7,953 research outputs found

    Matching under Preferences

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    Matching theory studies how agents and/or objects from different sets can be matched with each other while taking agents\u2019 preferences into account. The theory originated in 1962 with a celebrated paper by David Gale and Lloyd Shapley (1962), in which they proposed the Stable Marriage Algorithm as a solution to the problem of two-sided matching. Since then, this theory has been successfully applied to many real-world problems such as matching students to universities, doctors to hospitals, kidney transplant patients to donors, and tenants to houses. This chapter will focus on algorithmic as well as strategic issues of matching theory. Many large-scale centralized allocation processes can be modelled by matching problems where agents have preferences over one another. For example, in China, over 10 million students apply for admission to higher education annually through a centralized process. The inputs to the matching scheme include the students\u2019 preferences over universities, and vice versa, and the capacities of each university. The task is to construct a matching that is in some sense optimal with respect to these inputs. Economists have long understood the problems with decentralized matching markets, which can suffer from such undesirable properties as unravelling, congestion and exploding offers (see Roth and Xing, 1994, for details). For centralized markets, constructing allocations by hand for large problem instances is clearly infeasible. Thus centralized mechanisms are required for automating the allocation process. Given the large number of agents typically involved, the computational efficiency of a mechanism's underlying algorithm is of paramount importance. Thus we seek polynomial-time algorithms for the underlying matching problems. Equally important are considerations of strategy: an agent (or a coalition of agents) may manipulate their input to the matching scheme (e.g., by misrepresenting their true preferences or underreporting their capacity) in order to try to improve their outcome. A desirable property of a mechanism is strategyproofness, which ensures that it is in the best interests of an agent to behave truthfully

    Two-Sided Matching for mentor-mentee allocations—Algorithms and manipulation strategies

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    In scenarios where allocations are determined by participant’s preferences, Two-Sided Matching is a well-established approach with applications in College Admissions, School Choice, and Mentor-Mentee matching problems. In such a context, participants in the matching have preferences with whom they want to be matched with. This article studies two important concepts in Two-Sided Matching: multiple objectives when finding a solution, and manipulation of preferences by participants. We use real data sets from a Mentor-Mentee program for the evaluation to provide insight on realistic effects and implications of the two concepts. In the first part of the article, we consider the quality of solutions found by different algorithms using a variety of solution criteria. Most current algorithms focus on one criterion (number of participants matched), while not directly taking into account additional objectives. Hence, we evaluate different algorithms, including multi-objective heuristics, and the resulting trade-offs. The evaluation shows that existing algorithms for the considered problem sizes perform similarly well and close to the optimal solution, yet multi-objective heuristics provide the additional benefit of yielding solutions with better quality on multiple criteria. In the second part, we consider the effects of different types of preference manipulation on the participants and the overall solution. Preference manipulation is a concept that is well established in theory, yet its practical effects on the participants and the solution quality are less clear. Hence, we evaluate the effects of three manipulation strategies on the participants and the overall solution quality, and investigate if the effects depend on the used solution algorithm as well

    Supervised Visitation and Monitored Exchange: Review of the Literature and Annotated Bibliography

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    Though courts increasingly rely on supervised visitation services in custody disputes and child welfare cases (Salem, Kulak, & Deutsch, 2007), a search of the literature produces few studies reporting empirically validated aspects of supervised visitation programs. The current literature about supervised visitation extensively documents the rationale for providing the service and contains numerous descriptions of provider programs (Birnbaum & Alaggia, 2006). The next generation of research must focus on long-term outcomes that demonstrate effectiveness of supervised visitation programs (Birnbaum & Alaggia, 2006). This project involves a review of the literature concerning supervised visitation and child access services. The intent of the research is to summarize best practices supported by empirical evidence. It identifies emerging trends, issues, and gaps in the relevant literature. It also integrates the best practices analysis with recommendations for further consideration by the leadership of the Maryland Judiciary
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