216 Jewish Hospital of St. Louis

https://digitalcommons.wustl.edu/bjc_216/1055/thumbnail.jp

Fair Allocation based on Diminishing Differences

Ranking alternatives is a natural way for humans to explain their preferences. It is being used in many settings, such as school choice, course allocations and residency matches. In some cases, several `items' are given to each participant. Without having any information on the underlying cardinal utilities, arguing about fairness of allocation requires extending the ordinal item ranking to ordinal bundle ranking. The most commonly used such extension is stochastic dominance (SD), where a bundle X is preferred over a bundle Y if its score is better according to all additive score functions. SD is a very conservative extension, by which few allocations are necessarily fair while many allocations are possibly fair. We propose to make a natural assumption on the underlying cardinal utilities of the players, namely that the difference between two items at the top is larger than the difference between two items at the bottom. This assumption implies a preference extension which we call diminishing differences (DD), where X is preferred over Y if its score is better according to all additive score functions satisfying the DD assumption. We give a full characterization of allocations that are necessarily-proportional or possibly-proportional according to this assumption. Based on this characterization, we present a polynomial-time algorithm for finding a necessarily-DD-proportional allocation if it exists. Using simulations, we show that with high probability, a necessarily-proportional allocation does not exist but a necessarily-DD-proportional allocation exists, and moreover, that allocation is proportional according to the underlying cardinal utilities. We also consider chore allocation under the analogous condition --- increasing-differences.Comment: Revised version, based on very helpful suggestions of JAIR referees. Gaps in some proofs were filled, more experiments were done, and mor

Washington University Record, November 16, 1995

https://digitalcommons.wustl.edu/record/1706/thumbnail.jp

Something New in Medical Residency Matching Markets

Worldwide medical residency markets commonly employ variants of the two-sided central clearinghouse designed by Roth and Peranson in 1999. In the NSW physiotherapy residency matching market, a one-sided and computationally efficient matching mechanism is used – the Kuhn-Munkres algorithm. The mechanism is new for medical matching markets, with no publicly known application and no existing literature. A crucial contribution of the thesis is presenting the algorithm and starting a discussion around the Kuhn-Munkres algorithm in matching. The thesis models the iterative working of the Kuhn-Munkres algorithm. I show that the Kuhn-Munkres algorithm is rank-efficient, outcome unfair, procedurally fair and not strategy-proof. Comparing the Roth-Peranson and Kuhn-Munkres algorithms on efficiency, fairness and incentive properties, the thesis concludes that there is no settled winner between the two algorithms. The competition eventually comes down to the trade-off between cost reductions and market complexities

The Communicator, October 21, 1971

The Communicator newspaper published on October 21, 1971

Lanthorn, vol. 48, no. 49, March 17, 2014

Lanthorn is Grand Valley State\u27s student newspaper, published from 1968 to the present