Ordinal Efficiency, Fairness, and Incentives in Large Markets

Liu, Qingmin; Pycia, Marek

doi:10.2139/ssrn.1872713

Cited by 64 publications

(60 citation statements)

References 34 publications

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“…A mechanism fails to be SP-L if even an agent who regards the aggregate distribution of play as exogenous may wish to misreport. In the case of mechanisms with prices that are a function of the 6 For example, Liu and Pycia (2011) define a mechanism as asymptotically strategy-proof if, given > 0, there exists n 0 such that for all n ≥ n 0 , types t i , t i , and a vector of n − 1 types t −i ,…”

Section: Definition Of Sp-lmentioning

confidence: 99%

Strategy-proofness in the Large

Azevedo

Budish

2017

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We propose a criterion of approximate incentive compatibility, strategy-proofness in the large (SP-L), and argue that it is a useful second-best to exact strategyproofness (SP) for market design. Conceptually, SP-L requires that an agent who regards a mechanism's "prices" as exogenous to her report -be they traditional prices as in an auction mechanism, or price-like statistics in an assignment or matching mechanism -has a dominant strategy to report truthfully. Mathematically, SP-L weakens SP in two ways: (i) truth-telling is required to be approximately optimal (within epsilon in a large enough market) rather than exactly optimal, and (ii) incentive compatibility is evaluated ex interim, with respect to all full-support i.i.d. probability distributions of play, rather than ex post with respect to all possible realizations of play. This places SP-L in between the traditional notion of approximate strategy-proofness, which evaluates incentives to manipulate ex post, and the traditional notion of approximate Bayes-Nash incentive compatibility, which evaluates incentives to manipulate ex interim with respect to the single common-knowledge probability distribution associated with Bayes-Nash equilibrium. * First version: October 2011. We thank the editor and four anonymous referees for comments and suggestions that improved the paper considerably. We are grateful to

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Section: Definition Of Sp-lmentioning

confidence: 99%

Strategy-proofness in the Large

Azevedo

Budish

2017

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“…Particularly relevant here is the asymptotic equivalence of PS and RP along certain expansion paths of the economy with a …xed, …nite number of types of objects, while the number of copies of each object grows at roughly the same rate as the number of agents. First established in [12], this result was recently generalized in [23] to a broad class of random assignment mechanisms. However for any …xed …nite number of agents, the expected sizes achieved by PS and RP are not comparable at all preference pro…les.…”

Section: Related Literaturementioning

confidence: 99%

Size versus fairness in the assignment problem

Bogomolnaia

Moulin

2015

Games and Economic Behavior

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“…The core ideas behind the proof appeared previously in Liu and Pycia (2012), which shows that without priorities and in the large market, any mechanism that is non-atomic, strategyproof, symmetric and efficient is equivalent to the so-called probabilistic serial mechanism, or equivalently lottery-plus-cutoff with one priority class. The main difference with our result is that while their setup does not have priorities, we allow arbitrary priorities.…”

Section: A Characterization Theoremmentioning

confidence: 99%

“…Azevedo and Leshno (2010) show that this proposed improvement may yield Nash equilibria in which the outcome is Pareto-dominated by the original mechanism. Che and Kojima (2011) show that in the large market, without school priorities, the deferred acceptance algorithm with a randomized tie-breaker is equivalent to the ordinal efficient probabilistic serial mechanism, which Liu and Pycia (2012) show is equivalent in the large market to any asymptotically efficient, symmetric, and asymptotically strategyproof ordinal allocation mechanisms. These works suggest that there may be little room for improvement over the status quo in terms of individual students' welfare, given requirements of strategyproofness and fairness.…”

Section: Related Workmentioning

confidence: 99%

Improving Community Cohesion in School Choice via Correlated-Lottery Implementation

Ashlagi

Shi

2014

Operations Research

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In school choice, children submit a preference ranking over schools to a centralized assignment algorithm, which takes into account schools' priorities over children and uses randomization to break ties. One criticism of existing school choice mechanisms is that they tend to disperse communities so children do not go to school with others from their neighborhood.We suggest to improve community cohesion by implementing a correlated lottery in a given school choice mechanism:we find a convex combination of deterministic assignments that maintains the original assignment probabilities, thus maintaining choice, but improving community cohesion.To analyze the gain in cohesion for a wide class of mechanisms, we first prove the following characterization which may be of independent interest: any mechanism which, in the large market limit, is non-atomic, Bayesian incentive compatible, symmetric and efficient within each priority class, is a "lottery-plus-cutoff" mechanism. This means that the large market limit can be described as follows: given the distribution of preferences, every student receives an identically distributed lottery number, every school sets a lottery cutoff for each priority class, and a student is assigned her most preferred school for which she meets the cutoff. This generalizes Liu and Pycia (2012) to allow arbitrary priorities. Using this, we derive analytic expressions for maximum cohesion under a large market approximation. We show that the benefit of lottery-correlation is greater when students' preferences are more correlated.In practice, although the correlated-lottery implementation problem is NP-hard, we present a heuristic that does well.We apply this to real data from Boston elementary school choice 2012 and find that we can increase cohesion by 79% for K1 and 37% for K2 new families. Greater cohesion gain is possible (tripling cohesion for K1 and doubling for K2) if we reduce the choice menus on top of applying lottery-correlation.

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Ordinal Efficiency, Fairness, and Incentives in Large Markets

Cited by 64 publications

References 34 publications

Strategy-proofness in the Large

Strategy-proofness in the Large

Size versus fairness in the assignment problem

Improving Community Cohesion in School Choice via Correlated-Lottery Implementation

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