A Few Queries Go a Long Way: Information-Distortion Tradeoffs in Matching

We consider the one-sided matching problem, where n agents have preferences over n items, and these preferences are induced by underlying cardinal valuation functions. The goal is to match every agent to a single item so as to maximize the social welfare. Most of the related literature, however, assumes that the values of the agents are not a priori known, and only access to the ordinal preferences of the agents over the items is provided. Consequently, this incomplete information leads to loss of efficiency, which is measured by the notion of distortion. In this paper, we further assume that the agents can answer a small number of queries, allowing us partial access to their values. We study the interplay between elicited cardinal information (measured by the number of queries per agent) and distortion for one-sided matching, as well as a wide range of well-studied related problems. Qualitatively, our results show that with a limited number of queries, it is possible to obtain significant improvements over the classic setting, where only access to ordinal information is given.

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

[2]  Ariel D. Procaccia,et al.  Preference Elicitation For Participatory Budgeting , 2017, AAAI.

[3]  H. W. Kuhn B R Y N Mawr College.  Variants of the Hungarian Method for Assignment Problems' , 1955 .

[4]  Atila Abdulkadiro.  Matching Markets: Theory and Practice , 2010 .

[5]  Aris Filos-Ratsikas,et al.  Peeking Behind the Ordinal Curtain: Improving Distortion via Cardinal Queries , 2019, AAAI.

[6]  Kamesh Munagala,et al.  Improved Metric Distortion for Deterministic Social Choice Rules , 2019, EC.

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

[8]  Elliot Anshelevich,et al.  Tradeoffs Between Information and Ordinal Approximation for Bipartite Matching , 2018, Theory of Computing Systems.

[9]  Varsha Dani,et al.  Truthful and Near-Optimal Mechanisms for Welfare Maximization in Multi-Winner Elections , 2018, AAAI.

[10]  Lars-Gunnar Svensson.  Strategy-proof allocation of indivisible goods , 1999 .

[11]  Kamesh Munagala,et al.  Metric Distortion of Social Choice Rules: Lower Bounds and Fairness Properties , 2016, EC.

[12]  Kristoffer Arnsfelt Hansen,et al.  Truthful Facility Assignment with Resource Augmentation: An Exact Analysis of Serial Dictatorship , 2016, WINE.

[13]  E. Rowland.  Theory of Games and Economic Behavior , 1946, Nature.

[14]  S. Hart,et al.  Handbook of Game Theory with Economic Applications , 1992 .

[15]  L. S. Shapley,et al.  College Admissions and the Stability of Marriage , 2013, Am. Math. Mon..

[16]  R. Zeckhauser,et al.  The Efficient Allocation of Individuals to Positions , 1979, Journal of Political Economy.

[17]  Elliot Anshelevich,et al.  Anarchy, stability, and utopia: creating better matchings , 2009, Autonomous Agents and Multi-Agent Systems.

[18]  Elliot Anshelevich,et al.  Utilitarians Without Utilities: Maximizing Social Welfare for Graph Problems using only Ordinal Preferences - Full Version , 2018, AAAI.

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

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

[21]  David P. Woodruff,et al.  Optimal Communication-Distortion Tradeoff in Voting , 2020, EC.

[22]  Nisarg Shah,et al.  Resolving the Optimal Metric Distortion Conjecture , 2020, 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS).

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

[24]  Elliot Anshelevich,et al.  Truthful Mechanisms for Matching and Clustering in an Ordinal World , 2016, WINE.

[25]  e distortion of distributed voting∗ , 2019 .

[26]  Tim Roughgarden,et al.  Almost Envy-Freeness with General Valuations , 2017, SODA.

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

[28]  A. Roth,et al.  Two-sided matching , 1990 .

[29]  Peter Bro Miltersen,et al.  Truthful Approximations to Range Voting , 2013, WINE.

[30]  Avrim Blum,et al.  Clearing algorithms for barter exchange markets: enabling nationwide kidney exchanges , 2007, EC '07.

[31]  Hervé Moulin,et al.  A New Solution to the Random Assignment Problem , 2001, J. Econ. Theory.

[32]  Elliot Anshelevich,et al.  Awareness of Voter Passion Greatly Improves the Distortion of Metric Social Choice , 2019, WINE.

[33]  M. Utku Ünver,et al.  Matching, Allocation, and Exchange of Discrete Resources , 2009 .

[34]  Ioannis Caragiannis,et al.  Truthful mechanisms for ownership transfer with expert advice , 2018, ArXiv.

[35]  David Manlove,et al.  Matching under Preferences , 2014, Handbook of Computational Social Choice.

[36]  Siddharth Barman,et al.  Approximation Algorithms for Maximin Fair Division , 2017, EC.

[37]  P. Hall.  On Representatives of Subsets , 1935 .

[38]  David P. Woodruff,et al.  Efficient and Thrifty Voting by Any Means Necessary , 2019, NeurIPS.

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

[40]  Ruosong Wang,et al.  Efficient Near-optimal Algorithms for Barter Exchange , 2017, AAMAS.

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

[42]  Aris Filos-Ratsikas,et al.  Approximate mechanism design for distributed facility location , 2020, SAGT.

[43]  Kamesh Munagala,et al.  Random Dictators with a Random Referee: Constant Sample Complexity Mechanisms for Social Choice , 2018, AAAI.

[44]  J. Edmonds.  Paths, Trees, and Flowers , 1965, Canadian Journal of Mathematics.