The Condorcet set: Majority voting over interconnected propositions

Sequential majority voting over interconnected binary decisions can lead to the overruling of unanimous consensus. We characterize, within the general framework of judgement aggregation, when this happens for some sequence of decisions. The large class of aggregation spaces for which this vulnerability is present includes the aggregation of preference orderings over at least four alternatives, the aggregation of equivalence relations over at least four objects, resource allocation problems, and most committee selection problems. We also ask whether it is possible to design respect for unanimity by choosing appropriate decision sequences (independently from the ballot). Remarkably, while this is not possible in general, it can be accomplished in some interesting special cases. Generalizing and sharpening a classic result by Shepsle and Weingast, we show that respect for unanimity can indeed be thus guaranteed in the cases of the aggregation of weak preference orderings, linear preference orderings, and equivalence relations. By contrast, impossibility results can be obtained for the aggregation of acyclic relations and separable preference orderings. As a key technical tool, we introduce the notion of a covering fragment that serves as a counterpart and generalization of the notions of covering relation/uncovered set in voting theory.

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“…The following result, proven in Nehring et al (2013), establishes a close connection between sequential majority voting and the Condorcet set:…”

mentioning

confidence: 86%

“…In Nehring et al (2013), we have thus proposed the notion of the Condorcet set Cond (X, µ) ⊆ X as the set of all views x ∈ X such that no y ∈ X agrees with Maj(µ) on a strictly larger set of issues than x. The elements of Cond (X, µ) are also referred to as the Condorcet admissible views.…”

Section: The Condorcet Setmentioning

confidence: 99%

Unanimity overruled: Majority voting and the burden of history

Nehring

Pivato

Puppe

2016

Journal of Theoretical Politics

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“…The output of the rule mc is called Condorcet admissible set by Nehring et al [28]. The rule mcc is called Slater rule [28], and Endpoint dH [25].…”

Section: Definition 1 (Maximal Condorcet and Maxcard Condorcet Rules)mentioning

confidence: 99%

A partial taxonomy of judgment aggregation rules and their properties

et al. 2016

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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 majoritypreservation 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.

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“…In voting theory, the well-known Condorcet principle requires that an election is won by a candidate that beats all other candidates in a pairwise comparison. Similarly, judgment aggregation procedures based on the Condorcet set have been proposed by Nehring et al (2014). Everaere et al (2014) propose judgment aggregation procedures that are based on the support (i.e., number of votes) that each member of the agenda receives.…”

Section: Related Workmentioning

confidence: 99%

“…Only one case remains open: What is the complexity of exact bribery with the premise-based procedure for a fixed number of judges? Also, it would be interesting to study bribery for other (classes of) judgment aggregation procedures, such as conclusion-based procedures (Kornhauser and Sager, 1986;List and Pettit, 2002;Dietrich, 2006), distance-based procedures (Miller and Osherson, 2009), procedures based on minimization (Lang et al, 2011), sequential procedures (List, 2004), procedures based on the Condorcet set (Nehring et al, 2014), or procedures based on the number of votes (Everaere et al, 2014).…”

Section: Tablementioning

confidence: 99%