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on Economic Design |
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Issue of 2022‒06‒13
eight papers chosen by Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford |
| By: | Agustín G. Bonifacio (Universidad Nacional de San Luis/CONICET); Noelia Juarez (Universidad Nacional de San Luis/CONICET); Pablo Neme (Universidad Nacional de San Luis/CONICET); Jorge Oviedo (Universidad Nacional de San Luis/CONICET) |
| Abstract: | In a many-to-one matching model with responsive preferences in which indifferences are allowed, we study three notions of core, three notions of stability, and their relationships. We show that (i) the core contains the stable set, (ii) the strong core coincides with the strongly stable set, and (iii) the super core coincides with the super stable set. We also show how the core and the strong core in markets with indifferences relate to the stable matchings of their associated tie-breaking strict markets. |
| Keywords: | Matching with indifferences; Stability; Strong Stability; Super Stability; Core; Strong Core; Super Core |
| JEL: | C78 D47 |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:aoz:wpaper:138&r= |
| By: | Eric Kamwa (LC2S - Laboratoire caribéen de sciences sociales - UA - Université des Antilles - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | Preference Approval Voting (PAV) and Fallback Voting (FV) are two voting rules that combine approval and preferences. They were first introduced by Brams and Sanver (2009). Under PAV, voters rank the candidates and indicate which ones they approve of; with FV, they rank only those candidates they approve of. In this paper, we supplement the work of Brams and Sanver (2009) by exploring some other normative properties of FV and PAV. We show among other that FV and PAV satisfy and fail the same criteria; they possess two properties that AV does not: Pareto optimality and the fact of always electing the absolute Condorcet winner when he exists. For threecandidate elections and a very large electorate, we compare FV and PAV to other voting rules by evaluating the probabilities of satisfying the Condorcet majority criteria. We find that PAV performs better than the Borda rule. We also find that in terms of agreement, FV and PAV are closer to scoring rules than to Approval voting. Our analysis is performed under the Impartial Anonymous Culture assumption. |
| Keywords: | Approval Voting,Rankings,Condorcet,Properties,Impartial and Anonymous Culture |
| Date: | 2022–03–20 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03614585&r= |
| By: | Edith Elkind; Martin Lackner; Dominik Peters |
| Abstract: | Social choice becomes easier on restricted preference domains such as single-peaked, single-crossing, and Euclidean preferences. Many impossibility theorems disappear, the structure makes it easier to reason about preferences, and computational problems can be solved more efficiently. In this survey, we give a thorough overview of many classic and modern restricted preference domains and explore their properties and applications. We do this from the viewpoint of computational social choice, letting computational problems drive our interest, but we include a comprehensive discussion of the economics and social choice literatures as well. Particular focus areas of our survey include algorithms for recognizing whether preferences belong to a particular preference domain, and algorithms for winner determination of voting rules that are hard to compute if preferences are unrestricted. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.09092&r= |
| By: | Fujun Hou |
| Abstract: | I present an example in which the individuals' preferences are strict orderings, and under the majority rule, a transitive social ordering can be obtained and thus a non-empty choice set can also be obtained. However, the individuals' preferences in that example do not satisfy any conditions (restrictions) of which at least one is required by Inada (1969) for social preference transitivity under the majority rule. Moreover, the considered individuals' preferences satisfy none of the conditions of value restriction (VR), extremal restriction (ER) or limited agreement (LA), some of which is required by Sen and Pattanaik (1969) for the existence of a non-empty social choice set. Therefore, the example is an exception to a number of theorems of social preference transitivity and social choice set existence under the majority rule. This observation indicates that the collection of the conditions listed by Inada (1969) is not as complete as might be supposed. This is also the case for the collection of conditions VR, ER and LA considered by Sen and Pattanaik (1969). This observation is a challenge to some necessary conditions in the current social choice theory. In addition to seeking new conditions, one possible way to deal with this challenge may be, from a theoretical prospective, to represent the identified conditions (such as the VR, ER and LA) in terms of a common mathematical tool, and then, people may find more. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.02040&r= |
| By: | Sarvesh Bandhu (Indian Institute of Management, Bangalore); Ratul Lahkar (Ashoka University) |
| Abstract: | We consider the implementation of efficiency with minimum inequality in a large population model of negative externalities. Formally, the model is one of tragedy of the commons with the aggregate strategy at the efficient state being lower than at the Nash equilibrium. A planner can restore efficiency by imposing an externality equivalent tax and then redistribute the tax revenue as transfers to lower inequality. We characterize the transfer vector that minimizes inequality at the efficient state subject to incentive compatibility and budget balance. We then construct a mechanism that implements efficiency with minimum inequality in dominant strategies. We also show that minimizing inequality at the efficient state maximizes the minimum payoff at efficiency. But it is not equivalent to implementing the Rawlsian social choice function. |
| Date: | 2022–03–15 |
| URL: | http://d.repec.org/n?u=RePEc:ash:wpaper:76&r= |
| By: | Ahmad Awde (FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE] - ENSMM - Ecole Nationale Supérieure de Mécanique et des Microtechniques - CNRS - Centre National de la Recherche Scientifique - UTBM - Université de Technologie de Belfort-Montbeliard); Mostapha Diss (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE]); Eric Kamwa (LC2S - Laboratoire caribéen de sciences sociales - UA - Université des Antilles - CNRS - Centre National de la Recherche Scientifique); Julien Yves Rolland (LMB - Laboratoire de Mathématiques de Besançon (UMR 6623) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE] - CNRS - Centre National de la Recherche Scientifique - UB - Université de Bourgogne); Abdelmonaim Tlidi (MAE2D - Laboratory MAE2D, University of Abdelmalek Essaadi) |
| Abstract: | A candidate is said to be socially acceptable if the number of voters who rank her among the most preferred half of the candidates is at least as large as the number of voters who rank her among the least preferred half (Mahajne and Volij, 2018). For every voting profile, there always exists at least one socially acceptable candidate. This candidate may not be elected by some well-known voting rules, which may even lead in some cases to the election of a socially unacceptable candidate, the latter being a candidate such that the number of voters who rank her among the most preferred half of the candidates is strictly less than the number of voters who rank her among the least preferred half. In this paper, our contribution is twofold. First, since the existence of a socially unacceptable candidate is not always guaranteed, we determine the probabilities of the existence of such a candidate. Then, we evaluate how often the Plurality rule, the Negative Plurality rule, the Borda rule and their two-round versions can elect a socially unacceptable candidate. We perform our calculations under both the Impartial Culture and the Impartial Anonymous Culture, |
| Keywords: | Voting,Social Unacceptability,Scoring Rules,Probability |
| Date: | 2022–03–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03614587&r= |
| By: | Nikhil Agarwal; Paulo J. Somaini |
| Abstract: | Consumer choices are constrained in many markets due to either supply-side rationing or information frictions. Examples include matching markets for schools and colleges; entry-level labor markets; limited brand awareness and inattention in consumer markets; and selective admissions to healthcare services. Accounting for these choice constraints is essential for estimating consumer demand. We use a general random utility model for consumer preferences that allows for endogenous characteristics and a reduced-form choice-set formation rule that can be derived from models of the examples described above. The choice-sets can be arbitrarily correlated with preferences. We study non-parametric identification of this model, propose an estimator, and apply these methods to study admissions in the market for kidney dialysis in California. Our results establish identification of the model using two sets of instruments, one that only affects consumer preferences and the other that only affects choice sets. Moreover, these instruments are necessary for identification. We find that dialysis facilities are less likely to admit new patients when they have higher than normal caseload and that patients are more likely to travel further when nearby facilities have high caseloads. Finally, we estimate consumers' preferences and facilities' rationing rules using a Gibbs sampler. |
| JEL: | C50 I11 L0 |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:29993&r= |
| By: | Ido Bright; Arthur Delarue; Ilan Lobel |
| Abstract: | Marketplace companies rely heavily on experimentation when making changes to the design or operation of their platforms. The workhorse of experimentation is the randomized controlled trial (RCT), or A/B test, in which users are randomly assigned to treatment or control groups. However, marketplace interference causes the Stable Unit Treatment Value Assumption (SUTVA) to be violated, leading to bias in the standard RCT metric. In this work, we propose a technique for platforms to run standard RCTs and still obtain meaningful estimates despite the presence of marketplace interference. We specifically consider a matching setting, in which the platform explicitly matches supply with demand via a matching algorithm. Our proposed technique is quite simple: instead of comparing the total value accrued by the treatment and control groups, we instead compare each group's average shadow price in the matching linear program. We prove that, in the fluid limit, our proposed technique corresponds to the correct first-order approximation (in a Taylor series sense) of the value function of interest. We then use this result to prove that, under reasonable assumptions, our estimator is less biased than the RCT estimator. At the heart of our result is the idea that it is relatively easy to model interference in matching-driven marketplaces since, in such markets, the platform intermediates the spillover. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.02274&r= |