press, London, UK, 1984. I. Farkas, D. Helbing, T. Vicsek, Mexican waves in an excitable medium. 419, 131–132 (2002). W. B. Arthur, Competing Technologies, Increasing Returns, and Lock-In by Historical Events, The Economic Journal, 99 (394) 116–131 (1989). Helbing, D. and Molnar,´ P., Social force model for pedestrian dynamics, Physical Review E 51, 4282–4286 (1995). A. Adamatzky, Dynamics of Crowd Minds, World Scientific Publishing Company, UK, 2005.

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References C. R. Sunstein, Infotopia, OUP, USA, 2006. S. D. Levitt and S. J. Dubner, Freakonomics: A Rogue Economist Explores the Hidden Side of Everything, HarperLargePrint, USA, 2006. D. Nilsson, A. Johansson, during the initial phase of a fire evacuation – Analysis of evacuation experiments in a cinema theatre, Fire Safety J, doi:10.1016/j.firesaf.2008.03.008 (2008). T. C. Schelling. 1971. Dynamic Models of Segregation. Journal of Mathematical Sociology 1:143-186. A. Mintz, Non-adaptive group behavior, The Journal of Abnormal and Normal Social Psychology 46, 150–159 (1951). R. Brown, R., Social Psychology, Free Press, New York, 1965.

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References

J. D. Averill, D. Mileti, R. Peacock, E. Kuligowski, N. Groner, G. Proulx, P. Reneke, and H. Nelson, Federal Investigation of the Evacuation of the World Trade Center on September 11, 2001, in: Waldau et al. (eds) Pedestrian and Evacuation Dynamics 2005, 1–12, Springer Berlin Heidelberg, Germany, 2007. J. S. Macionis, Sociology. Prentice Hall, 2007. R. Turner, and L. M. Killian, Collective Behavior 4th ed, Englewood Cliffs, NJ: Prentice Hall, 1993. M. Sherif, Group Norms and Conformity, 1936. W. O. Kermack and A. G. McKendrick, A Contribution to the Mathematical Theory of Epidemics, Proc. Roy. Soc. Lond. A 115, 700–721, 1927.

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