Luba Sapir

Monotonicity in Condorcet’s Jury Theorem with dependent voters

Condorcet’s Jury Theorem (CJT) provides a theoretical basis of public choice theory and political science. This paper provides an extension of CJT for random subcommittees consisting of dependent heterogeneous experts. Necessary and sufficient conditions for beneficial augmentation (reduction) of the size of a random subcommittee are provided. These results are applied in several dependency models.

Monotonicity in Condorcet Jury Theorem

Abstract.Consider a committee of experts dealing with dichotomous choice problem, where the correctness probabilities are all greater than We prove that, if a random subcommittee of odd size m is selected randomly, and entrusted to make a decision by majority vote, its probability of deciding correctly increases with m. This includes a result of Ben-Yashar and Paroush (2000), who proved that a random subcommittee of size m≥3 is preferable to a random single expert.

The Optimality of the Expert and Majority Rules Under Exponentially Distributed Competence

We study the uncertain dichotomous choice model. In this model a set of decision makers is required to select one of two alternatives, say ‘support’ or ‘reject’ a certain proposal. Applications of this model are relevant to many areas, such as political science, economics, business and management. The purpose of this paper is to estimate and compare the probabilities that different decision rules may be optimal. We consider the expert rule, the majority rule and a few in-between rules. The information on the decisional skills is incomplete, and these skills arise from an exponential distribution. It turns out that the probability that the expert rule is optimal far exceeds the probability that the majority rule is optimal, especially as the number of the decision makers becomes large.

Expert rule versus majority rule under partial information, II

The main purpose of this paper is clarifying the connection between some characteristics of a deciding body and the probability of its making correct decisions. In our model a group of decision makers is required to select one of two alternatives. We assume the probabilities of the decision makers being correct are independent random variables distributed according to the same given distribution rule. This distribution belongs to a general family, containing the uniform distribution as a particular case. We investigate the behavior of the probability of the expert rule being optimal, as well as that of the majority rule, both as functions of the distribution parameter and the group size. The main result is that for any value of the distribution parameter the expert rule is far more likely to be optimal than the majority rule, especially as the deciding body becomes larger.

A nonstationary iterative second-order method for solving nonlinear equations

Abstract This paper presents a new nonstationary iterative method of second order for solving nonlinear equations, that does not require the use of any derivatives. For algebraic equations our method coincides with Newton’s method, from a certain step of iteration on. Due to the methodology of Ostrowski [8] , the efficiency index of our process equals 2, which is higher than the efficiency indices of classical iterative methods, such as Newton’s process and the secant method, to mention just a few.

Between the expert and majority rules

Sapir (1998) calculated the probabilities of the expert rule and of the simple majority rule being optimal under the assumption of exponentially distributed logarithmic expertise levels. Here we find the analogous probabilities for the family of restricted majority rules, including the above two extreme rules as special cases, and the family of balanced expert rules. We compare the two families, the rules within each family, and all rules of the two families with the extreme rules.

Optimality of the Expert Rule Under Partial Information

We study the uncertain dichotomous choice model. In this model a group of decision makers is required to select one of two alternatives. The applications of this model are relevant to a wide variety of areas, such as medicine, management and banking. The decision rule may be the simple majority rule; however, it is also possible to assign more weight to the opinion of members known to be more qualified. The extreme example of such a rule is the expert decision rule. We are concerned with the probability of the expert rule to be optimal. Our purpose is to investigate the behaviour of this probability as a function of the group size for several rather general types of distributions. One such family of distributions is that where the density function of the correctness probability is a polynomial (on the interval [1/2,1]). Our main result is an explicit formula for the probability in question. This contains formerly known results as very special cases.

Airplane boarding, disk scheduling and space-time geometry

We show how the process of passengers boarding an airplane and the process of optimal I/O scheduling to a disk drive with a linear seek function can be asymptotically modeled by 2-dimensional space-time geometry. We relate the space-time geometry of the models to important quantities such as total boarding time and total service time. We show that the efficiency of a boarding policy depends crucially on a parameter k which depends on the interior design of the airplane. Policies which are good for small values of k are bad for large values of k and vice versa.

Generalized means of jurors' competencies and marginal changes of jury's size☆

Abstract A manager facing a dilemma might consult some of his senior employees, and decide according to the advice of the majority. Should he consult only those on whom he relies most, or let more people share in the decision? We analyze how does the augmentation of a jury by adding two potential jurors influence the probability of making the “correct” choice. We obtain a necessary and sufficient condition for the total correctness probability to increase, assuming that the competence structure of the committee is known. The intuitive meaning of the condition is explained in terms of a certain mean competence.

OPTIMAL BOARDING POLICIES FOR THIN PASSENGERS

We deal with the problem of seating an airplanes passengers optimally, namely in the fastest way. Under several simplifying assumptions, whereby the passengers are infinitely thin and react within a constant time to boarding announcements, we are able to rewrite the asymptotic problem as a calculus of variations problem with constraints. This problem is solved in turn using elementary methods. While the optimal policy is not unique, we identify a rigid discrete structure which is common to all solutions. We also compare the (nontrivial) optimal solutions we find with some simple boarding policies, one of which is shown to be near-optimal.