ALBERT

Notes: This paper analyzes an expert resolution problem under an uncertain dichotomous choice situation. The experts share a common system of norms and therefore they all prefer the alternative that best suits their purpose. The selection of such an alternative is referred to as a correct choice. Our analysis of optimal decision rules for panels of independent experts is pursued for n-member decision-making bodies, n≤ 5. The suggested optimality criterion is the maximization of the probability of the panel's making the correct choice. Within our framework, this criterion is equivalent to the more common criterion of expected-utility maximization. For three-member panels of experts, the expert resolution problem is solved and illustrated by means of a medical application. For four-member panels, we list the three relevant decision rules, specify the conditions for all possible rankings of these rules, and, finally, present an extended consulting application. We conclude by listing seven relevant decision rules in the case of five-member decision-making bodies.

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.