scholarly journals Probabilistic Verification for Obviously Strategyproof Mechanisms

2018 ◽  
Author(s):  
Diodato Ferraioli ◽  
Carmine Ventre
Keyword(s):  
Social Choice ◽  
Research Agenda ◽  
Choice Function ◽  
Social Choice Function ◽  
Incentive Compatibility ◽  
Probabilistic Verification ◽  
Small Set ◽  
The Cost

Obviously strategyproof (OSP) mechanisms maintain the incentive compatibility of agents that are not fully rational. They have been object of a number of studies since their recent definition. A research agenda, initiated in [Ferraioli and Ventre, 2017], is to find a small set (possibly, the smallest) of conditions allowing to implement an OSP mechanism. To this aim, we define a model of probabilistic verification wherein agents are caught misbehaving with a certain probability, and show how OSP mechanisms can implement every social choice function at the cost of either imposing very large fines or verifying a linear number of agents.

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 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.

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