On Two Kinds of Manipulation for School Choice Problems

Many school districts in the US employ centralized clearing houses for the placement of students to public schools. A popular mechanism from two-sided matching theory, the Gale-Shapley student- optimal stable mechanism, has recently replaced two defi…cient mechanisms that were in use in NYC and Boston. An important potential threat against any school choice mechanism is the tendency of schools to circumvent the procedure via two kinds of strategic manipulations introduced by Sönmez (1997, 1999): manipulation via underreporting capacities and manipulation via pre-arranged matches. This paper studies the extent of the vulnerability of a school choice mechanism, and in particular, that of the student-optimal stable mechanism, to the two manipulations, and identifi…es conditions under which they can be avoided

School Choice with Consent

An increasingly popular practice for student assignment to public schools in the U.S. is the use of school choice systems. The celebrated Gale-Shapley student-optimal stable mechanism (SOSM) has recently replaced two de…ficient student assignment mechanisms that were in use in New York City and Boston. We provide theoretical evidence that the SOSM outcome may produce large welfare losses. Then we propose an efficiency adjusted deferred acceptance mechanism (EADAM) that allows a student to consent to waive a certain priority that has no effect on his assignment. Under EADAM a consenting student causes himself no harm, but may help many others bene…fit as a consequence. We show that EADAM can recover any welfare losses due to SOSM while also preserving immunity against strategic behavior in a particular way. It is also possible to use EADAM to eliminate welfare losses due to randomly breaking ties in student priorities.

Why Do Popular Mechanisms Lack Efficiency in Random Environments?

We consider the problem of randomly assigning n indivisible objects to n agents. Recent research introduced a promising mechanism, the probabilistic serial that has superior efficiency properties than the most common real-life mechanism random priority. On the other hand, mechanisms based on Gale's celebrated top trading cycles method have long dominated the indivisible goods literature (with the exception of the present context) thanks to their outstanding efficiency features. We present an equivalence result between the three kinds of mechanisms, that may help better understand why efficiency differences among popular mechanisms might arise in random environments. This result also suggests that the probabilistic serial and the random priority mechanisms can be viewed as two top trading cycles based mechanisms that essentially differ in the initial conditions of the market before trading starts

On-Campus Housing: Theory vs. Experiment

Many universities in the US offer on-campus housing opportunities to incoming as well as already enrolled students. Recent research has theoretically as well as experimentally shown that the most common student assignment mechanism used in the US is subject to serious efficiency losses. In this paper we fi…rst show that a particular mechanism which is currently in use at the MIT for about two decades is in fact equivalent to a natural adaptation of the well-known Gale-Shapley mechanism of two-sided matching theory. Motivated from the increasing popularity and success of the Gale-Shapley mechanism in a number of markets, we next experimentally compare the performances of the MIT mechanism with that of the leading theory mechanism Top Trading Cycles. Contrary to theory, the MIT mechanism performs better in terms of efficiency and participation rates, while we observe no signi…ficant difference between the two mechanisms in terms of truth-telling rates

Matching Markets with Mixed Ownership: The Case for A Real-life Assignment Mechanism

We consider a common indivisible good allocation problem in which agents have both social and private endowments. Popular applications include student assignment to on-campus housing, kidney exchange, and particular school choice problems. In a series of experiments Chen and Sönmez (American Economic Review 92: 1669-1686, 2002) have shown that a popular mechanism from recent theory, the Top Trading Cycles (TTC) mechanism, induces a significantly higher participation rate by agents with private endowments and leads to significantly more efficient outcomes than the most commonly used real-life mechanism, the Random Serial Dictatorship with Squatting Rights We first show that a particular mechanism, the so-called New House 4 (NH4) mechanism, which has been in use at MIT since the 1980s, is in fact outcome-equivalent to a natural adaptation of the well-known Gale-Shapley mechanism of two-sided matching theory. This implies that the NH4 mechanism is the most efficient mechanism within the class of fair and individually rational mechanisms, and that it is essentially the only incentive compatible mechanism satisfying the two properties. We then experimentally compare NH4 and TTC. We find that under NH4, the participation rate is significantly higher than under TTC. We also propose a new efficiency test based on ordinal preference information and show that NH4 also outperforms TTC in terms of efficiency.</p

The Pareto Dominant Strategy-Proof and Equitable Rule for Problems with Indivisible Goods

We study the problem of allocating indivisible goods to agents when monetary compensations are not allowed. Our central requirements are strategy-proofness and equity. For each of two different cases of this problem we identify a strategy-proof and equitable [in the sense of equal-treatment-of-equals, or envy-freeness] rule that Pareto dominates all other equitable and strategy-proof rules

The Pennsylvania Adoption Exchange Improves Its Matching Process

he Pennsylvania Adoption Exchange (PAE) helps case workers representing children in state custody by recommending prospective families for adoption. We describe PAE's operational challenges using case worker surveys and a regression analysis of data on child outcomes over multiple years. Using a discrete-event simulation of PAE, we justify the value of a statewide adoption network and demonstrate the importance of the family preference information quality on the percentage of children who successfully nd adoptive placements. Finally, we detail a series of simple improvements implemented by PAE to increase the adoptive placement rate through collecting more valuable information, improving the family ranking algorithm, and aligning incentives for families to provide useful preference information.</p