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Full-Text Articles in Social and Behavioral Sciences
Decomposability And Strategy-Proofness In Multidimensional Models, Shurojit Chatterji, Huaxia Zeng
Decomposability And Strategy-Proofness In Multidimensional Models, Shurojit Chatterji, Huaxia Zeng
Research Collection School Of Economics
We introduce the notion of a multidimensional hybrid preference domain on a (finite) set of alternatives that is a Cartesian product of finitely many components. We demonstrate that in a model of public goods provision, multidimensional hybrid preferences arise naturally through assembling marginal preferences under the condition of semi-separability - a weakening of separability. The main result shows that under a suitable “richness” condition, every strategy-proof rule on this domain can be decomposed into component-wise strategy-proof rules, and more importantly every domain of preferences that reconciles decomposability of rules with strategy-proofness must be a multidimensional hybrid domain.
Local Dominance, Emiliano Catonini, Jingyi Xue
Local Dominance, Emiliano Catonini, Jingyi Xue
Research Collection School Of Economics
We define notions of dominance between two actions in a dynamic game. Local dominance considers players who have a blurred view of the future and compare the two actions by first focusing on the outcomes that may realize at the current stage. When considering the possibility that the game may continue, they can only check that the local comparison is not overturned under the assumption of "continuing in the same way" after the two actions (in a newly defined sense). Despite the lack of forward planning, local dominance solves dynamic mechanisms that were found easy to play and implements social …
A Taxonomy Of Non-Dictatorial Unidimensional Domains, Shurojit Chatterji, Huaxia Zeng
A Taxonomy Of Non-Dictatorial Unidimensional Domains, Shurojit Chatterji, Huaxia Zeng
Research Collection School Of Economics
Non-dictatorial preference domains allow the design of unanimous social choice functions (henceforth, rules) that are non-dictatorial and strategy-proof. On a class of preference domains called unidimensional domains, we show that the unique seconds property characterizes all non-dictatorial domains. Subsequently, we provide an exhaustive classification of all non-dictatorial, unidimensional domains, based on a simple property of two-voter rules called invariance. The domains constituting the classification are semi-single-peaked domains and semi-hybrid domains (introduced here) which are two appropriate weakenings of single-peaked domains and shown to allow strategy-proof rules to depend on non-peak information of voters' preferences; the canonical strategy-proof rules for these …
Mechanism Design By Observant And Informed Planners, Shurojit Chatterji, Arunava Sen
Mechanism Design By Observant And Informed Planners, Shurojit Chatterji, Arunava Sen
Research Collection School Of Economics
We study the mechanism design problem where the planner can observe ex-post the first-ranked alternatives or peaks of voter preferences. We contrast this with the design problem where the planner has ex-ante information regarding the peaks of voter preferences.
On Strategy-Proofness And The Salience Of Single-Peakedness In A Private Goods Economy, Shurojit Chatterji, Masso Jordi, Serizawa Shigehiro
On Strategy-Proofness And The Salience Of Single-Peakedness In A Private Goods Economy, Shurojit Chatterji, Masso Jordi, Serizawa Shigehiro
Research Collection School Of Economics
We consider strategy-proof rules operating on a rich domain of preference profiles in a set up where multiple private goods have to be assigned to a set of agents with entitlements where preferences display satiation. We show that if the rule is in addition "desirable", in that it is tops-only, continuous, same-sided and individually rational with respect to the entitlements, then the preferences in the domain have to satisfy a variant of single-peakedness (referred to as smilattice single-peakedness). We also provide a converse of this main finding. It turns our that this domain coincides with the one already identified in …
A Taxonomy Of Non-Dictatorial Domains, Shurojit Chatterji, Huaxia Zeng
A Taxonomy Of Non-Dictatorial Domains, Shurojit Chatterji, Huaxia Zeng
Research Collection School Of Economics
We provide an exhaustive classification of all preference domains that allow the design of unanimous social choice functions (henceforth, rules) that are non-dictatorial and strategy-proof. This taxonomy is based on a richness assumption and employs a simple property of two-voter rules called invariance. The preference domains that form the classification are semi-single-peaked domains (introduced by Chatterji et al. (2013)) and semi-hybrid domains (introduced here) which are two appropriate weakenings of the single-peaked domains, and which, more importantly, are shown to allow strategy-proof rules to depend on non-peak information of voters’ preferences. As a refinement of the classification, single-peaked domains and …
Restricted Probabilistic Fixed Ballot Rules And Hybrid Domains, Shurojit Chatterji, Souvik Roy, Soumyarup Sadhukhan, Arunava Sen, Huaxia Zeng
Restricted Probabilistic Fixed Ballot Rules And Hybrid Domains, Shurojit Chatterji, Souvik Roy, Soumyarup Sadhukhan, Arunava Sen, Huaxia Zeng
Research Collection School Of Economics
We study Random Social Choice Functions (or RSCFs) in a standard ordinal mech-anism design model. We introduce a new preference domain called a hybrid domain which includes as special cases as the complete domain and the single-peaked domain. We characterize the class of unanimous and strategy-proof RSCFs on these domains and refer to them as Restricted Probabilistic Fixed Ballot Rules (or RPFBRs). These RSCFs are not necessarily decomposable, i.e., cannot be written as a convex combina-tion of their deterministic counterparts. We identify a necessary and sufficient condition under which decomposability holds for anonymous RPFBRs. Finally, we provide an axiomatic justification …
On Strategy-Proofness And The Salience Of Single-Peakedness, Shurojit Chatterji, Jordi Masso
On Strategy-Proofness And The Salience Of Single-Peakedness, Shurojit Chatterji, Jordi Masso
Research Collection School Of Economics
We consider strategy-proof social choice functions operating on a rich domain of preference profiles. We show that if the social choice function satisfies in addition tops-onlyness, anonymity and unanimity then the preferences in the domain have to satisfy a variant of single-peakedness (referred to as semilattice single-peakedness). We do so by deriving from the social choice function an endogenous partial order (a semilattice) from which the notion of a semilattice single-peaked preference can be defined. We also provide a converse of this main finding. Finally, we show how well-known restricted domains under which nontrivial strategy-proof social choice functions are admissible …
On Random Social Choice Functions With The Tops-Only Property, Shurojit Chatterji, Huaxia Zeng
On Random Social Choice Functions With The Tops-Only Property, Shurojit Chatterji, Huaxia Zeng
Research Collection School Of Economics
We study the standard voting model with randomization. A Random Social Choice Function (or RSCF) satisfies the tops-only property if the social lottery under each preference profile depends only on the peaks of voters' preferences. We identify a general condition on domains of preferences (the Interior Property and the Exterior Property) which ensures that every strategy-proof RSCF satisfying unanimity has the tops-only property. We show that our condition applies to important classes of voting domains which include restricted connected domains (Sato, 2013) and the multi-dimensional single-peaked domain (Barberà et al., 1993). As an application of our result, we show that …
On Random Social Choice Functions With The Tops-Only Property, Shurojit Chatterji, Huaxia Zeng
On Random Social Choice Functions With The Tops-Only Property, Shurojit Chatterji, Huaxia Zeng
Research Collection School Of Economics
We study the standard voting model with randomization. A Random Social Choice Function (or RSCF) satisfies the tops-only property if the social lottery under each preference profile depends only on the peaks of voters' preferences. We identify a general condition on domains of preferences (the Interior Property and the Exterior Property) which ensures that every strategy-proof RSCF satisfying unanimity has the tops-only property. We show that our condition applies to important classes of voting domains which include restricted connected domains (Sato, 2013) and the multi-dimensional single-peaked domain (Barberà et al., 1993). As an application of our result, we show that …
A Characterization Of Single-Peaked Preferences Via Random Social Choice Functions, Shurojit Chatterji, Arunava Sen, Huaxia Zeng
A Characterization Of Single-Peaked Preferences Via Random Social Choice Functions, Shurojit Chatterji, Arunava Sen, Huaxia Zeng
Research Collection School Of Economics
This paper proves the following result: every path-connected domain of preferences that admits a strategy-proof, unanimous, tops-only random social choice function satisfying a compromise property is single-peaked. Conversely, every single-peaked domain admits a random social choice function satisfying these properties. Single-peakedness is defined with respect to arbitrary trees. The paper provides a justification of the salience of single-peaked preferences and evidence in favor of the Gul conjecture (Barber\303\240 2010).
A Characterization Of Single-Peaked Preferences Via Random Social Choice Functions, Shurojit Chatterji, Arunava Sen, Huaxia Zeng
A Characterization Of Single-Peaked Preferences Via Random Social Choice Functions, Shurojit Chatterji, Arunava Sen, Huaxia Zeng
Research Collection School Of Economics
The paper proves the following result: every path-connected domain of preferences that admits a strategy-proof, unanimous, tops-only random social choice function satisfying a compromise property, is single-peaked. Conversely, every single-peaked domain admits a random social choice function satisfying these properties. Single-peakedness is defined with respect to arbitrary trees. We also show that a maximal domain that admits a strategy-proof, unanimous, tops-only random social choice function satisfying a stronger version of the compromise property, is single-peaked on a line. A converse to this result also holds. The paper provides justification of the salience of single-peaked preferences and evidence in favour of …
Random Dictatorship Domains, Shurojit Chatterji, Arunava Sen, Huaxia Zeng
Random Dictatorship Domains, Shurojit Chatterji, Arunava Sen, Huaxia Zeng
Research Collection School Of Economics
A domain of preference orderings is a random dictatorship domain if every strategy-proof random social choice function satisfying unanimity defined on the domain is a random dictatorship. Gibbard (1977) showed that the universal domain is a random dictatorship domain. We ask whether an arbitrary dictatorial domain is a random dictatorship domain and show that the answer is negative by constructing dictatorial domains that admit anonymous, unanimous, strategy-proof random social choice functions which are not random dictatorships. Our result applies to the constrained voting model. Lastly, we show that substantial strengthenings of linked domains (a class of dictatorial domains introduced in …
On Domains That Admit Well-Behaved Strategy-Proof Social Choice Functions, Shurojit Chatterji, Rezmi Sanver, Arunava Sen
On Domains That Admit Well-Behaved Strategy-Proof Social Choice Functions, Shurojit Chatterji, Rezmi Sanver, Arunava Sen
Research Collection School Of Economics
In this paper, we investigate domains that admit “well-behaved” strategy-proof social choice functions. We show that if the number of voters is even, then every domain that satisfies a richness condition and admits an anonymous, tops-only, unanimous and strategy-proof social choice function, must be semi-single-peaked. Conversely every semi-single-peaked domain admits an anonymous, tops-only, unanimous and strategy-proof social choice function. Semi-single-peaked domains are generalizations of single-peaked domains on a tree introduced by Demange (1982).
The Structure Of Strategy-Proof Random Social Choice Functions Over Product Domains And Lexicographically Separable Preferences, Shurojit Chatterji, Souvik Roy, Arunava Sen
The Structure Of Strategy-Proof Random Social Choice Functions Over Product Domains And Lexicographically Separable Preferences, Shurojit Chatterji, Souvik Roy, Arunava Sen
Research Collection School Of Economics
We characterize the class of dominant-strategy incentive-compatible (or strategy-proof) random social choice functions in the standard multi-dimensional voting model where voter preferences over the various dimensions (or components) are lexicographically separable. We show that these social choice functions (which we call generalized random dictatorships) are induced by probability distributions on voter sequences of length equal to the number of components. They induce a fixed probability distribution on the product set of voter peaks. The marginal probability distribution over every component is a random dictatorship. Our results generalize the classic random dictatorship result in Gibbard (1977) and the decomposability results for …
Random Dictatorship Domains, Shurojit Chatterji, Arunava Sen, Huaxia Zeng
Random Dictatorship Domains, Shurojit Chatterji, Arunava Sen, Huaxia Zeng
Research Collection School Of Economics
A domain of preference orderings is a random dictatorship domain if every strategy- proof random social choice function satisfying unanimity defined on the domain, is a random dictatorship. Gibbard (1977) showed that the universal domain is a random dictatorship domain. We investigate the relationship between dictatorial and random dictatorship domains. We show that there exist dictatorial domains that are not random dictatorship domains. We provide stronger versions of the linked domain condition (introduced in Aswal et al. (2003)) that guarantee that a domain is a random dictatorship domain. A key step in these arguments that is of independent interest, is …
Tops-Only Domains, Shurojit Chatterji, Arunava Sen
Tops-Only Domains, Shurojit Chatterji, Arunava Sen
Research Collection School Of Economics
In this paper we consider the standard voting model with a finite set of alternativesA and n voters and address the following question: what are the characteristics ofdomains D that induce the property that every strategy-proof social choice functionf : Dn → A satisfying unanimity, has the tops-only property? We first impose aminimal richness condition which ensures that for every alternative a, there exists anadmissible ordering where a is maximal. We identify conditions on D that are sufficientfor strategy-proofness and unanimity to imply tops onlyness in the general case of nvoters and in the special case, n = 2. We …
Tops-Only Domains, Shurojit Chatterji, Arunava Sen
Tops-Only Domains, Shurojit Chatterji, Arunava Sen
Research Collection School Of Economics
In this paper we consider the standard voting model with a finite set of alternatives A and n voters and address the following question: what are the characteristics of domains D" role="presentation">D that induce the property that every strategy-proof social choice function f:Dn→A" role="presentation">f:Dn→A satisfying unanimity, has the tops-only property? We first impose a minimal richness condition which ensures that for every alternative a, there exists an admissible ordering where a is maximal. We identify conditions on D" role="presentation">D that are sufficient for strategy-proofness and unanimity to imply tops onlyness in the general case of n …
On Domains That Admit Well-Behaved Strategy-Proof Social Choice Functions, Shurojit Chatterji, Remzi Sanver, Arunava Sen
On Domains That Admit Well-Behaved Strategy-Proof Social Choice Functions, Shurojit Chatterji, Remzi Sanver, Arunava Sen
Research Collection School Of Economics
In this paper, we investigate domains that admit “well-behaved” strategy-proof social choice functions. We show that if the number of voters is even, then every domain that satisfies a richness condition and admits an anonymous, tops-only, unanimous and strategy-proof social choice function, must be semi-single-peaked. Conversely every semi-single-peaked domain admits an anonymous, tops-only, unanimous and strategy-proof social choice function. Semi-single-peaked domains are generalizations of single-peaked domains on a tree introduced by Demange (1982
Tops-Only Domains, Shurojit Chatterji, Arunava Sen
Tops-Only Domains, Shurojit Chatterji, Arunava Sen
Research Collection School Of Economics
In this paper we consider the standard voting model with a finite set of alternatives A and n voters and address the following question: what are the characteristics of domains D that induce the property that every strategy-proof social choice function f : Dn → A satisfying unanimity, has the tops-only property? We first impose a minimal richness condition which ensures that for every alternative a, there exists an admissible ordering where a is maximal. We identify conditions on D that are sufficient for strategy-proofness and unanimity to imply tops onlyness in the general case of n voters and in …