Predicting Risky Behavior in Tribal Societies: Validating Decision

Paradigms and Exploring Models

Lawrence A. KuznarIndiana University – Purdue University, Fort Wayne

4th Lake Arrowhead Conference On Human Complex Systems

April 26, 2007

Exploratory Modeling

• Deep uncertainty makes theory evaluation difficult and suspect (Bankes, 1993 …)– Bankes considers uncertainty about parameter values– Evaluate ensembles of theories differentiated by

parameter values– Theories members of same class

• What about theories with paradigmatic differences?– Disagreements about variables, relationships, AND

parameters– Theories members of different classes

Exploratory Modeling Theory Spaces

• For Paradigmatically different theories, differences in variables, relationships, and parameter values create a complex theory space.

• Need to search theory spaces (likely to be topologically very complex) for areas of agreement/disagreement

• Result: Refutation of unstable/incorrect theories, suggestion of new directions and syntheses

Kapauku Particulars

• Tribal, territorial, yam/pig

economy, history of warfare• Tonowi (Bigmen) key • political players

• Prestige based on wealth, men strive in a self-interested manner to gain wealth

• Tonowi emulated

Kapaukuan Wealth and Inequality

Wealth Original Data

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Wealth Rank

Bea

d W

ealt

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“Tonowi, a rich man And a political leader”

“Kapauku place a highValue on wealth, fromWhich they derive theirGreatest prestige…. Thus Wealth is a prerequisite For attaining and keepingPolitical leadership.”

Pospisil 1963

Problems with Verbal Theory

• “Kapauku live in a wealth- and profit-oriented society….Wealth to a Kapauku is almost everything that he desires and strives for during his life. It gives him economic security and comfort, offers him great prestige,… (Leopold Pospisil 1963, The Kapauku Paupuans, p. 93).”

• Wealth maximization– Subject to what constraints?

• Prestige – How Measured?• Security – To what degree risk sensitive?

Political Decision Making and Decision Paradigms

• Rational Choice Theory• Sigmoid Utility Theory (risk sensitive)• Group Affiliative Behavior (altruism)• Prospect Theory• Bounded Rationality (prestige bias, conformist

transmission, other simple heuristics)

• Rules used to inform agents in a collective action coordination game (Joining risky)

Risk Sensitive Decision Making• Sigmoid Utility Theory

– Relative deprivation to one’s social neighbors– If Risk Prone - Increase Join proportionate to maximally risk prone agent, – If Risk Averse, decrease Join probability proportionate to maximally risk averse agent.

• Group Affiliation (altruism)– Social psychology, small group dynamics, risk sensitive

groups– Opposite rules from Sigmoid utility (Joining less likely with

outsiders the more risk prone and insular one’s group)

Prospect Theory• Probability Weighting (PW)

– Use experimentally determined weighting function (1 parameter) w(p)=EXP-(-ln(p)) alpha

• Loss Aversion (LA)– Utility Function with experimental parameters (3 parameters)V(x)=xalpha for gains; V(x)=-lambda*-xbeta for losses

• Framing Effects (FR)– Natural frame of loss/gain based on Miller’s Number 7+/-

2 memory

)ln()( pepw

Probability Weighting

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Loss Aversion

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Bounded Rationality: Cultural Norms and Imitative Heuristics

• Patrilineal Norm– Favor patrilineal kin PN

• Prestige Bias– Imitate superior partner P1– Imitate household head P2– Imitate coalition head P3– Imitate village head P4

• Conformism– Imitate household C1– Imitate coalition C2– Imitate village C3

• Naïve agents choose Join probabilities [0,1]

• Smart agents choose Join probabilities [0.3,0.9], bracketing Nash/evolutionary optimum

Decision Theoretic Paradigms and 25 Models Tested

Paradigms Models

Rational Choice Nash optimum (N)

Modified Rational Choice

Sigmoid utility (S)

Modified Rational Choice /Social Psychology / altruism

Sigmoid utility+Group affiliation (SG)

Bounded Rationality

Patrilineal Norms (PN)

Bounded Rationality

naïve Prestige bias 1 (nP1), naïve Prestige bias 2 (nP2), naïve Prestige bias 3 (nP3), naïve Prestige bias 4 (nP4), naïve Conformism 1 (nC1), naïve Conformism 2 (nC2), naïve Conformism 3 (nC3)

Bounded Rationality quasi-Rational Choice

smart Prestige bias 1 (sP1), smart Prestige bias 2 (sP2), smart Prestige bias 3 (sP3), smart Prestige bias 4 (sP4), smart Conformism 1 (sC1), smart Conformism 2 (sC2), smart Conformism 3 (sC3)

Prospect Theory Probability weighting (PW), Loss aversion (LA), Framing effects (FR), PW+LA, PW+FR, LA+FR, PW+LA+FR

Metrics

• Getting beyond “view-graph validation”Oberkampf and Trucano 2002 Prog. Aerospace Sci.

• Good model will predict:

– Number of coalitions– Mean Coalition Size– Coalition Size Distribution

Thiel’s Inequality Coefficient

zdydyzd

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iiz

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iiy

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iiziy

TIC

1

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2)(

Where yi is an empirical measure, zi is a model output,

and n is the number of runsVaries on [0,1], 0 = identical

Kolmogorov-Smirnov D Statistic

Where E(x) is empirical cumulative frequency distributionAnd Z(x) is simulation cumulative frequency distribution

)()(sup xZxEx

D

Coalition Size Distribution: Actual vs. Sigmoid and naive Prestige Models

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Coalition Size

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naïve Prestige 2

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Actual Distr

Cumulative Normed Coalition Size Distribution: Actual vs. Sigmoid and naïve Prestige Models

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Coalition Size

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naïve Prestige 2

Actual Median

Actual Distr

D sigmoid model = 0.16 (blue)D naïve prestige = 0.65 (pink)

Experimental Scheme

• Instantiate Kapauku

• Instantiate Decision Rules

• Simulate random mixing of Kapaukuans to see which decision rules best reproduce the actual alliances empirically observed (like “Survivor”)

• Focus on “growing” structurally similar coalitions (# coalitions, coalition size)

Model TIC Coalition Number

TIC Mean Coalition Size

Difference from Actual Coalition Number

Difference from Actual Coalition Size

No. Distribution Matches per 20 runs

Kologorov-Smirnov mean p-value

Nash 0.118 0.105 3.35 0.55 15 0.258

Sigmoid 0.074 0.066 1.40 0.24 15 0.252

Group Affiliation 0.095 0.085 2.30 0.39 11 0.199

Patrilineality 0.191 0.177 6.9 1.00 12 0.214

Prestige I 0.109 0.096 3 0.50 13 0.310

Prestige II [0,1] 0.267 0.252 11 1.37 1 0.024

Prestige III [0,1] 0.240 0.220 9.2 1.21 4 0.072

Prestige IV [0,1] 0.242 0.223 9.35 1.22 1 0.034

Prestige II [0.3,0.9] 0.145 0.128 4.2 0.64 14 0.275

Prestige III [0.3,0.9] 0.150 0.141 5.15 0.81 13 0.173

Prestige IV [0.3,0.9] 0.245 0.225 9.5 1.23 3 0.050

Conformism I [0,1] 0.204 0.181 7.1 0.99 5 0.112

Conformism II [0,1] 0.248 0.240 10.2 1.32 0 0.019

Conformism III [0,1] 0.213 0.192 7.7 1.07 7 0.172

Conformism I [0.3,0.9] 0.130 0.113 3.15 0.47 13 0.202

Conformism II [0.3,0.9] 0.083 0.073 2 0.35 15 0.230

Conformism III [0.3,0.9] 0.120 0.107 3.4 0.55 16 0.181

PW (probability Weighting) 0.171 0.163 6.2 0.94 10 0.199

FR (Framing) 0.210 0.199 8 1.12 7 0.079

LA (Loss Aversion) 0.090 0.103 1.7 0.49 17 0.371

PW FR 0.187 0.175 6.8 1.00 5 0.088

FR LA 0.365 0.365 17.95 1.80 0 0.004

PW FR LA (Full Prospect Theory)

0.284 0.271 12.1 1.45 3 0.042

Mean 0.182 0.169 6.59 0.900 8.70 0.155

s.d. 0.075 0.073 4.06 0.413 5.77 0.104

Threshold <0.106 <0.096 <2.54 <0.413 >14.5 >0.259

Conclusion 1: Any Conclusions?

• A subset of the 25 models did comparatively well, including models derived from:

• Sigmoid Utility• Small Group Psychology• Prospect Theory• Bounded Rationality

• Result: A Postmodern Free-for-All?

Conclusion 2: Paradigm Comparison

• Where does a paradigm breakdown?• Paradigms that worked well:

– Sigmoid utility theory– Small group social psychology

• Paradigms that worked less well– Bounded Rationality Imitative Heuristics worked

less well (1/15 models)– Prospect Theory (1/7 models)

Conclusion 3: Getting Beyond Paradigms and Egos

• All theories are false

• What works in current theories?– Most well-performing models had two

characteristics:• Agents were quasi-optimal (smart)• Agents nonetheless diverse (heterogenous)

• Future theory will have these elements

Computer Coding: Synthesis of Paradigms

• RAT – rational choice

• PW – probability wt.

• LA – loss aversion

• FR – framing

• PB – prestige bias

• CT – conformism

• Weak synthesis

X Synthesis

RAT PW LA

PW X

LA X X

FR X X X

PB *

CT *