Rajat Deb

Bio: Rajat Deb is an academic researcher from Southern Methodist University. The author has contributed to research in topics: Public good & Social choice theory. The author has an hindex of 13, co-authored 31 publications receiving 589 citations.

Auction-like mechanisms for pricing excludable public goods

Abstract: We study the problem of strategy-proof mechanism design for indivisible and excludable public goods. Applying Vickrey's theory of auctions we associate a class of strategy-proof mechanisms to two types of procedures, the “English Auction-Like Mechanism” (EALM) and the “Sealed Bid Auction-Like Mechanism” (SBALM). We show that these two Auction-Like Mechanisms lead to identical outcomes. We justify the use of these mechanisms as compared to other strategy-proof mechanisms by arguing that outcomes of the SBALM maximize welfare. In the absence of capacity constraints the SBALM balances the budget and becomes Moulin's ( Rev. Econ. Stud. 61 (1994), 305–325) serial cost sharing rule and the conservative equal costs rule. If capacity constraints are binding, the SBALM does not necessarily balance the budget and becomes a generalized version of Vickrey's second price auction (see Kleindorfer and Sertel, J. Econ. Theory 64 (1994), 20–34). Thus our results unify and provide justification for different procedures arising in two separate strands of the literature on mechanism design. Journal of Economic Literature classification numbers: H41, C72, D78.

Strategy-proof assignment on the full preference domain

Abstract: We consider the problem of efficiently allocating several indivisible objects between agents who are to receive at most one object and whose preferences are private information. We examine this standard “assignment” problem from the perspective of mechanism design giving up the usual assumption of linear preferences and instead using a full preference domain (with indifferences permitted). We characterize two classes of mechanisms: (i) Bi-polar Serially Dictatorial Rules by Essential Single-Valuedness, Pareto Indifference, Strategy-Proofness and Non-Bossiness; and (ii) all selections from Bi-polar Serially Dictatorial Rules by Single-Valuedness, Efficiency, Strategy-Proofness and Weak Non-Bossiness. We compare the outcomes from the (Bi-polar) Serially Dictatorial Rules with the outcomes obtained using a market based approach, namely the “core” of the market. We show that all strongly efficient outcomes in the core can be generated using Serially Dictatorial Rules. Moreover, we argue that Serially Dictatorial Rules have an advantage over the market based approach in that they yield strongly efficient solutions for all preference profiles, making it possible to use randomization to restore equity. When preferences are private information, this type of ex ante equity cannot be implemented using the market based approach.

Soft sets: an ordinal formulation of vagueness with some applications to the theory of choice

Abstract: In the theory of fuzzy sets, it is usual to represent the ‘degree of belongingness’ by a number lying between 0 and 1. This paper develops an alternative framework which dispenses with such cardinal numerical representations of the degree of belongingness, and relies, instead, on an ordinal formulation. The ordinal notion of a vague set is called a soft set. Soft sets are shown to have a tight logical relation with the concept of L -sets introduced earlier by Goguen. The paper also discusses applications of the framework of soft sets to several problems in the theory of choice.

Fuzzy choice functions

Abstract: The R-greatest and maximal sets of standard choice theory are extended to fuzzy R-greatest and fuzzy maximal sets. Unlike the precise counterparts of these concepts, these two sets do not in general coincide when preferences are reflexive and connected. A stronger than usual version of connectedness under which the two sets are equal is provided. The concept of a fuzzy choice function is introduced and conditions under which a fuzzy choice function may be rationalized as a fuzzy R-greatest or a fuzzy maximal set are discussed. Rationalizability with transitive and weakly transitive fuzzy preference relations is also considered.

Coalition structure generation with worst case guarantees

Abstract: Coalition formation is a key topic in multiagent systems. One may prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. Furthermore, finding the optimal coalition structure is NP-complete. But then, can the coalition structure found via a partial search be guaranteed to be within a bound from optimum? We show that none of the previous coalition structure generation algorithms can establish any bound because they search fewer nodes than a threshold that we show necessary for establishing a bound. We present an algorithm that establishes a tight bound within this minimal amount of search, and show that any other algorithm would have to search strictly more. The fraction of nodes needed to be searched approaches zero as the number of agents grows. If additional time remains, our anytime algorithm searches further, and establishes a progressively lower tight bound. Surprisingly, just searching one more node drops the bound in half. As desired, our algorithm lowers the bound rapidly early on, and exhibits diminishing returns to computation. It also significantly outperforms its obvious contenders. Finally, we show how to distribute the desired search across self-interested manipulative agents. © 1999 Elsevier Science B.V. All rights reserved.

The Possibility of Social Choice

Abstract: The subject of social choice includes within its capacious frame various problems with the common feature of relating social judgments and group decisions to the views and interests of the individuals who make up the society or the group. Some challenges and foundational problems faced by social choice theory as a discipline are discussed. Social choice theory is a subject in which formal and mathematical techniques have been very extensively used. Voting-based procedures are entirely natural for some kinds of social choice problems, such as elections, referendums, or committee decisions. They are, however, altogether unsuitable for many other problems of social choice. Impossibility results in social choice theory - led by the pioneering work of Arrow (1951) - have often been interpreted as being thoroughly destructive of the possibility of reasoned and democratic social choice, including welfare economics. That view is argued against.

Evaluation and Decision Models: A Critical Perspective

Abstract: 1. Introduction. 2. Choosing on the basis of several opinions. 3. Building and aggregating evaluations. 4. Constructing measures. 5. Assessing competing projects. 6. Comparing on several attributes. 7. Deciding automatically. 8. Dealing with uncertainty. 9. Supporting decisions. Appendix A. Appendix B. 10. Conclusion. Bibliography. Index.

A Historical Account of Types of Fuzzy Sets and Their Relationships

Abstract: In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used.

Strategyproof sharing of submodular costs:budget balance versus efficiency

Abstract: A service is produced for a set of agents. The service is binary, each agent either receives service or not, and the total cost of service is a submodular function of the set receiving service. We investigate strategyproof mechanisms that elicit individual willingness to pay, decide who is served, and then share the cost among them. If such a mechanism is budget balanced (covers cost exactly), it cannot be efficient (serve the surplus maximizing set of users) and vice-versa. We characterize the rich family of budget balanced and group strategyproof mechanisms and find that the mechanism associated with the Shapley value cost sharing formula is characterized by the property that its worst welfare loss is minimal. When we require efficiency rather than budget balance – the more common route in the literature – we find that there is a single Clarke-Groves mechanism that satisfies certain reasonable conditions: we call this the marginal cost pricing mechanism. We compare the size of the marginal cost pricing mechanism's worst budget surplus with the worst welfare loss of the Shapley value mechanism.