Journal Article Counter-threats and Strategic Manipulation under Voting Schemes Get access Prasanta K. Pattanaik Prasanta K. Pattanaik Delhi School of Economics Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 43, Issue 1, February 1976, Pages 11–18, https://doi.org/10.2307/2296596 Published: 01 February 1976 Article history Received: 01 August 1974 Accepted: 01 March 1975 Published: 01 February 1976

Journal Article Strategic Voting Without Collusion Under Binary and Democratic Group Decision Rules Get access Prasanta K. Pattanaik Prasanta K. Pattanaik Delhi School of Economics Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 42, Issue 1, January 1975, Pages 93–103, https://doi.org/10.2307/2296823 Published: 01 January 1975

Journal Article A Note on Democratic Decision and the Existence of Choice Sets Get access Prasanta K. Pattanaik Prasanta K. Pattanaik Delhi School of Economics Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 35, Issue 1, January 1968, Pages 1–9, https://doi.org/10.2307/2974402 Published: 01 January 1968

This paper seeks to prove that under a large class of group decision rules some sincere voting situations will be unstable because of strategic manipulation by single individuals. The concept of stability used is weaker than the stability concepts figuring in many earlier contributions in this area, insofar as under the concept used here any individual, while disrupting a given voting situation, considers the possibility of retaliation by other individuals. DUMMETT AND FARQUHARSON [2], Murakami [7], Farquharson [3], Sen [14], Gibbard [4], Satterthwaite [13], and Pattanaik [10, 11, and 12] have discussed various aspects of the problem of stability in voting. The general conclusion which emerges from these writings seems to be that stability of all possible sincere voting situations (which implies the absence of strategic distortion of preferences by voters) is an extremely rare feature of democratic group decision procedures. However, the notion of stability or equilibrium underlying many of these contributions is a simple one and does not take into account several phenomena usually associated with strategic voting such as the possibility of counter-coalitions when a coalition (of one or more individuals) threatens to disrupt a voting situation. The purpose of this paper is twofold. First, it introduces a less demanding notion of stability which takes into account the possibility of formation of countercoalitions when an individual seeks to influence the outcome in his own favor by strategic manipulations in voting. Secondly, using this very weak notion of stability, it is shown that, while under the changed definition the possibility of having unstable sincere voting situations because of strategic voting by single individuals is somewhat reduced, invulnerability of all possible sincere voting situations to voting maneuvres of single individuals still remains a very rare property among democratic group decision rules based on pairwise comparisons. We lay down the basic notation and some preliminary definitions in Section 1. In Section 2 we introduce a notion of stability taking into account the possibility of counter-coalitions. Using this very weak definition of stability, in Section 3 we show that under most democratic group decision rules based on pairwise comparisons, there is the danger of having unstable sincere voting situations owing to strategic manipulations by single individuals. We conclude in Section 4.

The object of this note is to generalize a result of Dummet and Farquharson [3] on the existence of a choice set,2 i.e., the existence of an alternative socially considered to be best under a system of majority voting. In the first section the motivation of the exercise is explained and the relevance of the problem is discussed. In the second, the generalization is stated in the shape of a theorem and is proved. In the third, some observations are made on the nature of the theorem and its relation to conditions of transitivity of majority decision.

[Sufficient conditions (in terms of restrictions on individual preferences) have been already established in the literature for transitivity of simple majority decisions when individual preferences are quasi-transitive (but not necessarily transitive) and also for transitivity of multi-stage majority decisions when individual preferences are transitive. This paper establishes sufficient conditions for transitivity of multi-stage majority decisions when individual preferences are quasi-transitive, but not necessarily transitive. This constitutes a generalization of several results proved earlier.]

The purpose of this paper is to outline a formal analytical framework that can accommodate considerations of individual rights as well as the more familiar ethical concerns of conventional welfare economics. The failure to accommodate such fundamental values as rights has been at the heart of Amartya K. Sen's (1979) criticism of welfarism which is inherent in much of welfare economics and social-choice theory. However, the roots of the problem seem to lie quite deep. Even if one discards neutrality and similar properties which are regarded as capturing the essence of welfarism, the very concept of a social-decision function itself, so widely used in socialchoice theory, turns out to be too restrictive a vehicle for articulating our intuition about rights. We propose an extension of the standard framework of social-choice theory, which can overcome some of these difficulties and enables us to discuss individual rights and other social values in one integrated framework.