The Price of Anarchy

 Joseph Malkevitch revisits the concept of 'Price of Anarchy' in the latest AMS feature column.

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Smart Lotteries in School Choice Ex-ante Pareto-Improvement with Ex-post Stability

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Working Paper: https://cgi.cse.unsw.edu.au/~haziz/PIRMES.pdf  Abstract: In a typical school choice application, the students have strict preferences over the schools while the schools have coarse priorities over the students based on their distance and their enrolled siblings. The outcome of a centralized admission mechanism is then usually obtained by the Deferred Acceptance (DA) algorithm with random tie-breaking. Therefore, every possible outcome of this mechanism is a stable solution for the coarse priorities that will arise with certain probability. This implies a probabilistic assignment, where the admission probability for each student-school pair is specified. In this paper, we propose a new efficiency-improving stable `smart lottery' mechanism. We aim to improve the probabilistic assignment ex-ante in a stochastic dominance sense, while ensuring that the improved random matching is still ex-post stable, meaning that it can be decomposed into stable matchings regarding the ...
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H. Aziz, B. Lee, S. Morota Chu, and J. Vollen. Proportionally Representative Clustering.  WINE 2024 .  [  Pdf  ]  In recent years, there has been a surge in effort to formalize notions of fairness in machine learning. We focus on centroid clustering— one of the fundamental tasks in unsupervised machine learning. We pro- pose a new axiom “proportionally representative fairness” (PRF) that is designed for clustering problems where the selection of centroids re- flects the distribution of data points and how tightly they are clustered together. Our fairness concept is not satisfied by existing fair cluster- ing algorithms. We design efficient algorithms to achieve PRF both for unconstrained and discrete clustering problems. Our algorithm for the unconstrained setting is also the first known polynomial-time approxi- mation algorithm for the well-studied Proportional Fairness (PF) axiom [ 13 ]. Our algorithm for the discrete setting also matches the best kn...
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