On distance rationalizability of some voting rules

The concept of distance rationalizability has several applications within social choice. In the context of voting, it allows one to define ("rationalize") voting rules via a consensus class (roughly, a set of elections in which it is obvious who should win) and a distance function: namely, a candidate is said to be an election winner if it is ranked first in one of the nearest (with respect to the given distance) consensus elections. It is known that many classic voting rules can be represented in this manner. In this paper, we provide new results on distance rationalizability of several well-known voting rules such as all scoring rules, Approval, Young's rule and Maximin. We also show that a previously published proof of distance rationalizability of Young's rule is incorrect: the consensus notion and the distance function used in that proof give rise to a voting rule that is similar to---but distinct from---the Young's rule. Finally, we demonstrate that some voting rules cannot be rationalized via certain notions of consensus. To the best of our knowledge, these are the first non-distance-rationalizability results for voting rules.

[1]  Nick Baigent.  Metric rationalisation of social choice functions according to principles of social choice , 1987 .

[2]  Michael Wooldridge,et al.  Proceedings of the 21st International Joint Conference on Artificial Intelligence , 2009 .

[3]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[4]  Vincent Conitzer,et al.  Common Voting Rules as Maximum Likelihood Estimators , 2005, UAI.

[5]  Piotr Faliszewski,et al.  Swap Bribery , 2009, SAGT.

[6]  Peter C. Fishburn,et al.  Chapter 4 Voting procedures , 2002 .

[7]  Jörg Rothe,et al.  Exact Complexity of the Winner Problem for Young Elections , 2001, Theory of Computing Systems.

[8]  Christian Klamler.  The Copeland rule and Condorcet’s principle , 2005 .

[9]  Vincent Conitzer,et al.  Generalized scoring rules and the frequency of coalitional manipulability , 2008, EC '08.

[10]  P. Strevens.  Iii , 1985 .

[11]  Hannu Nurmi,et al.  Closeness Counts in Social Choice , 2008 .

[12]  Christian Klamler,et al.  Borda and Condorcet: Some Distance Results , 2005 .

[13]  H. Moulin,et al.  Axioms of Cooperative Decision Making. , 1990 .

[14]  P. Fishburn,et al.  Voting Procedures , 2022 .

[15]  Pierre Crépel,et al.  Marquis de Condorcet , 2001 .

[16]  Daphne Koller,et al.  Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence , 2001 .

[17]  Piotr Faliszewski,et al.  The Complexity of Bribery in Elections , 2006, AAAI.

[18]  K. Arrow,et al.  Social Choice and Individual Values , 1951 .

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

[20]  Michael A. Trick,et al.  How hard is it to control an election? Math , 1992 .

[21]  Keith Dowding,et al.  Power, freedom, and voting. , 2008 .

[22]  John Riedl,et al.  Proceedings of the 6th ACM conference on Electronic commerce , 2005, EC 2008.