Elicitation and Approximately Stable Matching with Partial Preferences

Algorithms for stable marriage and related matching problems typically assume that full preference information is available. While the Gale-Shapley algorithm can be viewed as a means of eliciting preferences incrementally, it does not prescribe a general means for matching with incomplete information, nor is it designed to minimize elicitation. We propose the use of maximum regret to measure the (inverse) degree of stability of a matching with partial preferences; minimax regret to find matchings that are maximally stable in the presence of partial preferences; and heuristic elicitation schemes that use max regret to determine relevant preference queries. We show that several of our schemes find stable matchings while eliciting considerably less preference information than Gale-Shapley and are much more appropriate in settings where approximate stability is viable.

[1]  Thomas Brendan Murphy,et al.  Mixtures of distance-based models for ranking data , 2003, Comput. Stat. Data Anal..

[2]  J. Marden.  Analyzing and Modeling Rank Data , 1996 .

[3]  C. A. R. Hoare.  Algorithm 63: partition , 1961, CACM.

[4]  Robert W. Irving.  Stable Marriage and Indifference , 1994, Discret. Appl. Math..

[5]  R. Luce,et al.  Individual Choice Behavior: A Theoretical Analysis. , 1960 .

[6]  A. Roth.  The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory , 1984, Journal of Political Economy.

[7]  L. Lau.  Stable Matchings , 2007 .

[8]  Chi-Jen Lu,et al.  Communication Requirements for Stable Marriages , 2010, CIAC.

[9]  D. Hensher,et al.  Stated Choice Methods: Analysis and Applications , 2000 .

[10]  Alvin E. Roth,et al.  Matching and Market Design , 2008 .

[11]  R. Shepard.  Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space , 1957 .

[12]  Craig Boutilier,et al.  Minimax regret based elicitation of generalized additive utilities , 2007, UAI.

[13]  Nicole Immorlica,et al.  Two-sided matching with partial information , 2013, EC '13.

[14]  Carlos Guestrin,et al.  Riffled Independence for Ranked Data , 2009, NIPS.

[15]  Alvin E. Roth,et al.  Stable Matchings, Optimal Assignments, and Linear Programming , 1993, Math. Oper. Res..

[16]  Craig Boutilier,et al.  Learning Mallows Models with Pairwise Preferences , 2011, ICML.

[17]  Craig Boutilier,et al.  Robust Approximation and Incremental Elicitation in Voting Protocols , 2011, IJCAI.

[18]  Patrick Prosser,et al.  An Empirical Study of the Stable Marriage Problem with Ties and Incomplete Lists , 2002, ECAI.

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

[20]  C. L. Mallows.  NON-NULL RANKING MODELS. I , 1957 .

[21]  Parag A. Pathak,et al.  The Boston Public School Match , 2005 .

[22]  Toby Walsh,et al.  Local Search for Stable Marriage Problems with Ties and Incomplete Lists , 2010, PRICAI.

[23]  Yi Mao,et al.  Non-parametric Modeling of Partially Ranked Data , 2007, NIPS.

[24]  R. Duncan Luce,et al.  Individual Choice Behavior: A Theoretical Analysis , 1979 .

[25]  Larry Samuelson,et al.  Matching with Incomplete Information , 2012 .

[26]  Marina Meila,et al.  Dirichlet Process Mixtures of Generalized Mallows Models , 2010, UAI.

[27]  Toby Walsh,et al.  Stability in Matching Problems with Weighted Preferences , 2011, ICAART.

[28]  Craig Boutilier,et al.  Constraint-based optimization and utility elicitation using the minimax decision criterion , 2006, Artif. Intell..

[29]  K. Arrow,et al.  The New Palgrave Dictionary of Economics , 2020 .

[30]  Colin Camerer,et al.  Advances in behavioral economics , 2004 .

[31]  David Manlove,et al.  Stable Marriage with Incomplete Lists and Ties , 1999, ICALP.

[32]  Péter Biró,et al.  Analysis of stochastic matching markets , 2013, Int. J. Game Theory.