11,394 research outputs found
The Complexity of Online Manipulation of Sequential Elections
Most work on manipulation assumes that all preferences are known to the
manipulators. However, in many settings elections are open and sequential, and
manipulators may know the already cast votes but may not know the future votes.
We introduce a framework, in which manipulators can see the past votes but not
the future ones, to model online coalitional manipulation of sequential
elections, and we show that in this setting manipulation can be extremely
complex even for election systems with simple winner problems. Yet we also show
that for some of the most important election systems such manipulation is
simple in certain settings. This suggests that when using sequential voting,
one should pay great attention to the details of the setting in choosing one's
voting rule. Among the highlights of our classifications are: We show that,
depending on the size of the manipulative coalition, the online manipulation
problem can be complete for each level of the polynomial hierarchy or even for
PSPACE. We obtain the most dramatic contrast to date between the
nonunique-winner and unique-winner models: Online weighted manipulation for
plurality is in P in the nonunique-winner model, yet is coNP-hard (constructive
case) and NP-hard (destructive case) in the unique-winner model. And we obtain
what to the best of our knowledge are the first P^NP[1]-completeness and
P^NP-completeness results in the field of computational social choice, in
particular proving such completeness for, respectively, the complexity of
3-candidate and 4-candidate (and unlimited-candidate) online weighted coalition
manipulation of veto elections.Comment: 24 page
Single-Crossing, Strategic Voting and the Median Choice Rule
This paper studies the strategic foundations of the Representative Voter Theorem (Rothstein, 1991), also called the "second version" of the Median Voter Theorem. As a by-product, it also considers the existence of non-trivial strategy-proof social choice functions over the domain of single-crossing preference profiles. The main result presented here is that single-crossing preferences constitute a domain restriction on the real line that allows not only majority voting equilibria, but also non-manipulable choice rules. In particular, this is true for the median choice rule, which is found to be strategy-proof and group-strategic-proof not only over the full set of alternatives, but also over every possible policy agenda. The paper also shows the close relation between single-crossing and order-restriction. And it uses this relation together with the strategy-proofness of the median choice rule to prove that the collective outcome predicted by the Representative Voter Theorem can be implemented in dominant strategies through a simple mechanism in which, first, individuals select a representative among themselves, and then the representative voter chooses a policy to be implemented by the planner.Single-crossing; order-restriction; median voter; strategyproofness.
Aggregating Dependency Graphs into Voting Agendas in Multi-Issue Elections
Many collective decision making problems have a
combinatorial structure: the agents involved must
decide on multiple issues and their preferences over
one issue may depend on the choices adopted for
some of the others. Voting is an attractive method
for making collective decisions, but conducting a
multi-issue election is challenging. On the one hand,
requiring agents to vote by expressing their preferences
over all combinations of issues is computationally
infeasible; on the other, decomposing the
problem into several elections on smaller sets of
issues can lead to paradoxical outcomes. Any pragmatic
method for running a multi-issue election will
have to balance these two concerns. We identify
and analyse the problem of generating an agenda
for a given election, specifying which issues to vote
on together in local elections and in which order to
schedule those local elections
The Theory of Implementation of Social Choice Rules
Suppose that the goals of a society can be summarized in a social choice rule, i.e., a mapping from relevant underlying parameters to final outcomes. Typically, the underlying parameters (e.g., individual preferences) are private information to the agents in society. The implementation problem is then formulated: under what circumstances can one design a mechanism so that the private information is truthfully elicited and the social optimum ends up being implemented? In designing such a mechanism, appropriate incentives will have to be given to the agents so that they do not wish to misrepresent their information. The theory of implementation or mechanism design formalizes this “social engineering” problem and provides answers to the question just posed. I survey the theory of implementation in this article, emphasizing the results based on two behavioral assumptions for the agents (dominant strategies and Nash equilibrium). Examples discussed include voting, and the allocation of private and public goods under complete and incomplete information.Implementation Theory, Mechanism Design, Asymmetric Information, Decentralization, Game Theory, Dominance, Nash Equilibrium, Monotonicity
Strategy-proof judgment aggregation.
Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premise-based voting”, which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy.
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