Condorcet domains of tiling type

Данилов, В. И.; Karzanov, Alexander V.; Koshevoy, Gleb A.

doi:10.1016/j.dam.2011.08.001

Cited by 21 publications

(51 citation statements)

References 9 publications

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“…The present study also informs the literature that aims at identifying 'large' Condorcet domains, see the excellent survey Monjardet [2009] and the more recent work on this topic by Danilov et al [2012], Danilov and Koshevoy [2013]. Indeed, our main result suggests that Condorcet domains with the maximal number of elements on a given set of alternatives, the so-called maximum Condorcet domains, are most likely not minimally rich.…”

Section: Relation To the Literaturementioning

confidence: 74%

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: Relation To the Literaturementioning

confidence: 74%

The single-peaked domain revisited: A simple global characterization

Puppe

2018

Journal of Economic Theory

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“…The representation by the rhombus tiling also admits a simple and good visualization. The notations and contents of this subsection are mainly adopted from the paper (Danilov et al 2012).…”

Section: Representing Cds By Rhombus Tilingmentioning

confidence: 99%

“…As wrote in Fishburn (1997), and mentioned in Danilov et al (2012): "...it is far from obvious how the restrictions should be selected jointly to produce a large acyclic B Ping Zhan zhan@edogawa-u.ac.jp 1 Department of Communication and Business, Edogawa University, 474, Komaki, Nagareyama, Chiba 270-0198, Japan sets". Our contribution is a neatly simple procedure of constructing complete singlepeaked domains of tiling type explicitly for any finite alternative sets.…”

Section: Introductionmentioning

confidence: 99%

A simple construction of complete single-peaked domains by recursive tiling

Zhan

2019

Math Meth Oper Res

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Single-peakedness was introduced by Black (J Political Econ 56:23-34, 1948) as a sufficient condition to overcome Condorcet paradox. Since then it has been attracting interest from researchers in various fields. In this paper, we propose a simple recursive procedure of constructing complete single-peaked domains of tiling type explicitly for any finite alternative sets, by combining two results published in recent years, and some observations of known results and examples by the author. The underlying basic structure of tiling type and properties of single-peaked domains provided here give a good visualization and make further developments on single-peakedness more easy.

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“…Note that the domain shown in Figure 5 is connected. Indeed, most of the known general results about the size and the structure of maximal Condorcet domains pertain to connected Condorcet domains; for instance, the domains described in Abello [1991], Chameni-Nembua [1989], Danilov et al [2012] and Galambos and Reiner [2008] are all connected. However, not all maximal Condorcet domains are connected, as we have already seen above.…”

Section: Maximal Condorcet Domains Revisitedmentioning

confidence: 99%

“…Later, Sen [1966] provided a characterization of Condorcet domains in terms of the well-known condition of value restriction. Since this early work some progress has been made in understanding the structure of Condorcet domains; see Abello [1991Abello [ , 2004, Chameni-Nembua [1989], Danilov et al [2012], Danilov and Koshevoy [2013], Fishburn [1997Fishburn [ , 2002, Galambos and Reiner [2008] for important contributions, and Monjardet [2009] for an excellent survey. However, with the exception of Danilov and Koshevoy [2013], the bulk of the results established in the literature pertains only to the special case of connected domains.…”

Section: Introductionmentioning

confidence: 99%

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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Condorcet domains of tiling type

Abstract: We propose a method to construct "large" Condorcet domains by use of socalled rhombus tilings. Then we explain that this method fits to unify several previously known constructions of Condorcet domains. Finally, we discuss some conjectures on the size of such domains.

Cited by 21 publications

References 9 publications

The single-peaked domain revisited: A simple global characterization

The single-peaked domain revisited: A simple global characterization

A simple construction of complete single-peaked domains by recursive tiling

Condorcet domains, median graphs and the single-crossing property

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