Majority relation and median representative ordering

Demange, Gabrielle

doi:10.1007/s13209-011-0052-9

Cited by 15 publications

(24 citation statements)

References 12 publications

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“…This result is remarkable in particular in view of the fact that quite a number of nonsingle-peaked Condorcet domains have been identified in the literature, among others the domains satisfying Sen's 'value restriction' condition (Sen [1966]) with the 'single-dipped' domain (Inada [1964]) as a special case, the domains satisfying the so-called 'intermediateness' property (Grandmont [1978], Demange [2012]), and the 'order-restricted' domains identified by Rothstein [1990]; the latter domains are sometimes also referred to as the domains with the single-crossing property (Gans and Smart [1996], Saporiti [2009], Puppe and Slinko [2015]). Our analysis shows that none of these domains can jointly satisfy the three conditions of minimal richness, connectedness and the inclusion of a pair of completely reversed orders unless it is also single-peaked.…”

Section: Introductionmentioning

confidence: 82%

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The single-peaked domain revisited: A simple global characterization

Puppe

2018

Journal of Economic Theory

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for particularly helpful comments.Abstract It is proved that, among all restricted preference domains that guarantee consistency (i.e. transitivity) of pairwise majority voting, the single-peaked domain is the only minimally rich and connected domain that contains two completely reversed strict preference orders. It is argued that this result explains the predominant role of single-peakedness as a domain restriction in models of political economy and elsewhere. The main result has a number of corollaries, among them a dual characterization of the single-dipped domain; it also implies that a single-crossing ('order-restricted') domain can be minimally rich only if it is a subdomain of a single-peaked domain. The conclusions are robust as the results apply both to domains of strict and of weak preference orders, respectively. JEL Classification D71, C72

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Section: Introductionmentioning

confidence: 82%

“…22 Some authors such as, e.g., Grandmont [1978] and Demange [2012] refer to orders that are between two others in this sense as 'intermediate' orders.…”

Section: A1 the Case Of Linear Ordersmentioning

confidence: 99%

The single-peaked domain revisited: A simple global characterization

Puppe

2018

Journal of Economic Theory

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“…Independently of this work Demange (2011) has developed some ideas quite similar to the ones presented here. She introduces a notably different set-up, in which a median graph represents the relation of the different preference orderings in a profile.…”

Section: Introductionmentioning

confidence: 93%

“…From the literature it is known that the existence of a Condorcet winner can be extended to single-peaked preferences on tree graphs (Demange 1982). For the characterization of Condorcet winners there are contributions in the field of location theory: For a special class of preferences, Wendell and McKelvey (1981) show that on tree graphs Condorcet winners coincide with the appropriately defined median; Bandelt and Barthélémy (1984) extend this result to so-called cube-free median graphs.…”

Section: Introductionmentioning

confidence: 99%

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Condorcet winners on median spaces

Buechel

2013

Soc Choice Welf

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We characterize the outcome of majority voting for single-peaked preferences on median spaces. This large class of preferences covers a variety of multi-dimensional policy spaces including products of lines (e.g. grids), trees, and hypercubes. Our main result is the following: If a Condorcet winner (i.e. a winner in pairwise majority voting) exists, then it coincides with the appropriately defined median ("the median voter"). This result generalizes previous findings which are either restricted to a one-dimensional policy space or to the assumption that any two voters with the same preference peak must have identical preferences. The result applies to models of spatial competition between two political candidates. A bridge to the graph-theoretic literature is built.

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Condorcet domains, median graphs and the single-crossing property

Puppe

Slinko

2017

Econ Theory

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Abstract. Condorcet domains are sets of linear orders with the property that, whenever the preferences of all voters of a society belong to this set, their majority relation has no cycles. We observe that, without loss of generality, every such domain can be assumed to be closed in the sense that it contains the majority relation of every profile with an odd number of voters whose preferences belong to this domain.We show that every closed Condorcet domain can be endowed with the structure of a median graph and that, conversely, every median graph is associated with a closed Condorcet domain (in general, not uniquely). Condorcet domains that have linear graphs (chains) associated with them are exactly the preference domains with the classical singlecrossing property. As a corollary, we obtain that a domain with the so-called 'representative voter property' is either a single-crossing domain or a very special domains containing exactly four different preference orders whose associated median graph is a 4-cycle.Maximality of a Condorcet domain imposes additional restrictions on the associated median graph. We prove that among all trees only (some) chains can be associated graphs of maximal Condorcet domains, and we characterize those single-crossing domains which are maximal Condorcet domains.Finally, using the characterization of Nehring and Puppe [2007] of monotone Arrovian aggregation, our analysis yields a rich class of strategy-proof social choice functions on any closed Condorcet domain. JEL Classification D71, C72

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Majority relation and median representative ordering

Cited by 15 publications

References 12 publications

The single-peaked domain revisited: A simple global characterization

The single-peaked domain revisited: A simple global characterization

Condorcet winners on median spaces

Condorcet domains, median graphs and the single-crossing property

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