Rumor Spreading They tell the rumor only to their nearest - PDF document

Cultural and Social Interactions • Rumor Spreading and Voting – Rumor models – Voting model Culture and Social • Cultural Exchange Interactions – The more alike we are, the more alike we become – Social status and role models • Grouping and Conforming – Forming neighbourhoods – Segregation Christian Jacob Dept. of Computer Science • Social Networking Dept. of Biochemistry & Molecular Biology – Nonlocal movement University of Calgary 1 2 The Rumor Mill Model • Models the spread of a rumor – The rumor is spread by people who know the rumor. Rumor Spreading – They tell the rumor only to their nearest neighbours (4: von Neumann; 8: Moore neighbourhood) and • At each time step: Voting – 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

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. 7 8 Axelrod’s Transmission of Culture Model • In 1997 Robert Axelrod proposed the following model for the transmission of culture: Cultural Exchange – On a square lattice, each site is occupied by an agent (homogeneous village). The more alike we are, the more – Agents interact with their four nearest neighbours. – An agent is characterized by having attributes ( features ), with an alike we become 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. 9 10 Axelrod’s Transmission of Culture Model (2) Extensions of Axelrod’s Model • Cultural Interaction Rules: • Mobility: – When an agent interacts with another agent, a comparison is made between their traits of corresponding features. – Axelrod: no movement, sites are static (‘homogeneous villages’) • If their traits are the same (e.g., {5, 9, 1, 3, 2} and {5, 9, 1, 3, 2}), – Extension: Some lattice sites are empty and some occupied by nothing happens. agents, that can walk around on the grid. • 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, • Bilateral Cultural Exchange: – ... 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). – Axelrod: pairwise interaction between agents is one-way or – Interaction: unilateral; only the active agent’s trait is changed. 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 . – Extension: Bilateral interactions; both the active and selected agents Example: A : {4, 2, 1, 2, 5}, B : {3, 2, 1, 7, 5} change their traits. 11 12

Extended Cultural Transmission Model Cultural Transmission Model (Simulation Results) Step 1 Step 500 • 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) • cultureSpreadingShared program on a 25 by 25 lattice • m k : meme k with an integer value between 1 and M . • 2 memes with 2 possible values (1 or 2) • 75% population density • 500 time steps. 13 14 Social Status and Role Models • Another variant of the Cultural Transmission Model Cultural Exchange • 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 Social Status and Role Models 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 1 15 16 Social Status and Role Models (Simulation Results) Social Status and Role Models (Simulation Results) Step 1 Step 500 Step 1 Step 100 • socialStatus program on a 25 by 25 lattice • socialStatus program on a 100 by 100 lattice • 2 memes with 2 possible values (1 or 2) • 2 memes with 2 possible values (1 or 2) • 70% population density • 70% population density • 500 time steps. • 500 time steps. 17 18

Forming Neighbourhoods • Previous models: bilateral interactions between two Grouping and individuals Conforming • Many social phenomena can be better described in terms of interactions between an individual and a group of other people. Forming Neighbourhoods 19 20 Schelling Model (Self-Forming Neighbourhoods) Self-Forming Neighbourhoods • Thomas Schelling (1978) proposed a model for self- • n by n square lattice with wrap-around boundary forming neighbourhoods based on the desire of people to • Population density p of individuals occupying lattice sites live with their own kind. • Lattice site values: • An individual is happy or unhappy with the number of – An empty site has value 0. nearest neighbours who are like him/her. – An agent site is a list of integers: { d , { a 1 , …, a v }} • An unhappy individual can move to the nearest empty site • d : random integer between 1 and 4 (north, south, east, west) that has a sufficient number of similar neighbours. • a k : attribute k with an integer value between 1 and w . – The attributes { a 1 , …, a v } may include unchangeable traits • Spatial segregation or ghettoization occurs spontaneously, • race, gender, ethnic identity, … without being imposed by a central authority (emergence!) – and/or changeable beliefs • Can result in clustering of people by • political views, moral values, personal interests, … – gender, age, race, beliefs, … 21 22 Self-Forming Neighbourhoods (Simulation Results) Step 1 Step 500 Grouping and Conforming Segregation • neighborhood program on a 20 by 20 lattice • one attribute with 2 possible values (1 or 2) • 60% population density • 500 time steps. 23 24

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) – … 25 26 Social Networking • Models with spatial neighbourhoods are realistic in situations such as a social gathering (a party) or in an Social Networking organization (a company), where people physically interact in space. • However, in human societies—with its economic and Nonlocal Movement social phenomena—not all interactions are spatial. • Technology also influences interactions (internet, email, telephone, mail, …). • In the following we look at one model for nonlocal interaction and movement. 27 28 Nonlocal Movement (Extension of Schelling Model) Nonlocal Movement: Simulation Results Step 1 Step 500 • 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. • 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. • flight program on a 20 by 20 lattice – For agents who want to move an empty site is determined. • v = 1 attribute with w = 2 possible values – Each agent that wants to move and has an empty site to move to is relocated, leaving an empty site behind. • 60% population density • 500 time steps. 29 30