24 research outputs found
The geometry of consistent majoritarian judgement aggregation
Given a set of propositions with unknown truth values, a `judgement aggregation rule' is a way to aggregate the personal truth-valuations of a set of jurors into some `collective' truth valuation. We introduce the class of `quasimajoritarian' judgement aggregation rules, which includes majority vote, but also includes some rules which use different weighted voting schemes to decide the truth of different propositions. We show that if the profile of jurors' beliefs satisfies a condition called `value restriction', then the output of any quasimajoritarian rule is logically consistent; this directly generalizes the recent work of Dietrich and List (2007). We then provide two sufficient conditions for value-restriction, defined geometrically in terms of a lattice ordering or an ultrametric structure on the set of jurors and propositions. Finally, we introduce another sufficient condition for consistent majoritarian judgement aggregation, called `convexity'. We show that convexity is not logically related to value-restriction
The geometry of consistent majoritarian judgement aggregation
Given a set of propositions with unknown truth values, a `judgement aggregation rule' is a way to aggregate the personal truth-valuations of a set of jurors into some `collective' truth valuation. We introduce the class of `quasimajoritarian' judgement aggregation rules, which includes majority vote, but also includes some rules which use different weighted voting schemes to decide the truth of different propositions. We show that if the profile of jurors' beliefs satisfies a condition called `value restriction', then the output of any quasimajoritarian rule is logically consistent; this directly generalizes the recent work of Dietrich and List (2007). We then provide two sufficient conditions for value-restriction, defined geometrically in terms of a lattice ordering or an ultrametric structure on the set of jurors and propositions. Finally, we introduce another sufficient condition for consistent majoritarian judgement aggregation, called `convexity'. We show that convexity is not logically related to value-restriction.judgement aggregation; discursive dilemma; doctrinal paradox; epistemic democracy; value restriction
Judgment aggregation on restricted domains
We show that, when a group takes independent majority votes on interconnected propositions, the outcome is consistent once the profile of individual judgment sets respects appropriate structural conditions. We introduce several such conditions on profiles, based on ordering the propositions or ordering the individuals, and we clarify the relations between these conditions. By restricting the conditions to appropriate subagendas, we obtain local conditions that are less demanding but still guarantee consistent majority judgments. By applying the conditions to agendas representing preference aggregation problems, we show parallels of some conditions to existing social-choice-theoretic conditions, specifically to order restriction and intermediateness, restricted to triples of alternatives in the case of our local conditions.mathematical economics;
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.
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
Strategy-Proofness and Single-Crossing
This paper analyzes strategy-proof collective choice rules when individuals have single-crossing preferences on a finite and ordered set of social alternatives. It shows that a social choice rule is anonymous, unanimous and strategy-proof on a maximal single-crossing domain if and only if it is an extended median rule with n - 1 fixed ballots located at the end points of the set of alternatives. As a by-product, the paper also proves that strategy-proofness implies the tops-only property. And it offers a strategic foundation for the so called "single-crossing version" of the Median Voter Theorem, by showing that the median ideal point can be implemented in dominant strategies by a direct mechanism in which every individual reveals his true preferences.Strategy-proofness; single-crossing; median voter; positional dictators
Introduction to Judgment Aggregation
This introduces the symposium on judgment aggregation. The theory of judgment aggregation asks how several individualsâ judgments on some logically connected propositions can be aggregated into consistent collective judgments. The aim of this introduction is to show how ideas from the familiar theory of preference aggregation can be extended to this more general case. We ďŹrst translate a proof of Arrowâs impossibility 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