nep-des New Economics Papers
on Economic Design
Issue of 2020‒08‒31
seven papers chosen by
Alex Teytelboym
University of Oxford

  1. Blocking Pairs versus Blocking Students : Stability Comparisons in School Choice By Battal Dogan; Lars Ehlers
  2. Two-Stage Majoritarian Choice By Sean Horan; Yves Sprumont
  3. Strategy-proof Choice under Monotonic Additive Preferences By Eric Bahel; Yves Sprumont
  4. Geometry of anonymous binary social choices that are strategy-proof By Achille Basile; Surekha Rao; K. P. S. Bhaskara Rao
  5. Equilibrium Design by Coarse Correlation in Quadratic Games By Trivikram Dokka Venkata Satyanaraya; Herve Moulin; Indrajit Ray; Sonali Sen Gupta
  6. Stable source connection and assignment problems as multi-period shortest path problems By Streekstra, Leanne; Trudeau, Christian
  7. The acceptability of lotteries in allocation problems By Elias Bouacida; Renaud Foucart

  1. By: Battal Dogan (University of Bristol); Lars Ehlers (Université de Montréal and CIREQ)
    Abstract: It is known that there are school choice problems without an efficient and stable assignment. We consider comparing assignments in terms of their stability by comparing their sets of blocking (student-school) pairs or comparing their sets of blocking students who are involved in at least one blocking pair. Although there always exists a Pareto improvement over the student-optimal stable (DA) assignment which is minimally unstable among efficient assignments when the stability comparison is based on comparing the sets of blocking pairs in the set-inclusion sense, we show that this is not necessarily true when the stability comparison is based on comparing the sets of blocking pairs in the cardinal sense, or when it is based on comparing sets of blocking students (in the set-inclusion or cardinal sense). Given the latter impossibilities, we characterize the priority profiles where there exists a Pareto improvement over the DA mechanism which is cardinally minimally stable among efficient assignments when counting blocking pairs or counting blocking students. The resulting domain restrictions suggest to take with caution school choice analysis which relies on a particular stability comparison method.
    Keywords: school choice, stability comparisons, minimal instability, deferred acceptance
    JEL: C70 D47 D61 D63
    Date: 2020–04
  2. By: Sean Horan (Université de Montréal and CIREQ); Yves Sprumont (Université de Montréal and CIREQ)
    Abstract: We propose a class of decisive collective choice rules that rely on an exogenous linear ordering to partition the majority relation into two acyclic relations. The first relation is used to obtain a shortlist of the feasible alternatives while the second is used to make a final choice. In combination with faithfulness to the underlying majority relation, rules in this class are characterized by two desirable rationality properties: Sen’s expansion consistency and a version of Manzini and Mariotti’s weak WARP. The rules also satisfy natural adaptations of Arrow’s independence of irrelevant alternatives and May’s positive responsiveness.
    Keywords: majority rule, decisiveness, IIA, monotonicity, rational shortlist methods
    JEL: D71 D72
    Date: 2020–05
  3. By: Eric Bahel (Virginia Polytechnic Institute and State University, Blacksburg, VA); Yves Sprumont (Université de Montréal and CIREQ)
    Abstract: We describe the class of strategy-proof mechanisms for choosing sets of objects when preferences are additive and monotonic.
    JEL: D71
    Date: 2020–05
  4. By: Achille Basile; Surekha Rao; K. P. S. Bhaskara Rao
    Abstract: Let $V$ be society whose members express preferences about two alternatives, indifference included. Identifying anonymous binary social choice functions with binary functions $f=f(k,m)$ defined over the integer triangular grid $G=\{(k,m)\in \mathbb{N}_0\times\mathbb{N}_0 : k+m\le |V|\} $, we show that every strategy-proof, anonymous social choice function can be described geometrically by listing, in a sequential manner, groups of segments of G, of equal (maximum possible) length, alternately horizontal and vertical, representative of preference profiles that determine the collective choice of one of the two alternatives. Indeed, we show that every function which is anonymous and strategy-proof can be described in terms of a sequence of nonnegative integers $(q_1, q_2, \cdots, q_s)$ corresponding to the cardinalities of the mentioned groups of segments. We also analyze the connections between our present representation with another of our earlier representations involving sequences of majority quotas. A Python code is available with the authors for the implementation of any such social choice function.
    Date: 2020–08
  5. By: Trivikram Dokka Venkata Satyanaraya; Herve Moulin; Indrajit Ray; Sonali Sen Gupta
    Abstract: In a public good provision or a public bad abatement situation, the non-cooperative interplay of the participants typically results in low levels of provision or abatement. In the familiar class of n-person quadratic games, we show that Coarse Correlated equilibria (CCEs) - simple mediated communication devices that do not alter the strategic structure of the game - can significantly outperform the Nash equilibrium in terms of the policy objective above.
    Keywords: Quadratic game, Coarse correlated equilibrium, Abatement level, Efficiency gain
    JEL: C72 Q52
    Date: 2020
  6. By: Streekstra, Leanne (Department of Business and Economics); Trudeau, Christian (Department of Economics)
    Abstract: We extend the familiar shortest path problem by supposing that agents have demands over multiple periods. This potentially allows agents to combine their paths if their demands are complementary; for instance if one agent only needs a connection to the source in the summer while the other requires it only in the winter. We show that the resulting cost sharing problem always has a non-empty core, regardless of the number of agents and periods, the cost structure or the demand profile. We then exploit the fact that the model encompasses many well-studied problems to obtain or reobtain non-vacuity results for the cores of source-connection problems, (m-sided) assignment problems and minimum coloring problems.
    Keywords: Shortest path; demand over multiple periods; cooperative game; core; source-connection; assignment
    JEL: C71 D63
    Date: 2020–08–19
  7. By: Elias Bouacida; Renaud Foucart
    Abstract: We report the results of two experiments on the social acceptability of random devices in allocation mechanisms. A majority of subjects do not opt for a lottery if they can rationalize an alternative mechanism as non-random. It is, however, possible to design a payoff-equivalent mechanism to the lottery that is more acceptable. Our results shed light on the real-world reliance on obscure criteria in allocation problems where lotteries seem to be simpler and more efficient.
    Keywords: lotteries, mechanism design
    JEL: D01 D78 D91
    Date: 2020

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