ALBERT

Notes: Concluding remarks This paper focuses on two properties of points voting schemes: their vulnerability to preference misrepresentation and their potential for preference expression. In the spirit of the seminal work of Buchanan and Tullock [2], this dual criterion might be used for the choice of an optimal points voting scheme when the above two aspects only are considered. Unlike recent treatment of the manipulability phenomenon, Gardenfors [3], Gibbard [4], Satterthwaite [8], we do suggest measures for the immunity to mispresentation of a given method. The first measure I[X, f)] is interpreted as a lower bound for δ-manipulation. In other words, I[(X, f)] = c implies that there exists at least one preference profile [x ij] ∈ X, such that δ-manipulation is possible for δ 〉 c. The second measure K ranges from 0 to 1, and it is interpreted as the relative frequency of preference profiles in X under which the scheme is immune. Another measure D is proposed for the potential of preference expression under each variation. This measure counts the number of possible preference configurations under the scheme (X, f). The use of this measure for the comparison of two voting schemes (T, f), (Z, f) is especially meaningful whenever T ⊂ Z. This approach is illustrated by five variations of the points voting scheme: the well-known points voting method, the Borda scores method, the plurality rule, the federative plurality rule and a dictatorial type voting scheme. It is shown that, as these variations become more restrictive in terms of preference expression (D decreases), they tend to be more immune to individual preference misrepresentation (I increases). We conjecture, first, that a similar relationship will be generally obtained for variations of the points voting method, and, second, that such a relationship also exists between K and D. Finally, two comments with respect to the commonly used plurality rule are now in order. First, this rule is associated with moderate values of both measures, D(V 3) = m n and I(V 3) = 1/2. Roughly speaking, it can be considered a ‘reasonable’ voting scheme for a society, or committee, which is ‘equally demanding’ in terms of both criteria. Second, the definition of misrepresentation used in this paper, takes into account misrepresentation of preferences with no restriction on the type of motivations for such a behavior. An alternative, and more common, definition deals only with preference misrevelations which are consistent with the sincere preferences of the manipulator, i.e., the winning alternative under the reported preference profile has to be preferred to the outcome of the sincere profile from the non sincere voter's point of view. Obviously, vulnerability to manipulation implies vulnerability to misrepresentation but the converse is not true. Also notice that if the definition of misrepresentation is replaced by that of manipulation, then plurality becomes perfectly immune, since no voter can act contrary to his sincere preferences and alter the social choice in his favor.

Notes: Abstract This essay measures and analyzes for a special class of point-voting schemes (the Borda method, plurality rule and the unrestricted point-voting scheme) sensitivity to preference variation (a simple change in the socially winning alternative resulting from alteration of a single voter's preferences) and vulnerability to individual strategic manipulation (a change in the winning alternative that benefits the voter whose preferences are altered). Assuming that society (n voters with linear preference orders on a finite set of m alternatives) satisfies the impartial-culture assumption, that is, each randomly selected voter is equally likely to hold any one of the randomly picked possible preference orders on the alternatives, we demonstrate: (i) for a given rule and a fixed number of voters, the sensitivity to individual preference variation and the vulnerability to individual strategic manipulation are greater, the larger the total number of alternatives. (ii) For a given rule and a fixed number of alternatives, the vulnerability to individual strategic manipulation, in general, is not greater the smaller the total number of voters. Such a relationship does hold, however, if n is sufficiently large. (iii) For any given combination of number of voters and number of alternatives, the unrestricted point-voting scheme is more sensitive to preference variation than the Borda method, which, in turn, is more exposed to such variation relative to the plurality rule. A similar conclusion does not hold with respect to vulnerability to individual strategic manipulation, unless the number of voters is sufficiently small.

Notes: Abstract The primary object of this paper is to examine the role of differential sharing rules within a collective rent-seeking setting on the possible non-existence of Nash equilibrium. Focusing on groups that distribute part of the rent equally among their members and the residual according to relative effort, we show that in rent-seeking societies applying the two polar sharing rules equilibrium never exists. In the general case where groups apply different but not necessarily the polar sharing rules, we study the relationship between group variability in distributing rents and the problem of non-existence of equilibrium in the rent-seeking game.

Notes: Abstract Employing the symmetric uncertain dichotomous choice model, this paper is concerned with the effect of two types of changes in individual decisional competencies on the optimal collective decision rule and, in particular, on the optimal number of essential decision makers (individuals who are effectively involved in the decision-making process). The first change is simply a decrease in the decisional skills of some of the existing more competent essential decision makers. The second change is a rank and mean-preserving equalization of decisional skills. We show that the number of essential decision makers is not necessarily positively related to both of these changes. This surprising observation implies that a more egalitarian distribution of decisional skills may justify a reduction in the optimal number of individuals effectively participating in the collective decision-making process.

Notes: Abstract This essay provides a formal justification for qualified majority rules. Specifically, within an uncertain dichotomous choice framework, in which individual preferences are identical but actual judgments may differ, special majority rules emerge as decision rules that maximize the probability of making correct decisions. The main result specifies the optimal special majority as a function of a priori bias in favor of the status quo, ability, and size of the decision-making body. The analysis of the relationships among these three variables in generating certain common qualified majority rules is then pursued.

Notes: Abstract In this paper we present a formal analysis of rent-seeking for public goods by two or more groups with different numbers of individuals. We begin by considering equally wealthy groups under risk neutrality, a case which constitutes our basic model. Several surprising and interesting results emerge from the analysis of this basic case. The problem is then extended to deal with (a) groups with different wealth levels, and (b) risk aversion. This last extension brings about a further crop of interesting and useful results.

Notes: Abstract This essay clarifies the relationship between the “technology” of organizational decision making and the limits on the size of the group of decision makers within the organization. Viewing the number and quality of decision makers, and the time required for decision making as inputs in the production of collective decisions, we show that there exist generic organizational forces that offset the incentive to unlimited expansion of the organization. Even in a long run competitive environment with perfect markets for managers, unlimited duplication of the firm may not be economically feasible. We first analyze in a general setting and then illustrate in two stylized examples, the interplay between individual decisional quality, time required for an individual decision, direct and indirect costs of decision making, and the optimal number of decision makers (for example, management size).

Notes: Abstract Recently, Karotkin (1993) has shown that in the symmetric uncertain dichotomous choice model the set of restricted majority rules (RMRs) is special in the sense that a member of this family of rules is always the worst rule among the potentially optimal weighted majority rules (WMRs). In the current paper we establish two additional special properties of RMRs. First, given a particular configuration of the group members' decisions, the collective choice is invariant to the selection of WMRs if it is invariant to the selection of RMRs. Second, given a particular decision profile, a potentially optimal WMR can result in a distinctive collective choice which is different from the choice of any other potentially optimal WMR, if and only if it is a RMR.

Notes: Abstract. The common choice theory in economics is based on the assumption that an individual is defined in terms of a binary preference relation. This preference relation is defined over alternatives without taking into account menu dependence and, in particular, freedom of choice or, more generally, the set that contains the alternatives. In this study we clarify the nature and the significance of freedom of choice which may positively or negatively affect the individual's welfare. Our proposed extended preference relation of the individual takes into account both the particular alternative and the opportunity set that he faces. This extended relation does not induce ranking of opportunity sets. Its restriction to a particular opportunity set is the paradigmatic preference relation and it can capture the dependence of preferences on freedom of choice. Our main result establishes the inconsistency between dependence of extended preferences on freedom of choice and the existence of a utility that represents the paradigmatic preference relation and any of its restrictions.