Self-government a nd Impossibility Theorem: How to find a good allocation mechanism?

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

2. Motivation • 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? 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 = 13.50 Euro • Parameters: 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 * 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 Self-government and Impossibility Theorem