Predicting Risky Behavior in Tribal Societies: Validating Decision Paradigms and Exploring Models Lawrence A. Kuznar Indiana University – Purdue University, Fort Wayne 4 th Lake Arrowhead Conference On Human Complex Systems April 26, 2007
Dec 19, 2015
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
-10000
0
10000
20000
30000
40000
50000
60000
70000
80000
0 10 20 30 40 50 60
Wealth Rank
Bea
d W
ealt
h
“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
0
0.1
0.2
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0.9
1
0 0.2 0.4 0.6 0.8 1
Probability
Wei
gh
tin
g
Loss Aversion
-40
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-20
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0
10
20
-100 -50 0 50 100
Val
ue
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
n
iiz
n
iiy
n
iiziy
TIC
1
2
1
2
1
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
-5
0
5
10
15
20
0 5 10 15 20
Coalition Size
Fre
qu
ency
Sigmoid
naïve Prestige 2
Actual Median
Actual Distr
Cumulative Normed Coalition Size Distribution: Actual vs. Sigmoid and naïve Prestige Models
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
Coalition Size
Sigmoid
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 *