16,479 research outputs found
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 âconclusion-based votingâ is less vulnerable to manipulation than âpremise-based votingâ, which is strategy-proof only for âreason-orientedâ individuals. Surprisingly, for âoutcome-orientedâ 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.
Strategy-proof judgment aggregation
In the theory of judgment aggregation on logically connected propositions, an important question remains open: Which aggregation rules are manipulable and which are strategy-proof? We define manipulability and strategy-proofness in judgment aggregation, characterize all strategy-proof aggregation rules, and prove an impossibility theorem similar to the Gibbard-Satterthwaite theorem. Among other escape-routes from the impossibility, we discuss weakening strategy-proofness itself. Comparing two prominent aggregation rules, we show that conclusion-based voting is strategy-proof, but generates incomplete judgments, while premise-based voting is only strategy-proof 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
Judgment aggregation in search for the truth
We analyze the problem of aggregating judgments over multiple issues from the perspective of whether aggregate judgments manage to efficiently use all voters' private information. While new in judgment aggregation theory, this perspective is familiar in a different body of literature about voting between two alternatives where voters' disagreements stem from conflicts of information rather than of interest. Combining the two bodies of literature, we consider a simple judgment aggregation problem and model the private information underlying voters' judgments. Assuming that voters share a preference for true collective judgments, we analyze the resulting strategic incentives and determine which voting rules efficiently use all private information. We find that in certain, but not all cases a quota rule should be used, which decides on each issue according to whether the proportion of âyesâ votes exceeds a particular quota
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 rulesâindependence. 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
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A partial taxonomy of judgment aggregation rules, and their properties
The literature on judgment aggregation is moving from studying impossibility
results regarding aggregation rules towards studying specific judgment
aggregation rules. Here we give a structured list of most rules that have been
proposed and studied recently in the literature, together with various
properties of such rules. We first focus on the majority-preservation property,
which generalizes Condorcet-consistency, and identify which of the rules
satisfy it. We study the inclusion relationships that hold between the rules.
Finally, we consider two forms of unanimity, monotonicity, homogeneity, and
reinforcement, and we identify which of the rules satisfy these properties
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 individualsâ 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
Introduction to Judgment Aggregation
This introduces the symposium on judgment aggregation. The theory of judgment agÂgregation asks how several individuals' judgments on some logically connected propoÂsitions can be aggregated into consistent collective judgments. The aim of this introÂduction is to show how ideas from the familiar theory of preference aggregation can be extended to this more general case. We first translate a proof of Arrow's imposÂsibility theorem into the new setting, so as to motivate some of the central concepts and conditions leading to analogous impossibilities, as discussed in the symposium. We then consider each of four possible escape-routes explored in the symposium.Judgment aggregation, Arrow's theorem, Escape routes
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