scholarly journals School Choice with Flexible Diversity Goals and Specialized Seats

2021 ◽  
Author(s):  
Haris Aziz ◽  
Zhaohong Sun
Keyword(s):  
Decision Making ◽  
School Choice ◽  
Public Housing ◽  
General Model ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Clear Understanding ◽  
Scarce Resources ◽  
Multi Agent ◽  
Housing Allocation

We present a new and rich model of school choice with flexible diversity goals and specialized seats. The model also applies to other settings such as public housing allocation with diversity objectives. Our method of expressing flexible diversity goals is also applicable to other settings in moral multi-agent decision making where competing policies need to be balanced when allocating scarce resources. For our matching model, we present a polynomial-time algorithm that satisfies desirable properties, including strategyproofness and stability under several natural subdomains of our problem. We complement the results by providing a clear understanding about what results do not extend when considering the general model.

scholarly journals Fair Allocation based on Diminishing Differences

2017 ◽  
Author(s):  
Erel Segal-Halevi ◽  
Haris Aziz ◽  
Avinatan Hassidim
Keyword(s):  
School Choice ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Conservative Extension ◽  
Score Functions ◽  
Full Characterization ◽  
Proportional Allocation ◽  
The Difference ◽  
Natural Way

Ranking alternatives is a natural way for humans to explain their preferences. It is being used in many settings, such as school choice (NY, Boston), Course allocations, and the Israeli medical lottery. In some cases (such as the latter two), several ``items'' are given to each participant. Without having any information on the underlying cardinal utilities, arguing about fairness of allocation requires extending the ordinal item ranking to ordinal bundle ranking. The most commonly used such extension is stochastic dominance (SD), where a bundle X is preferred over a bundle Y if its score is better according to all additive score functions. SD is a very conservative extension, by which few allocations are necessarily fair while many allocations are possibly fair. We propose to make a natural assumption on the underlying cardinal utilities of the players, namely that the difference between two items at the top is larger than the difference between two items at the bottom. This assumption implies a preference extension which we call diminishing differences (DD), where a X is preferred over Y if its score is better according to all additive score functions satisfying the DD assumption. We give a full characterization of allocations that are necessarily-proportional or possibly-proportional according to this assumption. Based on this characterization, we present a polynomial-time algorithm for finding a necessarily-DD-proportional allocation if it exists. Using simulations, we show that with high probability, a necessarily-proportional allocation does not exist but a necessarily-DD-proportional allocation exists, and moreover, that allocation is proportional according to the underlying cardinal utilities.

scholarly journals What's the Matter with Tie-Breaking? Improving Efficiency in School Choice

2008 ◽  
Vol 98 (3) ◽  
pp. 669-689 ◽  
Author(s):  
Aytek Erdil ◽  
Haluk Ergin
Keyword(s):  
United States ◽  
School Choice ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
The United States ◽  
Stable Mechanism ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Stable Improvement

In several school choice districts in the United States, the student proposing deferred acceptance algorithm is applied after indifferences in priority orders are broken in some exogenous way. Although such a tie-breaking procedure preserves stability, it adversely affects the welfare of the students since it introduces artificial stability constraints. Our main finding is a polynomial-time algorithm for the computation of a student-optimal stable matching when priorities are weak. The idea behind our construction relies on a new notion which we call a stable improvement cycle. We also investigate the strategic properties of the student-optimal stable mechanism. (JEL C78, D82, I21)

scholarly journals Fair Allocation with Diminishing Differences

2020 ◽  
Vol 67 ◽  
Author(s):  
Erel Segal-Halevi ◽  
Avinatan Hassidim ◽  
Haris Aziz
Keyword(s):  
School Choice ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Conservative Extension ◽  
Score Functions ◽  
Full Characterization ◽  
Proportional Allocation ◽  
The Difference ◽  
Natural Way

Ranking alternatives is a natural way for humans to explain their preferences. It is used in many settings, such as school choice, course allocations and residency matches. Without having any information on the underlying cardinal utilities, arguing about the fairness of allocations requires extending the ordinal item ranking to ordinal bundle ranking. The most commonly used such extension is stochastic dominance (SD), where a bundle X is preferred over a bundle Y if its score is better according to all additive score functions. SD is a very conservative extension, by which few allocations are necessarily fair while many allocations are possibly fair. We propose to make a natural assumption on the underlying cardinal utilities of the players, namely that the difference between two items at the top is larger than the difference between two items at the bottom. This assumption implies a preference extension which we call diminishing differences (DD), where X is preferred over Y if its score is better according to all additive score functions satisfying the DD assumption. We give a full characterization of allocations that are necessarily-proportional or possibly-proportional according to this assumption. Based on this characterization, we present a polynomial-time algorithm for finding a necessarily-DD-proportional allocation whenever it exists. Using simulations, we compare the various fairness criteria in terms of their probability of existence, and their probability of being fair by the underlying cardinal valuations. We find that necessary-DD-proportionality fares well in both measures. We also consider envy-freeness and Pareto optimality under diminishing-differences, as well as chore allocation under the analogous condition --- increasing-differences.

Learning Importance of Preferences

10.29007/v68w ◽  
2018 ◽  
Author(s):  
Ying Zhu ◽  
Mirek Truszczynski
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Scoring Rules ◽  
Np Hard ◽  
Individual Preferences

We study the problem of learning the importance of preferences in preference profiles in two important cases: when individual preferences are aggregated by the ranked Pareto rule, and when they are aggregated by positional scoring rules. For the ranked Pareto rule, we provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decides all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples (also under the ranked Pareto rule) is NP-hard. We obtain similar results for the case of weighted profiles when positional scoring rules are used for aggregation.

The Oxford Handbook of Impulse Control Disorders

2012 ◽  
Keyword(s):  
Decision Making ◽  
Impulse Control ◽  
Treatment Options ◽  
Impulse Control Disorders ◽  
Clear Understanding ◽  
Intermittent Explosive Disorder ◽  
Normal Behavior ◽  
Assessment And Treatment ◽  
Decision Making Processes ◽  
Psychopathological Disorders

Impulsivity, to varying degrees, is what underlies human behavior and decision-making processes. As such, a thorough examination of impulsivity allows us to better understand modes of normal behavior and action as well as a range of related psychopathological disorders, including kleptomania, pyromania, trichotillomania, intermittent explosive disorder, and pathological gambling—disorders grouped under the term "impulse control disorders" (ISDs). Recent efforts in the areas of cognitive psychology, neurobiology, and genetics have provided a greater understanding of these behaviors and given way to improved treatment options. The Oxford Handbook of Impulse Control Disorders provides a clear understanding of the developmental, biological, and phenomenological features of a range of ICDs, as well as detailed approaches to their assessment and treatment. Bringing together founding ICD researchers and leading experts from psychology and psychiatry, this volume reviews the biological underpinnings of impulsivity and the conceptual challenges facing clinicians as they treat individuals with ICDs.

scholarly journals Metric Dimension Parameterized By Treewidth

Algorithmica ◽  
2021 ◽  
Author(s):  
Édouard Bonnet ◽  
Nidhi Purohit
Keyword(s):  
Computable Function ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Minimum Size ◽  
Metric Dimension ◽  
Resolving Set ◽  
Input Graph ◽  
Outerplanar Graphs ◽  
Bounded Treewidth ◽  
Fpt Algorithm

AbstractA resolving set S of a graph G is a subset of its vertices such that no two vertices of G have the same distance vector to S. The Metric Dimension problem asks for a resolving set of minimum size, and in its decision form, a resolving set of size at most some specified integer. This problem is NP-complete, and remains so in very restricted classes of graphs. It is also W[2]-complete with respect to the size of the solution. Metric Dimension has proven elusive on graphs of bounded treewidth. On the algorithmic side, a polynomial time algorithm is known for trees, and even for outerplanar graphs, but the general case of treewidth at most two is open. On the complexity side, no parameterized hardness is known. This has led several papers on the topic to ask for the parameterized complexity of Metric Dimension with respect to treewidth. We provide a first answer to the question. We show that Metric Dimension parameterized by the treewidth of the input graph is W[1]-hard. More refinedly we prove that, unless the Exponential Time Hypothesis fails, there is no algorithm solving Metric Dimension in time $$f(\text {pw})n^{o(\text {pw})}$$ f ( pw ) n o ( pw ) on n-vertex graphs of constant degree, with $$\text {pw}$$ pw the pathwidth of the input graph, and f any computable function. This is in stark contrast with an FPT algorithm of Belmonte et al. (SIAM J Discrete Math 31(2):1217–1243, 2017) with respect to the combined parameter $$\text {tl}+\Delta$$ tl + Δ , where $$\text {tl}$$ tl is the tree-length and $$\Delta$$ Δ the maximum-degree of the input graph.

scholarly journals Spending Political Capital*

2021 ◽  
Author(s):  
Arthur Campbell
Keyword(s):  
Decision Making ◽  
Incentive Contracts ◽  
Important Task ◽  
Political Capital ◽  
Alternative Mechanism ◽  
Team Size ◽  
Current Period ◽  
Multi Agent ◽  
Participation In Decision Making ◽  
Number Of Individuals

Abstract An important task for organizations is establishing truthful communication between parties with differing interests. This task is made particularly challenging when the accuracy of the information is poorly observed or not at all. In these settings, incentive contracts based on the accuracy of information will not be very effective. This paper considers an alternative mechanism that does not require any signal of the accuracy of any information communicated to provide incentives for truthful communication. Rather, an expert sacrifices future participation in decision-making to influence the current period’s decision in favour of their preferred project. This mechanism captures a notion often described as ‘political capital’ whereby an individual is able to achieve their own preferred decision in the current period at the expense of being able to exert influence in future decisions (‘spending political capital’). When the first-best is not possible in this setting, I show that experts hold more influence than under the first-best and that, in a multi-agent extension, a finite team size is optimal. Together these results suggest that a small number of individuals hold excessive influence in organizations.

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