The single-peaked domain revisited: A simple global characterization

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.This result has a number of corollaries, among other things it implies that a single-crossing (‘order-restricted’) domain can be minimally rich only if it is a subdomain of a single-peaked domain.

[1]  John G. Kemeny,et al.  Mathematical models in the social sciences , 1964 .

[2]  Christian List,et al.  Judgement Aggregation: A Survey , 2009, The Handbook of Rational and Social Choice.

[3]  M. Remzi Sanver,et al.  On domains that admit well-behaved strategy-proof social choice functions , 2013, J. Econ. Theory.

[5]  Klaus Nehring,et al.  The structure of strategy-proof social choice - Part I: General characterization and possibility results on median spaces , 2007, J. Econ. Theory.

[6]  D. Black.  On the Rationale of Group Decision-making , 1948, Journal of Political Economy.

[7]  Julius Margolis.  The public economy of urban communities , 2016 .

[8]  Peter C. Fishburn,et al.  Acyclic sets of linear orders: A progress report , 2002, Soc. Choice Welf..

[9]  H. Moulin.  Axioms of Cooperative Decision Making , 1988 .

[10]  W. Gaertner.  Domain Conditions in Social Choice Theory , 2001 .

[11]  Van de M. L. J. Vel.  Theory of convex structures , 1993 .

[12]  Arunava Sen,et al.  A Characterization of Single-Peaked Preferences via Random Social Choice Functions , 2016 .

[13]  H. Moulin.  Generalized condorcet-winners for single peaked and single-plateau preferences , 1984 .

[14]  Hans Peters,et al.  Strategy-proof division of a private good when preferences are single-dipped , 1997 .

[15]  Gleb A. Koshevoy,et al.  Maximal Condorcet Domains , 2013, Order.

[16]  Joshua S. Gans,et al.  Majority voting with single-crossing preferences , 1996 .

[17]  Arkadii M. Slinko,et al.  Condorcet domains, median graphs and the single-crossing property , 2015, ArXiv.

[18]  Marcus Pivato,et al.  Unanimity overruled: Majority voting and the burden of history , 2016 .

[19]  Peter C. Fishburn,et al.  Acyclic sets of linear orders , 1996 .

[20]  M. Satterthwaite,et al.  Strategy-proofness and single-peakedness , 1976 .

[21]  Paul Rothstein,et al.  Order restricted preferences and majority rule , 1990 .

[22]  Patrick J. Egan,et al.  “Do Something” Politics and Double-Peaked Policy Preferences , 2014, The Journal of Politics.

[23]  Amartya Sen,et al.  A Possibility Theorem on Majority Decisions , 1966 .

[24]  John Duggan.  Preference exclusions for social rationality , 2016, Soc. Choice Welf..

[25]  Jean-Michel Grandmont,et al.  INTERMEDIATE PREFERENCES AND THE MAJORITY RULE , 1978 .

[26]  Paul Rothstein,et al.  Representative voter theorems , 1991 .

[27]  Kevin Roberts,et al.  Voting over income tax schedules , 1977 .

[28]  Bernard Monjardet,et al.  Condorcet domains and distributive lattices , 2006 .

[29]  Alexander V. Karzanov,et al.  Condorcet domains of tiling type , 2010, Discret. Appl. Math..

[30]  Guillaume Haeringer,et al.  A characterization of the single-peaked domain , 2011, Soc. Choice Welf..

[31]  Nora Szech,et al.  Optimal Revelation of Life-Changing Information , 2016, Manag. Sci..

[32]  Alejandro Saporiti,et al.  Strategy-proofness and single-crossing , 2009 .

[33]  Roman M. Sheremeta,et al.  Designing Contests between Heterogeneous Contestants: An Experimental Study of Tie-Breaks and Bid-Caps in All-Pay Auctions , 2015, Games Econ. Behav..

[34]  Christian List,et al.  Deliberation, Single-Peakedness, and the Possibility of Meaningful Democracy: Evidence from Deliberative Polls , 2006, The Journal of Politics.

[35]  Shin Sato,et al.  A sufficient condition for the equivalence of strategy-proofness and nonmanipulability by preferences adjacent to the sincere one , 2013, J. Econ. Theory.

[36]  Ken-ichi Inada,et al.  A Note on the Simple Majority Decision Rule , 1964 .

[37]  P. DeMarzo,et al.  Persuasion Bias, Social Influence, and Uni-Dimensional Opinions , 2001 .

[38]  Arunava Sen,et al.  Tops-only domains , 2011 .

[39]  Gabrielle Demange,et al.  Majority relation and median representative ordering , 2012 .

[40]  J. Banks,et al.  Positive Political Theory I: Collective Preference , 1998 .

[41]  C. List,et al.  Judgment aggregation: A survey , 2009 .

[42]  David Spector.  Rational Debate And One-Dimensional Conflict , 2000 .

[43]  Arunava Sen,et al.  Dictatorial domains , 2003 .

[44]  Marcus Pivato,et al.  The Condorcet set: Majority voting over interconnected propositions , 2014, J. Econ. Theory.

[45]  Bernard Monjardet,et al.  Acyclic Domains of Linear Orders: A Survey , 2006, The Mathematics of Preference, Choice and Order.

[46]  S. Chatterji,et al.  On Strategy‐Proofness and the Salience of Single‐Peakedness , 2018 .

[47]  Victor Reiner,et al.  Acyclic sets of linear orders via the Bruhat orders , 2008, Soc. Choice Welf..

[48]  Ehud Kalai,et al.  Characterization of domains admitting nondictatorial social welfare functions and nonmanipulable voting procedures , 1977 .

[49]  James Abello.  The Weak Bruhat Order of SSigma, Consistent Sets, and Catalan Numbers , 1991, SIAM J. Discret. Math..

[50]  Célestin Chameni Nembua.  Permutoèdre et choix social , 1989 .

[51]  L. A. Goodman,et al.  Social Choice and Individual Values , 1951 .