Aggregating Sets of Judgments: An Impossibility Result

List, Christian; Pettit, Philip

doi:10.1017/s0266267102001098

Cited by 506 publications

(459 citation statements)

References 14 publications

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“…A central problem that has triggered much work in the field of judgement aggregation is the so-called "doctrinal paradox" (Kornhauser and Sager, 1986) or, more generally, the "discursive dilemma" (List and Pettit, 2002). I start by describing two examples that illustrate the problem.…”

Section: The Discursive Dilemmamentioning

confidence: 99%

“…Systematicity ensures an equal treatment of all propositions, so that the aggregation procedure does not have an ex ante bias to define some propositions as "special" or "more important". List and Pettit (2002) discuss several options to relax one of the three desiderata, or one of the three rationality conditions completeness, consistency, and deductive closure. Relaxing collective consistency and deductive closure is unattractive, because it results in irrational collective judgement sets.…”

Section: Systematicitymentioning

confidence: 99%

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Judgement Aggregation and Distributed Thinking

Spiekermann

2013

Cognition Beyond the Brain

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In recent years, judgement aggregation has emerged as an important area of social choice theory. Judgement aggregation is concerned with aggregating sets of individual judgements over logically connected propositions into a set of collective judgements. It has been shown that even seemingly weak conditions on the aggregation function make it impossible to find functions that produce rational collective judgements from all possible rational individual judgements. This implies that the step from individual judgements to collective judgements requires trade-offs between different desiderata, such as universal domain, rationality, epistemological quality, and unbiasedness. These dilemmas challenge us to decide which conditions we should relax. The typical application for judgement aggregation is the problem of group decision making. Juries and expert committees are the stock examples. However, the relevance of judgement aggregation goes beyond these cases. In this survey I review some core results in the field of judgement aggregation and social epistemology and discuss their implications for the analysis of distributed thinking.

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Section: The Discursive Dilemmamentioning

confidence: 99%

Section: Systematicitymentioning

confidence: 99%

Judgement Aggregation and Distributed Thinking

Spiekermann

2013

Cognition Beyond the Brain

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“…This paradox is related to the discursive dilemma familiar from judgment aggregation [15]. In judgment aggregation, we are asked to aggregate the views of several individuals regarding the truth or falsity of a number of formulas of propositional logic, and the discursive dilemma is a family of paradoxical situations that we may encounter in this framework.…”

Section: The Paradox Of Individual Uncertainty Resolutionmentioning

confidence: 99%

Voting on Actions with Uncertain Outcomes

Endriss

2013

Algorithmic Decision Theory

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Abstract. We introduce a model for voting under uncertainty where a group of voters have to decide on a joint action to take, but the individual voters are uncertain about the current state of the world and thus about the effect that the chosen action would have. Each voter has preferences about what state they would like to see reached once the action has been executed. That is, we need to integrate two kinds of aggregation: beliefs regarding the current state and preferences regarding the next state.

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“…A large literature on judgment aggregation exists, motivated by List and Pettit (2002) initial contribution. 1 The literature is concerned with aggregating profiles of individual judgment sets into a collective judgment set.…”

Section: Introductionmentioning

confidence: 99%

“…Just as the majority voting paradox can be generalised through Arrow's (1963) impossibility theorem, so can this "doctrinal paradox". List and Pettit (2002) arrived at the first systematic result in this area by showing that no aggregation rule applied to an agenda containing certain propositions can satisfy four conditions. More general results have been obtained by Dietrich (2006Dietrich ( , 2007, Dietrich andList (2009, 2010), Dokow and Holzman (2010) and Nehring and Puppe (2010) amongst others.…”

Section: Introductionmentioning

confidence: 99%

A measure of distance between judgment sets

Duddy

Piggins

2011

Soc Choice Welf

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In the literature on judgment aggregation, an important open question is how to measure the distance between any two judgment sets. This is relevant for issues of social choice: if two individuals hold different beliefs then we might want to find a compromise that lies somewhere between them. We propose a set of axioms that determine a measure of distance uniquely. This measure differs from the widely used Hamming metric. The difference between Hamming's metric and ours boils down to one axiom. Given judgment sets A and B, this axiom says that if the propositions in A ∩ B jointly imply that the propositions in A−B share the same truth value, then the disagreement between A and B over those propositions in A−B should be counted as a single disagreement. We consider the application of our metric to judgment aggregation, and also use the metric to measure the distance between preference rankings.

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Aggregating Sets of Judgments: An Impossibility Result

Abstract: Aggregating sets of judgments : an impossibility result Christian List LSE has developed LSE Research Online so that users may access research output of the School.

Cited by 506 publications

References 14 publications

Judgement Aggregation and Distributed Thinking

Judgement Aggregation and Distributed Thinking

Voting on Actions with Uncertain Outcomes

A measure of distance between judgment sets

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