
A Quantitative Version of the GibbardSatterthwaite Theorem for Three Alternatives
The GibbardSatterthwaite theorem states that every nondictatorial elec...
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Probabilistic Serial Mechanism for MultiType Resource Allocation
In multitype resource allocation (MTRA) problems, there are p ≥ 2 types...
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Random Serial Dictatorship versus Probabilistic Serial Rule: A Tale of Two Random Mechanisms
For assignment problems where agents, specifying ordinal preferences, ar...
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Multitype Resource Allocation with Partial Preferences
We propose multitype probabilistic serial (MPS) and multitype random p...
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ShapleyScarf Housing Markets: Respecting Improvement, Integer Programming, and Kidney Exchange
In a housing market of Shapley and Scarf, each agent is endowed with one...
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The Frisch–Waugh–Lovell Theorem for Standard Errors
The Frisch–Waugh–Lovell Theorem states the equivalence of the coefficien...
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A Phase Transition in Arrow's Theorem
Arrow's Theorem concerns a fundamental problem in social choice theory: ...
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The Crawler: Two Equivalence Results for Object (Re)allocation Problems when Preferences Are Singlepeaked
For object reallocation problems, if preferences are strict but otherwise unrestricted, the Top Trading Cycle rule (TTC) is the leading rule: It is the only rule satisfying efficiency, the endowment lower bound, and strategyproofness; moreover, TTC coincides with the core. However, on the subdomain of singlepeaked preferences, Bade (2019a) defines a new rule, the "crawler", which also satisfies the first three properties. Our first theorem states that the crawler and a naturally defined "dual" rule are actually the same. Next, for object allocation problems, we define a probabilistic version of the crawler by choosing an endowment profile at random according to a uniform distribution, and applying the original definition. Our second theorem states that this rule is the same as the "random priority rule" which, as proved by Knuth (1996) and Abdulkadiroglu and Sönmez (1998), is equivalent to the "core from random endowments".
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