Self-government and
Impossibility Theorem:
How to find a good allocation mechanism?
Anita Gantner
Wolfgang Höchtl
Rupert Sausgruber
University of Innsbruck
ESA Rome 2007
1
Motivation
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City of Vienna supports artists through grants
allocation by jury of experts
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now the community can distribute the funds in
self-governance according to own rules
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increasing discontent with outcomes
jury members accused of supporting their protégés
In 2006: 315,000 Euros allocated by self-government
Question:
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What is a good allocation mechanism?
What behavior can be expected in such situation?
Self-government and Impossibility Theorem
2
Economist's Approach
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Goal of artists' community:
to find a system that leads to a good representation of the
preferences in the community
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Goal in Economist's language:
to find a solution by means of
 Mechanism design
 Political decision making (voting systems)
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In search for a suitable mechanism
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Desirable property: members should vote sincerely
 need to confine strategic voting
Self-government and Impossibility Theorem
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Theory: General Results
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Impossibility results of Gibbard and Satterthwaite
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for arbitrary environments: any preference aggregation
method is vulnerable to strategic manipulation by voters
Positive result of Clarke Groves mechanism
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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
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Specifics of the Situation
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Network structure
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Selection of winners
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artists cooperate, thus networks are built
 collusion is possible
strong likes and dislikes encourage strategic voting
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
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Our Approach
Test various mechanisms in the experimental lab
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overall goal: find a good mechanism
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preliminary goal: understand behavior
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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
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Representation in the Lab
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A community is represented by 5 voters
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Network
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majority: group of 3 voters with identical preferences
minority: group of 2 voters with identical preferences
voting over 4 alternatives
communication within groups
no communication between groups
Winner selection: multiple winners
Self-government and Impossibility Theorem
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Three Mechanisms
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Cumulative voting
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Borda count method
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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
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
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each voter reports a value for each alternative
if sum of reports for an alternative is positive  „winner“
winners: endogenous number
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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
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Parameters:
alternative 
Alpha
Beta
Gamma
Delta
30
-20
-30
10
10
40
-20
-40
voters 
Majority
(3 voters)
Minority
(2 voters)
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Properties of Parametrization
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If all agents vote according to true preferences,
Alpha & Beta will be selected
Cumulative voting:
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Borda count:
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minority can ensure winner Beta
majority should ensure winner Alpha
majority can ensure winners Alpha & Delta by strategically ranking
Delta over Alpha
minority has no leverage
Pivotal mechanism
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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
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Results: Winners in Three Treatments
Payoffs
Maj Min
Cumulative
Borda
Pivot
A&B
10
50
80%
20%
8%
A&D
40
-30
3%
58%
83%
B & D*
-10
0
18%
0%
0%
A & C*
0
-10
0%
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
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Results: Cumulative voting and Borda
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Cumulative voting:
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minority votes strategically in 98%
 winner Beta ensured
majority makes mistakes: in 18% Delta > Alpha
 inefficient outcome Beta & Delta
Borda count: sophisticated
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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
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Results: Behavior in Cumulative & Borda
Behavior over time
1
0.9
0.96
Cumulative
0.8
0.87
Borda
proportion
0.7
0.6
0.61
0.5
0.4
0.44
0.3
0.2
0.29
0.30
0.16
0.1
0.17
0
early games
late games
early games
truthful
late games
strategic
Over time: subjects vote less truthful and more strategic
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Results: Behavior in Pivotal Mechanism
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Minority
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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
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for all alternatives: overreport if positive payoff,
underreport if negative payoff
Self-government and Impossibility Theorem
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Summary
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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:
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truthful reports of minority
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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
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