A unified characterization of the randomized strategy-proof rules

Roy, Souvik; Sadhukhan, Soumyarup

doi:10.1016/j.jet.2020.105131

Cited by 4 publications

(4 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An important observation of Theorems 1 and 2 is that every strategyproof and non-imposing SDS on the respective domains can be represented as a mixture of deterministic voting rules, each of which is strategyproof and non-imposing. This is sometimes called deterministic extreme point property and it is remarkable that many important domains satisfy this condition [40]. On one side, this shows that randomization does not lead to completely new strategyproof SDSs.…”

Section: Results For the Tie-breaking Condorcet Domainmentioning

confidence: 99%

“…For instance, Ehlers et al [18] have shown the existence of attractive strategyproof SDSs on the domain of single-peaked preference profiles [see also 36,37]. The existence of strategyproof and non-imposing SDSs other than random dictatorships has also been investigated for a variety of other domains [34,35,40]. Following a more general approach, Chatterji et al [14] and Chatterji and Zeng [15] identify criteria for deciding whether a domain admits such SDSs.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Strategyproof Social Decision Schemes on Super Condorcet Domains

Brand¹,

Lederer²,

Tausch³

2023

Preprint

View full text Add to dashboard Cite

One of the central economic paradigms in multi-agent systems is that agents should not be better off by acting dishonestly. In the context of collective decision-making, this axiom is known as strategyproofness and turns out to be rather prohibitive, even when allowing for randomization. In particular, Gibbard's random dictatorship theorem shows that only rather unattractive social decision schemes (SDSs) satisfy strategyproofness on the full domain of preferences. In this paper, we obtain more positive results by investigating strategyproof SDSs on the Condorcet domain, which consists of all preference profiles that admit a Condorcet winner. In more detail, we show that, if the number of voters is odd, every strategyproof and non-imposing SDS on the Condorcet domain can be represented as a mixture of dictatorial SDSs and the Condorcet rule (which chooses the Condorcet winner with probability 1). Moreover, we prove that the Condorcet domain is a maximal connected domain that allows for attractive strategyproof SDSs if is odd as only random dictatorships are strategyproof and nonimposing on any sufficiently connected superset of it. We also derive analogous results for even by slightly extending the Condorcet domain. Finally, we also characterize the set of group-strategyproof and non-imposing SDSs on the Condorcet domain and its supersets. These characterizations strengthen Gibbard's random dictatorship theorem and establish that the Condorcet domain is essentially a maximal domain that allows for attractive strategyproof SDSs.

show abstract

Section: Results For the Tie-breaking Condorcet Domainmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Strategyproof Social Decision Schemes on Super Condorcet Domains

Brand¹,

Lederer²,

Tausch³

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Inspired by this, many works in the literature express RSCFs as convex combinations of DSCFs [27,26,28,25,29]. The Lemma 2 provides such a characterization of all the unanimous and strategy-proof RSCFs by proving that they are equivalent to random min-max rules.…”

Section: Extreme Point Characterization (Epc)mentioning

confidence: 99%

Characterization of Group-Fair Social Choice Rules under Single-Peaked Preferences

Sreedurga¹,

Sadhukhan²,

Roy³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

We study fairness in social choice settings under single-peaked preferences. Construction and characterization of social choice rules in the single-peaked domain has been extensively studied in prior works. In fact, in the single-peaked domain, it is known that unanimous and strategy-proof deterministic rules have to be min-max rules and those that also satisfy anonymity have to be median rules. Further, random social choice rules satisfying these properties have been shown to be convex combinations of respective deterministic rules. We non-trivially add to this body of results by including fairness considerations in social choice. Our study directly addresses fairness for groups of agents. To study group-fairness, we consider an existing partition of the agents into logical groups, based on natural attributes such as gender, race, and location. To capture fairness within each group, we introduce the notion of group-wise anonymity. To capture fairness across the groups, we propose a weak notion as well as a strong notion of fairness. The proposed fairness notions turn out to be natural generalizations of existing individual-fairness notions and moreover provide non-trivial outcomes for strict ordinal preferences, unlike the existing group-fairness notions. We provide two separate characterizations of random social choice rules that satisfy group-fairness: (i) direct characterization (ii) extreme point characterization (as convex combinations of fair deterministic social choice rules). We also explore the special case where there are no groups and provide sharper characterizations of rules that achieve individual-fairness.

show abstract

“…Almost all unanimous and weak elementary monotonic swap-LOBIC RBRs on the single-crossing domain are swap-LDSIC. Roy and Sadhukhan (2019) show that an RSCF on the single-crossing domain is unanimous and DSIC if and only if it is a tops-restricted probabilistic fixed ballot rules (TPFBRs). Moreover, Cho (2016) shows that every swap-LDSIC RSCF on the singlecrossing domain is DSIC.…”

Section: Single-dipped Domainsmentioning

confidence: 99%

The structure of (local) ordinal Bayesian incentive compatible random rules

Karmokar

Roy

2022

Econ Theory

Self Cite

View full text Add to dashboard Cite

We explore the structure of local ordinal Bayesian incentive compatible (LO-BIC) random Bayesian rules (RBRs). We show that under lower contour monotonicity, almost all (with Lebesgue measure 1) LOBIC RBRs are local dominant strategy incentive compatible (LDSIC). We also provide conditions on domains so that unanimity implies lower contour monotonicity for almost all LOBIC RBRs.We provide sufficient conditions on a domain so that almost all unanimous RBRs on it (i) are Pareto optimal, (ii) are tops-only, and (iii) are only-topset. Finally, we provide a wide range of applications of our results on the unrestricted, singlepeaked (on graphs), hybrid, multiple single-peaked, single-dipped, single-crossing, multidimensional separable, lexicographic, and domains under partitioning. We additionally establish the marginal decomposability property for both random social choice functions and almost all RBRs on multi-dimensional domains, and thereby generalize Breton and Sen (1999). Since OBIC implies LOBIC by definition, all our results hold for OBIC RBRs. KEYWORDS. random Bayesian rules; random social choice functions; (local) ordinal Bayesian incentive compatibility; (local) dominant strategy incentive compatibility JEL CLASSIFICATION CODES. D71; D82 * The authors would like to thank Arunava Sen and Debasis Mishra for their invaluable suggestions.

show abstract

A unified characterization of the randomized strategy-proof rules

Cited by 4 publications

References 55 publications

Strategyproof Social Decision Schemes on Super Condorcet Domains

Strategyproof Social Decision Schemes on Super Condorcet Domains

Characterization of Group-Fair Social Choice Rules under Single-Peaked Preferences

The structure of (local) ordinal Bayesian incentive compatible random rules

Contact Info

Product

Resources

About