2,217 research outputs found

    Aggregating Dependency Graphs into Voting Agendas in Multi-Issue Elections

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    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

    Individual versus group strategy-proofness: when do they coincide?

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    A social choice function is group strategy-proof on a domain if no group of agents can manipulate its final outcome to their own benefit by declaring false preferences on that domain. Group strategy-proofness is a very attractive requirement of incentive compatibility. But in many cases it is hard or impossible to find nontrivial social choice functions satisfying even the weakest condition of individual strategy-proofness. However, there are a number of economically significant domains where interesting rules satisfying individual strategy-proofness can be defined, and for some of them, all these rules turn out to also satisfy the stronger requirement of group strategy-proofness. This is the case, for example, when preferences are single-peaked or single-dipped. In other cases, this equivalence does not hold. We provide sufficient conditions defining domains of preferences guaranteeing that individual and group strategy-proofness are equivalent for all rules defined on theStrategy-proofness, Group strategy-proofness, k-size strategy-proofness, Sequential inclusion, Single-peaked preferences, Single-dipped preferences, Separable preferences.

    Uncovered Sets

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    This paper covers the theory of the uncovered set used in the literatures on tournaments and spatial voting. I discern three main extant definitions, and I introduce two new concepts that bound exist- ing sets from above and below: the deep uncovered set and the shallow uncovered set. In a general topological setting, I provide relationships to other solutions and give results on existence and external stability for all of the covering concepts, and I establish continuity properties of the two new uncovered sets. Of note, I characterize each of the uncovered sets in terms of a decomposition into choices from externally stable sets; I define the minimal generalized covering solution, a nonempty refinement of the deep uncovered set that employs both of the new relations; and I define the acyclic Banks set, a nonempty generalization of the Banks set.

    Cooperative Games on Antimatroids

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    AMS classification: 90D12;game theory;cooperative games;antimatroids

    The possibility of judgment aggregation for network agendas

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    Within social choice theory, the new field of judgment aggregation aims at reaching collective judgments on a set of logically interconnected propositions. I investigate decision problems, in which the agenda is a network, composed of atomic propositions and connection rules between them. Networks can represent various realistic decision problems, including most concrete examples given in the literature. Nevertheless, networks are unexplored so far due to problems when modelling connection rules in standard propositional logic. By extending the logic, I prove that, for any network, decision rules satisfying the common conditions always exist, in contrast to the literature's emphasis on impossibilities. I also characterise the class of such decision rules, and propose a simple way to select a decision rule.judgment aggregation, collective inconsistency, possibility theorems, network, connection rule, formal logic, material conditional, subjunctive conditional
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