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Mathematical Sociology, Agent-Based Modeling and Artificial Societies

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Mathematical Sociology, Agent-Based Modeling and Artificial Societies Crowds Prof. Dr. Dirk Helbing and Team Zurich November 2, 2008 1 / 62 Mathematical Sociology, Agent-Based Modeling and Artificial Societies 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 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 3 / 62 Introduction 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 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 4 / 62 Introduction 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. 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 5 / 62 Introduction 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. 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 6 / 62 Introduction 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. 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 7 / 62 Opinions and Decision Making in Crowds 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. 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 8 / 62 Opinions and Decision Making in Crowds 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!1 P = 1 for all 0 2000 4000 6000 8000 10000 Jury size (N) p > 1=2 (and limN!1 P = 0 for all p < 1=2) 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 9 / 62 Opinions and Decision Making in Crowds 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. 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 10 / 62 Opinions and Decision Making in Crowds 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. 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 11 / 62 Opinions and Decision Making in Crowds 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”. 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 12 / 62 Opinions and Decision Making in Crowds 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). 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 13 / 62 Opinions and Decision Making in Crowds Policy Analysis Market The United States’ Defense Advanced Research Projects Agency (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. 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 14 / 62 Stampedes and Modeling of Crowds 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. 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 15 / 62 Stampedes and Modeling of Crowds 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. 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 16 / 62 Stampedes and Modeling of Crowds Modeling of Pedestrian Crowds Modeling of pedestrian crowds can be done in various ways. 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 17 / 62 Stampedes and Modeling of Crowds Modeling of Pedestrian Crowds (II) Space and time can be either discrete or continuous: 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 18 / 62 Stampedes and Modeling of Crowds 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. 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 19 / 62 Stampedes and Modeling of Crowds Social-Force Model Chair of Sociology, in particular of Modeling and Simulation http://www.soms.ethz.ch/ Crowds Prof.
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