1 Self-government and Impossibility Theorem: How to find a good allocation mechanism? Anita Gantner Wolfgang Höchtl Rupert Sausgruber University of Innsbruck ESA Rome 2007

Self-government and Impossibility Theorem 2 City of Vienna supports artists through grants allocation by jury of experts increasing discontent with outcomes jury members accused of supporting their protégés now the community can distribute the funds in self-governance according to own rules In 2006: 315,000 Euros allocated by self-government Question: What is a good allocation mechanism? What behavior can be expected in such situation? Motivation

Self-government and Impossibility Theorem 3 Economist's Approach Goal of artists ' community: to find a system that leads to a good representation of the preferences in the community Goal in Economist's language: to find a solution by means of Mechanism design Political decision making (voting systems) In search for a suitable mechanism Desirable property: members should vote sincerely  need to confine strategic voting

Self-government and Impossibility Theorem 4 Theory: General Results Impossibility results of Gibbard and Satterthwaite for arbitrary environments: any preference aggregation method is vulnerable to strategic manipulation by voters Positive result of Clarke Groves mechanism for quasilinear environments: socially optimal implementation in dominant strategies is feasible  Need to characterize particular situation and behavior in order to find suitable solution

Self-government and Impossibility Theorem 5 Specifics of the Situation Network structure artists cooperate, thus networks are built  collusion is possible strong likes and dislikes encourage strategic voting Selection of winners not a unique winner, but: a subset of projects (candidates) is selected Clarke Groves mechanism is not collusion proof Are we in a hopeless quest for optimal solution? Then we should search for a "good" solution.

Self-government and Impossibility Theorem 6 Our Approach Test various mechanisms in the experimental lab overall goal: find a good mechanism preliminary goal: understand behavior take into account the specific network structure see whether and how this affects outcomes of different mechanisms try mechanisms that vary in amount of information they require maybe less information leads to better outcomes in a situation that is prone to collusion and strategic behavior?

Self-government and Impossibility Theorem 7 Representation in the Lab A community is represented by 5 voters majority: group of 3 voters with identical preferences minority: group of 2 voters with identical preferences voting over 4 alternatives Network communication within groups no communication between groups Winner selection: multiple winners

Self-government and Impossibility Theorem 8 Three Mechanisms Cumulative voting each voter distributes 100 points across all available alternatives each alternative thus gets between 0 and 100 points winners: 2 alternatives with highest total points Borda count method each voter ranks the 4 alternatives alternative with rank k gets 4-k points add points across voters for each alternative winners: 2 alternatives with highest total points Pivotal (Groves Clarke) mechanism each voter reports a value for each alternative if sum of reports for an alternative is positive  „ winner “ winners: endogenous number

Self-government and Impossibility Theorem 9 Experimental Setup Experiment at University of Innsbruck Lab 100 subjects (40 Cumul, 20 Borda, 40 Pivot) 10 repetitions within same group, same position payoff = sum of 10 rounds avg. payoff = Euro Parameters: alternative  voters  AlphaBetaGammaDelta Majority (3 voters) Minority (2 voters)

Self-government and Impossibility Theorem 10 Properties of Parametrization If all agents vote according to true preferences, Alpha & Beta will be selected Cumulative voting: minority can ensure winner Beta majority should ensure winner Alpha Borda count: majority can ensure winners Alpha & Delta by strategically ranking Delta over Alpha minority has no leverage Pivotal mechanism discrete values from [-60, 60] in steps of 10 possible dominant strategy: report true preferences  Alpha & Beta many Nash Equilibria, in particular one in which majority ensures Alpha & Delta by overreporting such that no one pays Clarke tax

Self-government and Impossibility Theorem 11 Results: Winners in Three Treatments Payoffs Maj Min CumulativeBordaPivot A & B105080%20%8% A & D40-303%58%83% B & D * %0% A & C * 0-100%18%1% * B & D and A & C are inefficient outcomes (A & B better for both types) Note: in Pivotal mechanism: - few outcomes with 3 or 1 winner (< 10%) observed - outcome ABD (4%): payoff 20 to majority, 10 to minority - outcome A (4%) : payoff 30 to majority, 10 to minority

Self-government and Impossibility Theorem 12 Results: Cumulative voting and Borda Cumulative voting: minority votes strategically in 98%  winner Beta ensured majority makes mistakes: in 18% Delta > Alpha  inefficient outcome Beta & Delta Borda count: sophisticated 1st strategic step: Delta ranked over Alpha on average not found 2nd strategic step: 2 vote DACB, 1 votes DABC no evidence for this sophisticated coordination

Self-government and Impossibility Theorem 13 Results: Behavior in Cumulative & Borda Over time: subjects vote less truthful and more strategic

Self-government and Impossibility Theorem 14 Results: Behavior in Pivotal Mechanism Minority Note: two dominant strategies: truthful report and next highest valuation for Beta, Gamma, Delta: evidence for truthful report only for Alpha: truthful report rejected, overreporting dominant strategy chosen Majority for all alternatives: overreport if positive payoff, underreport if negative payoff

Self-government and Impossibility Theorem 15 Summary environment with communication: outcomes are closer to theory predictions high proportion of strategic behavior in simpler setting (Cumulative voting) lower proportion of strategic behavior in more sophisticated setting and limited steps of reasoning (Borda) bad news for our problem: strong evidence of collusion without concern for other group Clarke Groves fails: truthful reports of minority efficient collusion of majority (not pivotal  no tax) Simplest system (Cumulative voting) yields best result from social point of view