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

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Culture and Social Interactions

Christian Jacob

• Dept. of Computer Science
• Dept. of Biochemistry & Molecular Biology

University of Calgary

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Cultural and Social Interactions

• 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

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Rumor Spreading and Voting

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The Rumor Mill Model

• 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?

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Rumor Mill: Single Seed

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Rumor Mill: Multiple Seeds

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Voting

• 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.

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Voting: Tradition vs. Near Losses for Loser

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Cultural Exchange

The more alike we are, the more alike we become

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Axelrod’s Transmission of Culture Model

• 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.

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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}

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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.

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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, {m1, …, ms}}

• d: random integer between 1 and 4 (north, south, east, west)
• mk: meme k with an integer value between 1 and M.

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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
• 500 time steps.

Step 1 Step 500

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Cultural Exchange

Social Status and Role Models

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Social Status and Role Models

• Another variant of the Cultural Transmission Model
• Two people with unequal social status interact culturally:

– Individual with lower status is more likely to adopt a meme value

• f 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 1

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Social Status and Role Models (Simulation Results)

• socialStatus program on a 25 by 25 lattice
• 2 memes with 2 possible values (1 or 2)
• 70% population density
• 500 time steps.

Step 1 Step 500

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Social Status and Role Models (Simulation Results)

• socialStatus program on a 100 by 100 lattice
• 2 memes with 2 possible values (1 or 2)
• 70% population density
• 500 time steps.

Step 1 Step 100

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Grouping and Conforming

Forming Neighbourhoods

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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.

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Schelling Model (Self-Forming Neighbourhoods)

• Thomas Schelling (1978) proposed a model for self-

forming 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, …

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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, {a1, …, av}}

• d: random integer between 1 and 4 (north, south, east, west)
• ak: attribute k with an integer value between 1 and w.

– The attributes {a1, …, av} may include unchangeable traits

• race, gender, ethnic identity, …

– and/or changeable beliefs

• political views, moral values, personal interests, …
• neighborhood program on a 20 by 20 lattice
• ne attribute with 2 possible values (1 or 2)
• 60% population density
• 500 time steps.

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Self-Forming Neighbourhoods (Simulation Results)

Step 1 Step 500

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Grouping and Conforming

Segregation

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Segregation Model

• 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) – …

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Segregation

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Social Networking

Nonlocal Movement

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Social Networking

• Models with spatial neighbourhoods are realistic in

situations such as a social gathering (a party) or in an

• rganization (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, email,

telephone, mail, …).

• In the following we look at one model for nonlocal

interaction and movement.

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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.

• 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
• 500 time steps.

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Nonlocal Movement: Simulation Results

Step 1 Step 500

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• flight program on a 100 by 100 lattice
• v = 1 attribute with w = 2 possible values
• 60% population density
• 500 time steps.

Nonlocal Movement: Simulation Results

Step 1 Step 500

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References

• Most of the simulations are based on:

– Gaylord, R. and D’Andria, L., Simulating Society, New York, Springer, 1991.

• Other references:

– Axelrod, R., The Complexity of Cooperation: Agent-Based Models of Competition and Cooperation, Princeton, NJ, Princeton University Press, 1997. – Schelling, T. C., Micromotives and Macrobehavior, New York, W. W. Norton, 1978. – Wilensky, U., Connected Models, Center for Connected Learning and Computer-based Modeling, Northwestern University, Evanston, IL.