Predicting Risky Behavior in Tribal Societies: Validating Decision Paradigms and Exploring Models

1. Predicting Risky Behavior in Tribal Societies: Validating Decision Paradigms and Exploring Models Lawrence A. Kuznar Indiana University – Purdue University, Fort Wayne 4th Lake Arrowhead Conference On Human Complex Systems April 26, 2007

2. 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

3. 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

5. 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

6. Kapaukuan Wealth and Inequality “Tonowi, a rich man And a political leader” “Kapauku place a high Value on wealth, from Which they derive their Greatest prestige…. Thus Wealth is a prerequisite For attaining and keeping Political leadership.” Pospisil 1963

7. 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?

8. 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)

9. 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)

10. 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)=xalphafor gains; V(x)=-lambda*-xbeta for losses • Framing Effects (FR) • Natural frame of loss/gain based on Miller’s Number 7+/-2 memory

11. 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 Bounded Rationality: Cultural Norms and Imitative Heuristics

12. 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 Decision Theoretic Paradigms and 25 Models Tested

13. 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

14. Thiel’s Inequality Coefficient Where yiis an empirical measure, zi is a model output, and n is the number of runs Varies on [0,1], 0 = identical

15. Kolmogorov-Smirnov D Statistic D sigmoid model = 0.16 (blue) D naïve prestige = 0.65 (pink) Where E(x) is empirical cumulative frequency distribution And Z(x) is simulation cumulative frequency distribution

16. 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)

17. 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

18. 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?

19. 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)

20. 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

22. RAT – rational choice PW – probability wt. LA – loss aversion FR – framing PB – prestige bias CT – conformism Weak synthesis X Synthesis Computer Coding: Synthesis of Paradigms