Shared Terminology in Social Science Shared Terminology in Social Science Using Multi-Agent SimulationsUsing Multi-Agent Simulations

Dante SuarezDante SuarezTrinity UniversityTrinity University

Lake Arrowhead, Human Complex Systems, 2007Lake Arrowhead, Human Complex Systems, 2007

This presentation includes work done in conjunction with professors at Trinity University:This presentation includes work done in conjunction with professors at Trinity University:

Yu Zhang & Mark Lewis, Computer Science, Christine Drennon, Yu Zhang & Mark Lewis, Computer Science, Christine Drennon, Sociology and Anthropology, Claudia Scholz, Research Programs Sociology and Anthropology, Claudia Scholz, Research Programs Coordinator, and Luis Schettino, Psychology. Coordinator, and Luis Schettino, Psychology.

Linear vs. Nonlinear ScienceLinear vs. Nonlinear Science Most science until now is based on linear Most science until now is based on linear

models.models. Linearity is based on independence of agents.Linearity is based on independence of agents. Under an assumption of linearity: Under an assumption of linearity:

The whole equals the sum of its parts.The whole equals the sum of its parts.

Nonlinear ScienceNonlinear Science

Agents are interrelated. Agents are interrelated. You cannot reduce the system.You cannot reduce the system. Solutions to the system are complex:Solutions to the system are complex:

the algorithm is the shortest solutionthe algorithm is the shortest solution. .

Emergence:Emergence:

The whole does not equal the sum of its parts.The whole does not equal the sum of its parts.

EmergenceEmergence

If emergence exists, then I expect to If emergence exists, then I expect to encounter a world full of emergence.encounter a world full of emergence.

A world of….my favorite word, levels.A world of….my favorite word, levels. A reductionist approach is insufficient.A reductionist approach is insufficient.

Bottom’s Up! Bottom’s Up! Modeling atomsModeling atoms

In Economics, society does not exist.In Economics, society does not exist. A paradigm based on the individual: an A paradigm based on the individual: an

exogenous entity.exogenous entity. All behavior is the product of current agents.All behavior is the product of current agents. The Utility function represents the individual, The Utility function represents the individual,

and it is set to reflect her preferences. and it is set to reflect her preferences.

Modeling Individuals in a Complex SystemModeling Individuals in a Complex System Societies are inherently complex, but yet individuals are Societies are inherently complex, but yet individuals are

still simple. They are still composed of little selfish ‘agents’.still simple. They are still composed of little selfish ‘agents’. The ant of Herbert Simon.The ant of Herbert Simon. However, somehow we must model them with the right However, somehow we must model them with the right

assumptions so that their aggregate reflects its true assumptions so that their aggregate reflects its true complexity.complexity.

U( x, y)U( x, y)

UUii(x(xii, y, yii, x, xjj) or U) or Uii(x(xii, y, yii, U, Ujj))

There has to be more to it. The utility functions of the There has to be more to it. The utility functions of the individuals themselves are interdependent, changing, and individuals themselves are interdependent, changing, and at some level a function of the actual aggregate behavior.at some level a function of the actual aggregate behavior.

StructureStructure

A reductionist approach is insufficient.A reductionist approach is insufficient. Models with Low-Cognition Agents.Models with Low-Cognition Agents. Endogenous utility functions.Endogenous utility functions. The agent represents a ‘level’: bounded and The agent represents a ‘level’: bounded and

binding.binding.

UUii

Realm of Action for the Utility function

Realm of Action for the Utility Function

Whose Utility Am I MaximizingWhose Utility Am I Maximizing

I maximize the utility of the one I am today.I maximize the utility of the one I am today. I maximize the utility of all my “I’s”.I maximize the utility of all my “I’s”.

Resulting behavior over timeResulting behavior over timeAimsAims

Resulting Resulting forceforce

Intertemporal Intertemporal aimsaims

t1 t4t2 t5t3

A. The static decomposition of desireA. The static decomposition of desire B. The intertemporal decomposition of utilityB. The intertemporal decomposition of utility

Patterns of BehaviorPatterns of Behavior

Whose Utility Am I MaximizingWhose Utility Am I Maximizing

I maximize the utility of the one I am today.I maximize the utility of the one I am today. I maximize the utility of all my “I’s”.I maximize the utility of all my “I’s”. I maximize the utility of my family, of my I maximize the utility of my family, of my

group, of my country, of my species.group, of my country, of my species. The lines of who are my own, who is not, The lines of who are my own, who is not,

and who are my enemies are not drawn, but and who are my enemies are not drawn, but are in constant change.are in constant change.

We must recognize the self interest of We must recognize the self interest of groups.groups.

Relative objects and subjects.Relative objects and subjects.

Back in to UtilityBack in to Utility

Individuals are another one of the many Individuals are another one of the many levels the maximization is happening at.levels the maximization is happening at.

In lower levels, individuals are a composition In lower levels, individuals are a composition of inter-temporal maximizations.of inter-temporal maximizations.

To form higher levels, sets of individuals To form higher levels, sets of individuals may decide to join and form groups that may decide to join and form groups that maximize their joint utility.maximize their joint utility.

These sets of individuals, or of other These sets of individuals, or of other subsets, have the incentive to become subsets, have the incentive to become cohesive and coordinated.cohesive and coordinated.

Environmental Optimality.Environmental Optimality.

The Hedonist vs. the CalvinistThe Hedonist vs. the Calvinist I believe there is evidence showing that I believe there is evidence showing that

warmer climate societies tend to be poorer.warmer climate societies tend to be poorer. Selfishness vs. Altruism / Coordination vs. AutonomySelfishness vs. Altruism / Coordination vs. Autonomy

Myopic Hedonist

Retirement-fixated

Agent’s Productivity

Upper levels’ Upper levels’ realms of actionrealms of action

Individual’s Individual’s UtilityUtility

CollectiveCollective ForceForce

BehaviorBehavior

UUss

CountryFamily

Self

Instinct

UUff

UUii

UUcc

A hierarchical decompositionA hierarchical decomposition

Lower levels Lower levels (emotions, instincts)(emotions, instincts)

A World Divided into LevelsA World Divided into Levels The agent in the model represents a level of:The agent in the model represents a level of:

1)1) Strategic decision making.Strategic decision making.

2)2) The evolution of adaptability and responsiveness.The evolution of adaptability and responsiveness. It confines the subcomponents that belong to it.It confines the subcomponents that belong to it. It is constrained by the upper level it belongs to.It is constrained by the upper level it belongs to. The upper levels may be created by a The upper levels may be created by a

conscious decision or by an evolutionary force.conscious decision or by an evolutionary force. Upper levels can represent coordination, Upper levels can represent coordination,

identification with others, institutions, implicit identification with others, institutions, implicit laws, religion, a credit bureau.laws, religion, a credit bureau.

The lower levels seemingly disappear as the The lower levels seemingly disappear as the subcomponents become more coordinated.subcomponents become more coordinated.

A Language to Describe A Language to Describe Social Behavior Social Behavior

Levels related to emergence: Disciplines.Levels related to emergence: Disciplines.

Scalability.Scalability.

FUZZY AGENTS.FUZZY AGENTS.

Fuzzy AgentsFuzzy Agents

Hispanics in USA

Latina Americans share culture among themselves

NAFTA Joins Canada, USA and Mexico

The United Stated and Europe share a historical alliance, but may struggle for world leadership

The European Union creates a more cohesive agglomerate

What is Science About? What is Science About? What I learned in School… What I learned in School…

Look for models with a unique equilibrium.Look for models with a unique equilibrium.

Karl Popper: Predict the Future, no matter Karl Popper: Predict the Future, no matter the assumptions.the assumptions.

Is this Science?Is this Science?

Chaos (sensitivity to initial conditions), Chaos (sensitivity to initial conditions), Complexity (irreducibility: the algorithm is Complexity (irreducibility: the algorithm is the shortest answer).the shortest answer).

A world with multiple equilibria.A world with multiple equilibria. Assumptions matter: Our theory explains, it Assumptions matter: Our theory explains, it

is descriptive.is descriptive.

Can we do this? / ValidationCan we do this? / Validation

I can write my name with enough degrees of I can write my name with enough degrees of freedom. freedom.

Every degree of freedom we use must be Every degree of freedom we use must be justified by higher predictive power.justified by higher predictive power.

Can we make a picture of the world? Can Can we make a picture of the world? Can we have a language to paint that picture?we have a language to paint that picture?

Picture in Picture: A movie.Picture in Picture: A movie. Connect the dots: History.Connect the dots: History.

Optimality in a Optimality in a Hierarchically Decomposed WorldHierarchically Decomposed World

To describe reality: a benchmark position To describe reality: a benchmark position can be one in which all behavior is optimal, can be one in which all behavior is optimal, so long as we identify the true active agent.so long as we identify the true active agent.

Suboptimal behavior is thus a product ofSuboptimal behavior is thus a product of too too much ‘zoom in’ or ‘zoom out’.much ‘zoom in’ or ‘zoom out’.

Reward FunctionsReward Functions

The Environment has something that the The Environment has something that the agents want; it provides it when they act in a agents want; it provides it when they act in a certain way, which may involve competition certain way, which may involve competition and cooperation.and cooperation.

The sugar of sugarscape.The sugar of sugarscape. Hansel and Gretel.Hansel and Gretel. Sugar is Free Energy.Sugar is Free Energy. Sugar multiplies with cooperation.Sugar multiplies with cooperation.

Current Work / ApplicationsCurrent Work / Applications

The imposition of a Geographical The imposition of a Geographical Citizenship/Nation State.Citizenship/Nation State.

The Social Value of a Micro Loan.The Social Value of a Micro Loan.

Measuring the Optimality of a Social Measuring the Optimality of a Social Structure.Structure.

KB

NADIA*NADIA*

(Neurologic Activity Driven Intuition-based Agent)(Neurologic Activity Driven Intuition-based Agent)

PerceptionModes of Decision-Making

Intuition Deliberation

Satisfying Decision-Making

actionmessage

Environment

Agent

communication

Social Constraints

Tone of decision-making

Arousal

Attention

Expectation

Motivation

Evaluation

Alternatives

Editing

Visualization Interface

NADIA*NADIA*

Each element in the Utility function should Each element in the Utility function should be reflecting the interaction with the levels or be reflecting the interaction with the levels or ‘creatures’ of our world.‘creatures’ of our world.

Positive and negative feedbacks Positive and negative feedbacks (reinforcement and dampening effects).(reinforcement and dampening effects).

Perception or Cognition of levels.Perception or Cognition of levels. Real vs. perceived probabilities.Real vs. perceived probabilities.

* These slides represent work done in conjunction with professors at Trinity University:* These slides represent work done in conjunction with professors at Trinity University:

Yu Zhang & Mark Lewis, Computer Science, Christine Drennon, Yu Zhang & Mark Lewis, Computer Science, Christine Drennon, Sociology and Anthropology, Claudia Scholz, Research Programs Sociology and Anthropology, Claudia Scholz, Research Programs Coordinator, and Luis Schettino, Psychology. Coordinator, and Luis Schettino, Psychology.

Our WorldOur World

What are the Physical, Chemical, Biological What are the Physical, Chemical, Biological laws of our world?laws of our world?

Does each level have it’s laws (the level as Does each level have it’s laws (the level as a dimension).a dimension).

Interconnections between dimensions.Interconnections between dimensions. Exchange Rates (which are not necessarily Exchange Rates (which are not necessarily

linear).linear).

Economics and its Realm of ActionEconomics and its Realm of Action

Pareto Optimality: The optimum you get to where Pareto Optimality: The optimum you get to where there is no way of making anyone happier without there is no way of making anyone happier without hurting someone else.hurting someone else.

Pareto optimality represents the core of Pareto optimality represents the core of Neoclassical economics’ welfare theorems.Neoclassical economics’ welfare theorems.

Revealed Social Preference.Revealed Social Preference. Do developed countries want poor ones to become Do developed countries want poor ones to become

wealthier? Do the rich care about the poor?wealthier? Do the rich care about the poor? Evolution ‘disentangles’ agents: Evolution ‘disentangles’ agents:

The Geneva Convention The Geneva Convention

An Example: Mexico’s DilemmasAn Example: Mexico’s Dilemmas

1818thth Century Mexico’s GDP higher than U.S.’s. Century Mexico’s GDP higher than U.S.’s. Weak upper level.Weak upper level. Rule following.Rule following. Niche production and supply.Niche production and supply. Colonial lock-in.Colonial lock-in. The ruling class in control.The ruling class in control. Democracy without issues.Democracy without issues. Lack of well established judicial norms.Lack of well established judicial norms. Part of the solution: Localized taxes & Part of the solution: Localized taxes &

Federalization.Federalization.

The Business of ViolenceThe Business of Violence

The model should classify conditions for The model should classify conditions for competition vs. mutualism.competition vs. mutualism.

Agents can be nasty.Agents can be nasty. Where does war fit? Where does war fit?

Is it competition that is in some sense optimal or a Is it competition that is in some sense optimal or a bad case of the prisoner’s dilemma?bad case of the prisoner’s dilemma?

What about the world economy?What about the world economy?

Income distribution?Income distribution?

Individual vs. Group SelectionIndividual vs. Group Selection

The ‘Reductionism Nightmare’.The ‘Reductionism Nightmare’.

Genes do not make sense by themselves.Genes do not make sense by themselves. Your children need a decent ‘pool of genes’ for them to preserve the species.Your children need a decent ‘pool of genes’ for them to preserve the species.

Individuals cannot survive by themselves.Individuals cannot survive by themselves.

Optimal species’ scales of environment Optimal species’ scales of environment exploitation.exploitation.

Many small and malleable individuals in species vs. large organized wholes.Many small and malleable individuals in species vs. large organized wholes.

Actor benefitsActor benefits Actor pays costActor pays cost

Recipient benefitsRecipient benefits Cooperative Cooperative behaviorbehavior

Altruistic behaviorAltruistic behavior

Recipient is Recipient is harmedharmed

Selfish behaviorSelfish behavior Spiteful behaviorSpiteful behavior

I. Introduction to altruismI. Introduction to altruism

+

Fig. 10

Delayedbenefit

Fig. 11

How can altruism evolve?How can altruism evolve?

Group-level selectionGroup-level selection

Individual-level selection:Individual-level selection:

Kin selectionKin selection

Reciprocal altruismReciprocal altruism

Group selectionGroup selection

Group selectionGroup selection

How can altruism evolve?How can altruism evolve?

Group-level selectionGroup-level selection

Individual-level selection:Individual-level selection:

Kin selectionKin selection

Reciprocal altruismReciprocal altruism

Opportunity for reciprocation of Opportunity for reciprocation of altruistic actsaltruistic acts

Repeated interactions between the Repeated interactions between the same individualssame individuals

Many opportunities for altruistic actsMany opportunities for altruistic acts

Altruists interact in symmetrical Altruists interact in symmetrical situationssituations

Individuals have good memoriesIndividuals have good memories

Cheaters are punishedCheaters are punished

II. Reciprocal altruismII. Reciprocal altruism

Robert Trivers(1971)

Game theoryGame theory

The best (optimal) strategy depends on what The best (optimal) strategy depends on what others are doingothers are doing

Evolutionary stable strategy (ESS): resists Evolutionary stable strategy (ESS): resists invasion from other strategiesinvasion from other strategies

Prisoner’s DilemmaPrisoner’s Dilemma

Fig. 14T

R

P

S

T > R > P > S

Opportunity for reciprocation of Opportunity for reciprocation of altruistic actsaltruistic acts

Repeated interactions between the Repeated interactions between the same individualssame individuals

Many opportunities for altruistic actsMany opportunities for altruistic actsAltruists interact in symmetrical Altruists interact in symmetrical

situationssituationsIndividuals have good memoriesIndividuals have good memoriesCheaters are punishedCheaters are punished

IteratedIterated prisoner’s dilemma prisoner’s dilemma

Tit for tat strategy won

III. Kin selectionIII. Kin selection

Inclusive fitness Inclusive fitness includes:includes:

1)1) Direct fitness Direct fitness (own (own offspring)offspring)

2)2) Indirect fitness Indirect fitness (additional (additional reproduction of reproduction of relatives due to help relatives due to help of actor)of actor)

W.D. Hamilton(1964)

IIIA. Hamilton’s ruleIIIA. Hamilton’s rule

An allele for altruistic behavior will be selected An allele for altruistic behavior will be selected if: if: r B > Cr B > C

r = coefficient of relatedness between actor and r = coefficient of relatedness between actor and recipientrecipient

B = benefit to the recipientB = benefit to the recipientC = cost to the actorC = cost to the actor

B and C measured in terms of surviving offspringB and C measured in terms of surviving offspring

Calculating Calculating rr (coefficient of relatedness) (coefficient of relatedness)

Probability that homologous Probability that homologous alleles in two individuals alleles in two individuals are are identical by descent identical by descent (ibd)(ibd)

What is the probability that What is the probability that the offspring will carry the offspring will carry the red allele?the red allele?

Parent 1 Parent 2

Offspring

?0.5

(r between parents & offspring is 1/2 or 0.5)

OR

Calculating Calculating r –Half Siblingsr –Half Siblings

actor recipient

1/2

Shared parent

1/2

r = (1/2) (1/2) = 1/4 or 0.25

Calculating Calculating r –Full Siblingsr –Full Siblings

actor recipient

1/21/2

mother father

1/21/2

r = [(1/2)(1/2)] + [(1/2)(1/2)] = 1/4 + 1/4 = 0.5

Calculating Calculating r –Cousinsr –Cousins

1/2

actor recipient

Actor’s parent Actor’s aunt or uncle

1/2

r = (1/2)(1/2)(1/2) = 1/8

1/2

I would lay down my life for 2 brothers or 8 cousins--J.B.S. Haldane

Hamilton’s rule:Hamilton’s rule:r B > Cr B > C

The likelihood of altruism through kin selection The likelihood of altruism through kin selection decreases with:decreases with:

Decreasing relatednessDecreasing relatedness

Decreasing benefits to recipientDecreasing benefits to recipient

Increasing costs to actorIncreasing costs to actor