A Characterization of Consistent Collective Choice Rules

We characterize a class of collective choice rules such that collective preference relations are consistent. Consistency is a weakening of transitivity and a strengthening of acyclicity requiring that there be no cycles with at least one strict preference. The properties used in our characterization are unrestricted domain, strong Pareto, anonymity and neutrality. If there are at most as many individuals as there are alternatives, the axioms provide an alternative characterization of the Pareto rule. If there are more individuals than alternatives, however, further rules become available

A pooling approach to judgment aggregation

The literature has focused on a particular way of aggregating judgments: Given a set of yes or no questions or issues, the individuals’ judgments are then aggregated separately, issue by issue. Applied in this way, the majority method does not guarantee the logical consistency of the set of judgments obtained. This fact has been the focus of critiques of the majority method and similar procedures. This paper focuses on another way of aggregating judgments. The main difference is that aggregation is made en bloc on all the issues at stake. The main consequence is that the majority method applied in this way does always guarantee the logical consistency of the collective judgments. Since it satisfies a large set of attractive properties, it should provide the basis for more positive assessment if applied using the proposed pooling approach than if used separately. The paper extends the analysis to the pooling supermajority and plurality rules, with similar result

A non-proposition-wise variant of majority voting for aggregating judgments

Majority voting is commonly used in aggregating judgments. The literature to date on judgment aggregation (JA) has focused primarily on proposition-wise majority voting (PMV). Given a set of issues on which a group is trying to make collective judgments, PMV aggregates individual judgments issue by issue, and satisfies a salient property of JA rules—independence. This paper introduces a variant of majority voting called holistic majority voting (HMV). This new variant also meets the condition of independence. However, instead of aggregating judgments issue by issue, it aggregates individual judgments en bloc. A salient and straightforward feature of HMV is that it guarantees the logical consistency of the propositions expressing collective judgments, provided that the individual points of view are consistent. This feature contrasts with the known inability of PMV to guarantee the consistency of the collective outcome. Analogously, while PMV may present a set of judgments that have been rejected by everyone in the group as collectively accepted, the collective judgments returned by HMV have been accepted by a majority of individuals in the group and, therefore, rejected by a minority of them at most. In addition, HMV satisfies a large set of appealing properties, as PMV also does. However, HMV may not return any complete proposition expressing the judgments of the group on all the issues at stake, even in cases where PMV does. Moreover, demanding completeness from HMV leads to impossibility results similar to the known impossibilities on PMV and on proposition-wise JA rules in genera

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.

Ontology Merging as Social Choice

The problem of merging several ontologies has important applications in the Semantic Web, medical ontology engineering and other domains where information from several distinct sources needs to be integrated in a coherent manner.We propose to view ontology merging as a problem of social choice, i.e. as a problem of aggregating the input of a set of individuals into an adequate collective decision. That is, we propose to view ontology merging as ontology aggregation. As a first step in this direction, we formulate several desirable properties for ontology aggregators, we identify the incompatibility of some of these properties, and we define and analyse several simple aggregation procedures. Our approach is closely related to work in judgment aggregation, but with the crucial difference that we adopt an open world assumption, by distinguishing between facts not included in an agent’s ontology and facts explicitly negated in an agent’s ontology

Efficiency and converse reduction-consistency in collective choice

We consider the problem of selecting a subset of a feasible set over which each agent has a strict preference. We propose an invariance property, converse reduction-consistency, which is the converse of reduction-consistency introduced by Yeh (2006), and study its implications. Our results are two characterizations of the Pareto rule: (1) it is the only rule satisfying efficiency and converse reduction-consistency and (2) it is the only rule satisfying one-agent efficiency, converse reduction-consistency, and reduction-consistency.consistency converse consistency efficiency Pareto rule social choice correspondences.

Propositionwise judgment aggregation

In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, non-dictatorship and propositionwise independence. But it is only partially known for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or implication preservation. We fully characterize the agendas for which there are such possibilities, thereby answering the most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (2002), Nehring (2006) and Dietrich and List (2007a).mathematical economics;