Democracy Under Uncertainty - Adaptive Robustness of Group ...
COE Symposium "Cultural and Adaptive Bases of Human Sociality" Democracy Under Uncertainty Sept.9-10, 2006, Tokyo Adaptive Robustness of Group Decision-Making Beyond the Voters Paradox Tatsuya Kameda Hokkaido University (in collaboration with Takafumi Tsu kasaki and Reid Hastie) 1 Ubiquity of Group DecisionMaking in Human Societies Every h uman society relies on groups to ma ke important decisions.
Industrialized societies Juries, committees, panels, electorates Tribal societies (cf. Boehm, 1996) Mae Enga in Papua New Guinea Raiding/warfare decisions Th ese groups are often called for to make th e mutually most beneficial decision in a stoc h astic, noisy environment. noisy environment. Investment teams: Coming up with the most profitable portfolio Juries: Seeking the truth in criminal trials 2 GDM Under Uncertainty: A Historic Example Lewis and Clarks expedition of th e American West (1804-1806) the Corps of Discovery Winter of 1805
St. Louis 1804 3 November 24, 1805 To make the crucial decision of where to spend the winter, the captains decide to put the matter to a vote. vote Significantly, in addition to the others, Clarks slave, York, is allowed to vote nearly 60 years before slaves in the U. S. would be But, noisy environment.and does majoritarian emancipated enfranchised. Sacagawea, the Indian woman, toowork more than a century GDM votes really
unde before either women or Indians are granted the full r uncertainty? rights of citizenship. ? ? ? ? ? ? The majority decides to cross to the south side of the Columbia, near modern-day Astoria, Oregon, to build winter quarters. (quoted from PBS Online) 4
GDM Under Uncertainty: Adaptive Advantages And Disadvantages Advantages Pooling of various knowledge and information Division of labor Two heads are better than one. Disadvantages Many th reats to effective deliberation Groupth ink Free-rider 5 Free-Rider Problems In GDM
Voters paradox Most th eoretical analysis of small group c ooperation conceptualize group enterpri ses as social dilemmas (Dawes, noisy environment. 1980). Given th is, noisy environment. peoples cooperation for GDM is a big puzzle. Some social ch oice th eorists argue th at p eople may feel good, noisy environment. experiencing expr essive benefits wh en th ey contribute to th e functioning of democracy (Downs, noisy environment. 195 7) or wh en th ey fulfill civic duties (Riker & Ordesh ook, noisy environment. 1973). 6 Research Question Rath er th an assuming such prosocial m otives, noisy environment. we revisit GDM under uncertaint y from a game-th eoretic perspective. If assuming only rational agents, noisy environment. does GDM under uncertainty degrade to mo b-rule? Or, noisy environment. is it workable despite th e i nh erent free-rider problem?
error Location js resource val ue, Qj Wi.3 .15 C3 error Forager is estim ate of location js value, Q ij 8 A Foraging Metaphor (contd)
A group of foragers Group decision task: Ch oosing th e most profitable patch Th e resource in th e ch osen patch is sh ared evenly among all members. However, noisy environment. cooperation cost for GDM (e.g., noisy environment. costs for information search and voting) must be incurred personally. Free-rider problem Does majoritarian GDM work? 9 1. Evolutionary Computer Simulations Cooperator Defector Infinite population
Sampling of 12person groups (hunting teams) Each group makes decisions (by majority rule) about where to hunt. Only cooperative members incur costs for information search in the noisy environment and voting in GDM. But, the resource in the chosen patch is shared evenly among all 12 members. Selectio n Agents with more fit strategies produce slightly more of fspring for next generation (replicator dynamic). 10 Defector Cooperator Sampling
12The simulation repeats theseofsteps person for many generations until groups an (hunting teams) equilibrium emerges in the population. Infinite population Selectio n 11 Simulation Results (1) Was th e population dominated by freeriding defectors at th e equilibrium, noisy environment. as expected for social dilemmas? NO ! Instead, noisy environment. mixed equilibrium emerged, noisy environment. wh ere cooperators and
defectors coexisted. 12 Equilibrium Proportions Of Cooperators And Defectors In Th e Population As A Function Of Cooperation Costs Defector Cooperat or Mixed equilibrium 13 Q. Wh y mixed equilibrium? A. Incentive structure in GDM under uncertainty is NOT a social dilemma! Expected group return 4 3.5
3 Group productivity (return curve) in GDM under uncertainty Marginally-diminishing 2.5 2 1.5 1 0.5 0 0 1 2 3 4
5 6 Number of cooperators in a group Because of redundancies among members inputs and coordination problems, problems incremental productivity diminishes at the margin. Difference from social dilemmas (-- 14 Individual Payoff Function In GDM Under Uncertainty 4 Expected net return to ego 3.5
3 When ego cooperates 2.5 2 When ego defects 1.5 1 Mixed equilibri um 0.5 0 0
1 2 3 4 5 Number of other cooperators in a group Different from th e social dilemma, noisy environment. no dominant strategy exists. Payoff to one strategy is dependent on th e frequency of th e oth er 15 OK, noisy environment. but is GDM really efficient under uncertainty, noisy environment. compared to oth er decision systems? Th e sustainablity of cooperators is surely e ncouraging for th e cause of th e majoritaria
n GDM. But, noisy environment. even if a small fraction of cooperators can survive in th e population, noisy environment. it does not n ecessarily mean th at GDM is th e most effec tive decision system under uncertainty. For example, noisy environment. a decision system th at is dict ated by th e best and brigh test individual in a group may provide a more efficient outco 16 me th an th e majoritarian GDM. A Follow-Up Simulation With Th e Rival Decision-System -Best Member RuleDefector Cooperator Infinite population Selectio n Sampling of 12person groups
(hunting teams) The most competent member among the cooperators is designated the leader, making decisions for the group. Only cooperative members incur costs for information search in the noisy environment and voting in GDM. But, the resource in the chosen patch 17 is shared evenly among all 12 members. Simulation Results (2) Q. How does the majoritarian GDM compare to the Best-Me mber-Rule in terms of individual net payoff at the equilib rium? Series of simulation runs, noisy environment. varying cooperation costs and number of ch oice alternatives Majoritarian GDM yields greater indi 0.05 vidual net payoffs 0.04
Difference than the Best Me 0.03 in mber Rule. 0.02 individual 0.01 payoff (Majority - 0 0 -0.01 Best) 11 8 5 0.27 0.24 Cooperation costs 0.21
0.18 0.15 0.12 0.09 0.06 0.03 -0.02 2 Number of choice alts (patches) 18
Th eoretical Conclusions From Th e Evolutionary Simulations GDM works reasonably well under uncertainty. 1. The majoritarian GDM is not a social dilemma, bu t has a non-linear group return curve (cf. Laury & Hol Cooperators can survive at the e quilibrium. t, in press). 2. GDM beats the Best Member Rule for fairly broad parametric regions. 19 2. Beh avioral Experiment - Does the theory hold empirically? Overview Overview Implemented th e foraging under uncertainty on computers connected by LAN.
Ss participated in 6-person groups (h unting teams). Th eir task was to ch oose th e most profitable patch for h unt. Resource in th e ch osen patch was sh ared evenly among all 6 members, noisy environment. wh ile cooperation costs for GDM were personal. Wh eth er or not to cooperate for GDM was up to each participant. No opportunity for sanctioning. Repeated game. 20 Overview (contd) Two conditions 1. Majoritarian GDM 2. Best Member Rule 180 participants in total. 15 six-person grou ps in each condition. Points to see 1. Does cooperation persist? Does a mixed equilibrium emerge? 2. Wh ich decision system yields greater in
dividual net payoffs, noisy environment. th e majoritarian GDM 21 or th e Best Member Rule? Experimental Results Q1. Did cooperation persist? Did a mixed equilibrium emerge? Mean frequencies of cooperative members across the trials. A. Members cooperation persisted (and stabilized) over time, and even at the rate Majoritarian GDM above the theoretical equilibrium. People cooperated for GDM more than t(14)s > 5.76, p<.001 theoretically expected. 6 5 4
3 2 1 Best Member Majoritarian GDM Best Member Rule Theoretical Equilibrium 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Experimental Results (contd) Q2. Which decision system yields greater in dividual net payoffs, the majoritarian GDM or the Best Member Rule?
Mean per-trial individual net payoffs (in Yen)A. The Majoritarian GDM. A. The Majoritarian GDM. 80 66.3 70 61.3 56.7 60 50 45.7 56.8 Majoritarian GDM
45.6 40 Best Member Rule 30 20 10 0 1st 2nd Block 3rd F(1,28) = 11.90, p<.01 23 Conclusion
Democracy Under Uncertainty Our theoretical and empirical analyses both de monstrated that majoritarian GDM works reas onably well under uncertainty, despite the inhe rent free-rider problem. 1. Cooperation for GDM can persist. 2. GDM can yield greater individual net pr ofits than the Best Member Rule. Democracy has a solid adaptive basis under 24 Captain Clark was correct usin g th e majoritarian GDM to deci de th e location of winter camp in 1805. His meta-decision ab out h ow to decide was adaptiv ely grounded under uncertaint y.
25 Thank you 26 Details 10 patch es differing in resource level 24 h unting trials For each block, noisy environment. Ss decide individually (a) wh eth er to vote or abstain from GDM, noisy environment. and (b) wh eth er to engage in information search or skip th e search . Voting/information-search each takes 3 yen off th e individual reward. Ss received feedback h ow much th ey earned in each trial. 27 Illustration A group of geologists collectively estimate probability of occurrence of a large scale
landslide. For simplicity, lets presume that they aggregate their individual estimates by averaging to yield a group estimate. Then, accuracy of group estimate (i.e., convergence to the true probability) improves monotonically, but marginally diminishes with each additional group member. Marginal improvement in group estimate by adding the N+1th individual is smaller than adding the Nth individual . Central Limit Theorem 28 Network Lab There are 16 cubicles and a control room connected by LAN. 29
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