scholarly journals Partial ex-post verifiability and unique implementation of social choice functions

2020 ◽  
Author(s):  
Hitoshi Matsushima
Keyword(s):  
Social Choice ◽  
Choice Function ◽  
Partial Information ◽  
Social Choice Function ◽  
The State ◽  
Equilibrium Path ◽  
Choice Functions ◽  
Central Planner ◽  
Ex Post ◽  
Social Choice Functions

Abstract This study investigates the unique implementation of a social choice function in iterative dominance in the ex-post term. We assume partial ex-post verifiability; that is, after determining an allocation, the central planner can observe partial information about the state as verifiable. We demonstrate a condition of the state space, termed “full detection,” and show that with full detection, any social choice function is uniquely implementable even if the information that can be verified ex-post is very limited. To prove this, we construct a dynamic mechanism according to which each player announces his (or her) private signal, before the other players observe this signal, at an earlier stage, and each player also announces the state at a later stage. In this construction, we can impose several severe restrictions such as boundedness, permission of only tiny transfers off the equilibrium path, and no permission of transfers on the equilibrium path. This study does not assume either expected utility or quasi-linearity.

scholarly journals Local‐global equivalence in voting models: A characterization and applications

2021 ◽  
Vol 16 (4) ◽  
pp. 1195-1220
Author(s):  
Ujjwal Kumar ◽  
Souvik Roy ◽  
Arunava Sen ◽  
Sonal Yadav ◽  
Huaxia Zeng
Keyword(s):  
Social Choice ◽  
Choice Function ◽  
Social Choice Function ◽  
Choice Functions ◽  
Local Strategy ◽  
Social Choice Functions ◽  
True Type ◽  
Strategy Proof ◽  
Voting Models ◽  
Strategy Proofness

The paper considers a voting model where each voter's type is her preference. The type graph for a voter is a graph whose vertices are the possible types of the voter. Two vertices are connected by an edge in the graph if the associated types are “neighbors.” A social choice function is locally strategy‐proof if no type of a voter can gain by misrepresentation to a type that is a neighbor of her true type. A social choice function is strategy‐proof if no type of a voter can gain by misrepresentation to an arbitrary type. Local‐global equivalence (LGE) is satisfied if local strategy‐proofness implies strategy‐proofness. The paper identifies a condition on the graph that characterizes LGE. Our notion of “localness” is perfectly general. We use this feature of our model to identify notions of localness according to which various models of multidimensional voting satisfy LGE. Finally, we show that LGE for deterministic social choice functions does not imply LGE for random social choice functions.

scholarly journals Finding Strategyproof Social Choice Functions via SAT Solving

2016 ◽  
Vol 55 ◽  
pp. 565-602 ◽  
Author(s):  
Felix Brandt ◽  
Christian Geist
Keyword(s):  
Social Choice ◽  
Choice Function ◽  
Social Choice Function ◽  
Search Space ◽  
Computational Social Choice ◽  
Choice Functions ◽  
Sat Solving ◽  
Computer Aided ◽  
Research Problems ◽  
Social Choice Functions

A promising direction in computational social choice is to address research problems using computer-aided proving techniques. In particular with SAT solvers, this approach has been shown to be viable not only for proving classic impossibility theorems such as Arrow's Theorem but also for finding new impossibilities in the context of preference extensions. In this paper, we demonstrate that these computer-aided techniques can also be applied to improve our understanding of strategyproof irresolute social choice functions. These functions, however, requires a more evolved encoding as otherwise the search space rapidly becomes much too large. Our contribution is two-fold: We present an efficient encoding for translating such problems to SAT and leverage this encoding to prove new results about strategyproofness with respect to Kelly's and Fishburn's preference extensions. For example, we show that no Pareto-optimal majoritarian social choice function satisfies Fishburn-strategyproofness. Furthermore, we explain how human-readable proofs of such results can be extracted from minimal unsatisfiable cores of the corresponding SAT formulas.

A Comment on Arrow’s Impossibility Theorem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Alec Sandroni ◽  
Alvaro Sandroni
Keyword(s):  
Social Choice ◽  
Choice Function ◽  
Social Preference ◽  
Social Choice Function ◽  
Individual Preference ◽  
Impossibility Theorem ◽  
Preference Order ◽  
Individual Choice ◽  
Choice Functions ◽  
Preference Orders

AbstractArrow (1950) famously showed the impossibility of aggregating individual preference orders into a social preference order (together with basic desiderata). This paper shows that it is possible to aggregate individual choice functions, that satisfy almost any condition weaker than WARP, into a social choice function that satisfy the same condition (and also Arrow’s desiderata).

scholarly journals Functional Form of Nonmanipulable Social Choice Functions with Two Alternatives

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2827
Author(s):  
Anna De Simone ◽  
Ciro Tarantino
Keyword(s):  
Social Choice ◽  
Functional Form ◽  
Social Choice Function ◽  
Choice Functions ◽  
The Family ◽  
Social Choice Functions ◽  
Universal Domain ◽  
Infinite Set ◽  
Class Of Functions

We propose a new functional form characterization of binary nonmanipulable social choice functions on a universal domain and an arbitrary, possibly infinite, set of agents. In order to achieve this, we considered the more general case of two-valued social choice functions and describe the structure of the family consisting of groups of agents having no power to determine the values of a nonmanipulable social choice function. With the help of such a structure, we introduce a class of functions that we call powerless revealing social choice functions and show that the binary nonmanipulable social choice functions are the powerless revealing ones.

scholarly journals Implementation with ex post hidden actions

2020 ◽  
Vol 5 (1) ◽  
pp. 1-35
Author(s):  
Caleb Koch ◽  
Keyword(s):  
Social Choice ◽  
Choice Functions ◽  
Strategic Actions ◽  
Competition Models ◽  
Ex Post ◽  
Study Implementation ◽  
Social Choice Functions ◽  
Groves Mechanism ◽  
Hidden Actions ◽  
Do So

We study implementation in settings where agents take strategic actions that influence preferences over mechanism outcomes and yet are hidden from the mechanism designer. We show that such settings can arise in entry auctions for markets, and that the Vickery-Clarke-Groves mechanism is not necessarily truthful. In this paper we first formalize so-called ex post hidden actions, we then characterize social choice functions that can be implemented in a way that is robust with respect to ex post hidden actions, and finally we propose a mechanism to do so. The model allows agents to have multi-dimensional types and to have quasi-linear utilities in money. We showcase these results by identifying social choice functions that can and cannot be implemented in entry auctions for Cournot competition models.

Full Implementation under Ambiguity

2021 ◽  
Vol 13 (1) ◽  
pp. 148-178
Author(s):  
Huiyi Guo ◽  
Nicholas C. Yannelis
Keyword(s):  
Social Choice ◽  
Expected Utility ◽  
Sufficient Conditions ◽  
Choice Functions ◽  
Maxmin Expected Utility ◽  
Special Cases ◽  
Social Choice Functions ◽  
Bayesian Implementation ◽  
Pareto Efficient ◽  
Choice Set

This paper introduces the maxmin expected utility framework into the problem of fully implementing a social choice set as ambiguous equilibria. Our model incorporates the Bayesian framework and the Wald-type maxmin preferences as special cases and provides insights beyond the Bayesian implementation literature. We establish necessary and almost sufficient conditions for a social choice set to be fully implementable. Under the Wald-type maxmin preferences, we provide easy-to-check sufficient conditions for implementation. As applications, we implement the set of ambiguous Pareto-efficient and individually rational social choice functions, the maxmin core, the maxmin weak core, and the maxmin value. (JEL D71, D81, D82)

scholarly journals Self-selective social choice functions

2007 ◽  
Vol 31 (1) ◽  
pp. 129-149 ◽  
Author(s):  
Semih Koray ◽  
Arkadii Slinko
Keyword(s):  
Social Choice ◽  
Choice Functions ◽  
Social Choice Functions
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