Homogeneity and monotonicity of distance-rationalizable voting rules

Distance rationalizability is a framework for classifying voting rules by interpreting them in terms of distances and consensus classes. It can also be used to design new voting rules with desired properties. A particularly natural and versatile class of distances that can be used for this purpose is that of votewise distances [12], which "lift" distances over individual votes to distances over entire elections using a suitable norm. In this paper, we continue the investigation of the properties of votewise distance-rationalizable rules initiated in [12]. We describe a number of general conditions on distances and consensus classes that ensure that the resulting voting rule is homogeneous or monotone. This complements the results of 12], where the authors focus on anonymity, neutrality and consistency. We also introduce a new class of voting rules, that can be viewed as "majority variants" of classic scoring rules, and have a natural interpretation in the context of distance rationalizability.

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

[2]  Claire Mathieu,et al.  Electronic Colloquium on Computational Complexity, Report No. 144 (2006) How to rank with few errors A PTAS for Weighted Feedback Arc Set on Tournaments , 2006 .

[3]  Piotr Faliszewski,et al.  On the role of distances in defining voting rules , 2010, AAMAS.

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

[5]  F. L. Bauer,et al.  Absolute and monotonic norms , 1961 .

[6]  Shmuel Nitzan,et al.  Some measures of closeness to unanimity and their implications , 1981 .

[7]  Vincent Conitzer,et al.  Aggregating preferences in multi-issue domains by using maximum likelihood estimators , 2010, AAMAS.

[8]  Piotr Faliszewski,et al.  Good Rationalizations of Voting Rules , 2010, AAAI.

[9]  Eithan Ephrati,et al.  A heuristic technique for multi‐agent planning , 1997, Annals of Mathematics and Artificial Intelligence.

[10]  Piotr Faliszewski,et al.  On distance rationalizability of some voting rules , 2009, TARK '09.

[11]  Ariel D. Procaccia,et al.  On the approximability of Dodgson and Young elections , 2009, Artif. Intell..

[12]  Atri Rudra,et al.  Ordering by weighted number of wins gives a good ranking for weighted tournaments , 2006, SODA '06.

[13]  Felix Brandt,et al.  Some Remarks on Dodgson's Voting Rule , 2009, Math. Log. Q..

[14]  H. Young.  Social Choice Scoring Functions , 1975 .

[15]  H. Young.  Extending Condorcet's rule , 1977 .

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

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

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

[19]  Ariel D. Procaccia,et al.  Socially desirable approximations for Dodgson's voting rule , 2010, EC.