Ordinal approximation in matching and social choice

In this note, we discuss several settings in which algorithms can provide good outcomes when given only ordinal information. We focus especially on voting mechanisms in settings with spacial preferences, and on the notion of distortion.

[1]  J. Harsanyi.  Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility , 1955 .

[2]  Vincent Conitzer.  Eliciting single-peaked preferences using comparison queries , 2007, AAMAS '07.

[3]  Elliot Anshelevich,et al.  Approximating Optimal Social Choice under Metric Preferences , 2015, AAAI.

[4]  James M. Enelow,et al.  The Spatial Theory of Voting: An Introduction , 1984 .

[5]  Craig Boutilier,et al.  Optimal social choice functions: A utilitarian view , 2015, Artif. Intell..

[6]  Elliot Anshelevich,et al.  Blind, Greedy, and Random: Ordinal Approximation Algorithms for Graph Problems , 2015, ArXiv.

[7]  Elliot Anshelevich,et al.  Randomized Social Choice Functions under Metric Preferences , 2015, IJCAI.

[8]  Elliot Anshelevich,et al.  Blind, Greedy, and Random: Algorithms for Matching and Clustering Using Only Ordinal Information , 2016, AAAI.

[9]  Craig Boutilier,et al.  Incomplete Information and Communication in Voting , 2016, Handbook of Computational Social Choice.

[10]  B. Grofman,et al.  A Unified Theory of Voting: Directional and Proximity Spatial Models , 1999 .

[11]  Jie Zhang,et al.  Social Welfare in One-Sided Matchings: Random Priority and Beyond , 2014, SAGT.

[12]  Ariel D. Procaccia,et al.  The Distortion of Cardinal Preferences in Voting , 2006, CIA.

[13]  Piotr Faliszewski,et al.  Recognizing 1-Euclidean Preferences: An Alternative Approach , 2014, SAGT.

[14]  Ariel D. Procaccia,et al.  Subset Selection via Implicit Utilitarian Voting , 2016, IJCAI.

[15]  Amos Fiat,et al.  On Voting and Facility Location , 2015, EC.

[16]  Moshe Tennenholtz,et al.  Approximate mechanism design without money , 2009, EC '09.