Median stable matching for college admission

We give a simple and concise proof that so-called generalized median stable matchings are well-defined stable matchings for college admissions problems. Furthermore, we discuss the fairness properties of median stable matchings and conclude with two illustrative examples of college admissions markets, the lattices of stable matchings, and the corresponding generalized median stable matchings.

The stability of the equilibrium outcomes in the admission games induced by stable matching rules

A stable matching rule is used as the outcome function for the Admission game where colleges behave straightforwardly and the students` strategies are given by their preferences over the colleges. We show that the college-optimal stable matching rule implements the set of stable matchings via the Nash equilibrium (NE) concept. For any other stable matching rule the strategic behavior of the students may lead to outcomes that are not stable under the true preferences. We then introduce uncertainty about the matching selected and prove that the natural solution concept is that of NE in the strong sense. A general result shows that the random stable matching rule, as well as any stable matching rule, implements the set of stable matchings via NE in the strong sense. Precise answers are given to the strategic questions raised.

On group strategy-proof mechanisms for a many-to-one matching model

For the many-to-one matching model in which firms have substitutable and quota q-separable preferences over subsets of workers we show that the workers-optimal stable mechanism is group strategy-proof for the workers. In order to prove this result, we also show that under this domain of preferences (which contains the domain of responsive preferences of the college admissions problem) the workers-optimal stable matching is weakly Pareto optimal for the workers and the Blocking Lemma holds as well. We exhibit an example showing that none of these three results remain true if the preferences of firms are substitutable but not quota q-separable.

Manipulability in matching markets: conflict and coincidence of interests

We study comparative statics of manipulations by women in the men-proposing deferred acceptance mechanism in the two-sided one-to-one marriage market. We prove that if a group of women employs truncation strategies or weakly successfully manipulates, then all other women weakly benefit and all men are weakly harmed. We show that our results do not appropriately generalize to the many-to-one college admissions model.

Matching Markets under (In)complete Information

We are the first to introduce incomplete information to centralized many-to-one matching markets such as those to entry-level labor markets or college admissions. This is important because in real life markets (i) any agent is uncertain about the other agents' true preferences and (ii) most entry-level matching is many-to-one (and not one-to-one). We show that for stable (matching) mechanisms there is a strong and surprising link between Nash equilibria under complete information and Bayesian Nash equilibria under incomplete information. That is,given a common belief, a strategy profile is a Bayesian Nash equilibrium under incomplete information in a stable mechanism if and only if, for any true profile in the support of the common belief, the submitted profile is a Nash equilibrium under complete information at the true profile in the direct preference revelation game induced by the stable mechanism. This result may help to explain the success of stable mechanisms in these markets.

Allocation via Deferred-Acceptance under Responsive Priorities

In many economic environments - such as college admissions, student placements at public schools, and university housing allocation - indivisible objects with capacity constraints are assigned to a set of agents when each agent receives at most one object and monetary compensations are not allowed. In these important applications the agent-proposing deferred-acceptance algorithm with responsive priorities (called responsive DA-rule) performs well and economists have successfully implemented responsive DA-rules or slight variants thereof. First, for house allocation problems we characterize the class of responsive DA-rules by a set of basic and intuitive properties, namely, unavailable type invariance, individual rationality, weak non-wastefulness, resource-monotonicity, truncation invariance, and strategy-proofness. We extend this characterization to the full class of allocation problems with capacity constraints by replacing resource- monotonicity with two-agent consistent con ict resolution. An alternative characterization of responsive DA-rules is obtained using unassigned objects invariance, individual rationality, weak non-wastefulness, weak consistency, and strategy-proofness. Various characterizations of the class of "acyclic" responsive DA-rules are obtained by using the properties efficiency, group strategy-proofness, and consistency.

Strategy-proofness makes the difference: deferred-acceptance with responsive priorities

In college admissions and student placements at public schools, the admission decision can be thought of as assigning indivisible objects with capacity constraints to a set of students such that each student receives at most one object and monetary compensations are not allowed. In these important market design problems, the agent-proposing deferred-acceptance (DA-)mechanism with responsive strict priorities performs well and economists have successfully implemented DA-mechanisms or slight variants thereof. We show that almost all real-life mechanisms used in such environments - including the large classes of priority mechanisms and linear programming mechanisms - satisfy a set of simple and intuitive properties. Once we add strategy-proofness to these properties, DA-mechanisms are the only ones surviving. In market design problems that are based on weak priorities (like school choice), generally multiple tie-breaking (MTB)procedures are used and then a mechanism is implemented with the obtained strict priorities. By adding stability with respect to the weak priorities, we establish the first normative foundation for MTB-DA-mechanisms that are used in NYC.

On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets

We consider two–sided many–to–many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market. We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshuffling). We study when truncation / dropping strategies are exhaustive for a group of agents on the same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation / dropping strategies. We prove that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 1). We show that this result cannot be extended neither to group manipulations (even when all quotas equal 1 – Example 1), nor to individual manipulations when the agent’s quota is larger than 1 (even when all other agents’ quotas equal 1 – Example 2). Finally, we prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 2), i.e., independently of the quotas.

Affirmative Action Endures Three Decades of Challenges: The Pursuit of Diversity on Campus

Race and affirmative action are among the most contentious issues in higher education. This talk will explore the constitutionality of affirmative action in college admissions. What principles and technicalities are dominating the discussion, and what strategies show the most promise?

Pareto Dominance of Deferred Acceptance through Early Decision

An early decision market is governed by rules that allow each student to apply to (at most) one college and require the student to attend this college if admitted. This market is ubiquitous in college admissions in the United States. We model this market as an extensive-form game of perfect information and study a refinement of subgame perfect equilibrium (SPE) that induces undominated Nash equilibria in every subgame (SPUE). Our main result shows that this game can be used to define a decentralized matching mechanism that weakly Pareto dominates student-proposing deferred acceptance.

Pareto Dominance of Deferred Acceptance through Early Decision

An early decision market is governed by rules that allow each student to apply to (at most) one college and require the student to attend this college if admitted. This market is ubiquitous in college admissions in the United States. We model this market as an extensive-form game of perfect information and study a refinement of subgame perfect equilibrium (SPE) that induces undominated Nash equilibria in every subgame (SPUE). Our main result shows that this game can be used to define a decentralized matching mechanism that weakly Pareto dominates student-proposing deferred acceptance.

Admissions to Trinity College, Cambridge ...

"Members of Kings's hall" by A.E. Stamp: v. 1, p. [79]-140.

Candida spp. isolated from inpatients, the environment, and health practitioners in the pediatric unit at the Universitary Hospital of the Jundiaí Medical College, state of São Paulo, Brazil

INTRODUCTION: This study aimed to isolate and identify Candida spp. from the environment, health practitioners, and patients with the presumptive diagnosis of candidiasis in the Pediatric Unit at the Universitary Hospital of the Jundiaí Medical College, to verify the production of enzymes regarded as virulence factors, and to determine how susceptible the isolated samples from patients with candidiasis are to antifungal agents. METHODS: Between March and November of 2008 a total of 283 samples were taken randomly from the environment and from the hands of health staff, and samples of all the suspected cases of Candida spp. hospital-acquired infection were collected and selected by the Infection Control Committee. The material was processed and the yeast genus Candida was isolated and identified by physiological, microscopic, and macroscopic attributes. RESULTS: The incidence of Candida spp. in the environment and employees was 19.2%. The most frequent species were C. parapsilosis and C. tropicalis among the workers, C. guilliermondii and C. tropicalis in the air, C. lusitanae on the contact surfaces, and C. tropicalis and C. guilliermondii in the climate control equipment. The college hospital had 320 admissions, of which 13 (4%) presented Candida spp. infections; three of them died, two being victims of a C. tropicalis infection and the remaining one of C. albicans. All the Candida spp. in the isolates evidenced sensitivity to amphotericin B, nystatin, and fluconazole. CONCLUSIONS: The increase in the rate of hospital-acquired infections caused by Candida spp. indicates the need to take larger measures regarding recurrent control of the environment.

Candida spp. isolated from inpatients, the environment, and health practitioners in the Pediatric Unit at the Universitary Hospital of the Jundiai Medical College, State of Sao Paulo, Brazil

Introduction: This study aimed to isolate and identify Candida spp. from the environment, health practitioners, and patients with the presumptive diagnosis of candidiasis in the Pediatric Unit at the Universitary Hospital of the Jundiai Medical College, to verify the production of enzymes regarded as virulence factors, and to determine how susceptible the isolated samples from patients with candidiasis are to antifungal agents. Methods: Between March and November of 2008 a total of 283 samples were taken randomly from the environment and from the hands of health staff, and samples of all the suspected cases of Candida spp. hospital-acquired infection were collected and selected by the Infection Control Committee. The material was processed and the yeast genus Candida was isolated and identified by physiological, microscopic, and macroscopic attributes. Results: The incidence of Candida spp. in the environment and employees was 19.2%. The most frequent species were C. parapsilosis and C. tropicalis among the workers, C. guilliermondii and C. tropicalis in the air, C. lusitanae on the contact surfaces, and C. tropicalis and C. guilliermondii in the climate control equipment. The college hospital had 320 admissions, of which 13 (4%) presented Candida spp. infections; three of them died, two being victims of a C. tropicalis infection and the remaining one of C. albicans. All the Candida spp. in the isolates evidenced sensitivity to amphotericin B, nystatin, and fluconazole. Conclusions: The increase in the rate of hospital-acquired infections caused by Candida spp. indicates the need to take larger measures regarding recurrent control of the environment.