Rumor Spreading and Voting

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1 1 Cultural and Social Interactions Culture and Social Interactions Christian Jacob Dept. of Computer Science Dept. of Biochemistry & Molecular Biology University of Calgary Rumor Spreading and Voting Rumor models Voting model Cultural Exchange The more alike we are, the more alike we become Social status and role models Grouping and Conforming Forming neighbourhoods Segregation Social Networking Nonlocal movement 2 The Rumor Mill Model Rumor Spreading and Voting Models the spread of a rumor The rumor is spread by people who know the rumor. They tell the rumor only to their nearest neighbours (4: von Neumann; 8: Moore neighbourhood) At each time step: Every person who knows the rumor randomly chooses a neighbour to tell the rumor to. Simulation keeps track of: How many people know the rumor? Where are the people, who know the rumor, located? How many repeated tellings of a rumor occur? 3 4 Rumor Mill: Single Seed Rumor Mill: Multiple Seeds 5 6

2 7 Voting Voting: Tradition vs. Near Losses for Loser Each patch takes a vote of its eight surrounding neighbours and itself. The patch changes its own vote according to the outcome: Traditional Voting Rule: The central patch changes its colour to match the majority vote. Near Losses Awarded to Loser: If five patches vote for white (and, consequently, four patches vote for black), the central patch becomes black. If five patches vote for black, the central patch becomes white. All other possible voting combinations are awarded traditionally. 8 Axelrod s Transmission of Culture Model Cultural Exchange The more alike we are, the more alike we become In 1997 Robert Axelrod proposed the following model for the transmission of culture: On a square lattice, each site is occupied by an agent (homogeneous village). Agents interact with their four nearest neighbours. An agent is characterized by having attributes (features), with an integer value (a trait) between 0 and 10. At each time step: An agent is randomly chosen (active agent). The active agent randomly selects an agent from its nearest neighbour site. The active agent interacts with the selected agent Axelrod s Transmission of Culture Model (2) Cultural Interaction Rules: When an agent interacts with another agent, a comparison is made between their traits of corresponding features. If their traits are the same (e.g., {5, 9, 1, 3, 2} and {5, 9, 1, 3, 2}), nothing happens. If any of the traits differ, a cultural interaction occurs: The probability of this interaction is equal to the fraction of features that share the same trait,... that is, to their degree of cultural similarity. Example: {4, 8, 1, 2, 5} and {3, 2, 1, 7, 5} have a 40% probability of interacting culturally, as features 3 and 5 have the same traits (2/5). Interaction: One of the features of the active agent A that differs from the corresponding feature of the selected agent B is set to the feature trait of B. Example: A: {4, 2, 1, 2, 5}, B: {3, 2, 1, 7, 5} Extensions of Axelrod s Model Mobility: Axelrod: no movement, sites are static ( homogeneous villages ) Extension: Some lattice sites are empty and some occupied by agents, that can walk around on the grid. Bilateral Cultural Exchange: Axelrod: pairwise interaction between agents is one-way or unilateral; only the active agent s trait is changed. Extension: Bilateral interactions; both the active and selected agents change their traits

3 13 Extended Cultural Transmission Model n by n square lattice with wrap-around boundary Population density p of individuals occupying lattice sites Each agent is characterized by the direction it is facing and a meme list with s elements. Note: A meme represents the basic unit of cultural transmission, analogous to the gene as the basic unit of genetic transmission (term coined by Richard Dawkins). Lattice site values: An empty site has value 0. An agent site is a list of integers: {d, {m 1,, m s }} d: random integer between 1 and 4 (north, south, east, west) m k : meme k with an integer value between 1 and M. Cultural Transmission Model (Simulation Results) culturespreadingshared program on a 25 by 25 lattice 2 memes with 2 possible values (1 or 2) 75% population density 14 Social Status and Role Models Another variant of the Cultural Transmission Model Cultural Exchange Social Status and Role Models Two people with unequal social status interact culturally: Individual with lower status is more likely to adopt a meme value of the individual with higher status. The meme value of the higher status individual will remain unchanged. Example: adoption of a role-model s attitude(s) Site representation: {direction, status, memelist} direction and memelist as in the previous model status: integer 0 or Social Status and Role Models (Simulation Results) Social Status and Role Models (Simulation Results) Step 1 Step 100 socialstatus program on a 25 by 25 lattice 2 memes with 2 possible values (1 or 2) 70% population density socialstatus program on a 100 by 100 lattice 2 memes with 2 possible values (1 or 2) 70% population density 17 18

4 19 Forming Neighbourhoods Grouping and Conforming Forming Neighbourhoods Previous models: bilateral interactions between two individuals Many social phenomena can be better described in terms of interactions between an individual and a group of other people. 20 Schelling Model (Self-Forming Neighbourhoods) Thomas Schelling (1978) proposed a model for selfforming neighbourhoods based on the desire of people to live with their own kind. An individual is happy or unhappy with the number of nearest neighbours who are like him/her. An unhappy individual can move to the nearest empty site that has a sufficient number of similar neighbours. Spatial segregation or ghettoization occurs spontaneously, without being imposed by a central authority (emergence!) Can result in clustering of people by gender, age, race, beliefs, Self-Forming Neighbourhoods n by n square lattice with wrap-around boundary Population density p of individuals occupying lattice sites Lattice site values: An empty site has value 0. An agent site is a list of integers: {d, {a 1,, a v }} d: random integer between 1 and 4 (north, south, east, west) a k : attribute k with an integer value between 1 and w. The attributes {a 1,, a v } may include unchangeable traits race, gender, ethnic identity, and/or changeable beliefs political views, moral values, personal interests, Self-Forming Neighbourhoods (Simulation Results) Grouping and Conforming Segregation neighborhood program on a 20 by 20 lattice one attribute with 2 possible values (1 or 2) 60% population density 23 24

5 25 Segregation Model Segregation Two types of turtles in a pond: red and green turtles. The red and green turtles get along with each other. But each turtle wants to make sure to live near some of its own. Each red turtle wants to live near at least some red turtles. Each green turtle wants to live near at least some green turtles. Similar phenomena: Housing patterns in cities Ethnic communities Professional communities (Ponte Veccio, Florence; university campus) 26 Social Networking Social Networking Nonlocal Movement Models with spatial neighbourhoods are realistic in situations such as a social gathering (a party) or in an organization (a company), where people physically interact in space. However, in human societies with its economic and social phenomena not all interactions are spatial. Technology also influences interactions (internet, , telephone, mail, ). In the following we look at one model for nonlocal interaction and movement Nonlocal Movement (Extension of Schelling Model) n by n square lattice with wrap-around boundary Population density p of individuals occupying lattice sites Population consists of two types of individuals: A fraction g are of one type and a fraction (1-g) are of the other type. Nonlocal Movement: Simulation Results Lattice site values: An empty site has value 0. An agent site is an integer: t t: integer 1 or 2, indicating what type the agent is For each time step: An agent which finds less than 50% of its neighbours share the same type wants to move. For agents who want to move an empty site is determined. Each agent that wants to move and has an empty site to move to is relocated, leaving an empty site behind. flight program on a 20 by 20 lattice v = 1 attribute with w = 2 possible values 60% population density 29 30

6 31 Nonlocal Movement: Simulation Results References Most of the simulations are based on: Gaylord, R. and D Andria, L., Simulating Society, New York, Springer, Other references: Axelrod, R., The Complexity of Cooperation: Agent-Based Models of Competition and Cooperation, Princeton, NJ, Princeton University Press, Schelling, T. C., Micromotives and Macrobehavior, New York, W. W. Norton, Wilensky, U., Connected Models, Center for Connected Learning and Computer-based Modeling, Northwestern University, Evanston, IL. flight program on a 100 by 100 lattice v = 1 attribute with w = 2 possible values 60% population density 32