Circumstantial power: Optimal persuadable voters

Let us suppose that certain committee is going to decide, using some fixed voting rules, either to accept or to reject a proposal that affects your interests. From your perception about each voter’s position, you can make an a priori estimation of the probability of the proposal being accepted. Wishing to increase this probability of acceptance before the votes are cast, assume further that you are able to convince (at least) one voter to improve his/her perception in favor of the proposal. The question is: which voters should be persuaded in order to get the highest possible increase in the probability of acceptance? In other words, which are the optimal persuadable voters? To answer this question a measure of “circumstantial power” is considered in this paper, which is useful to identify optimal persuadable voters. Three preorderings in the set of voters, based on the voting rules, are defined and they are used for finding optimal persuadable voters, even in the case that only a qualitative ranking of each voter’s inclination for the proposal has been made.     

A New Pareto Optimal Solution in a Lagrange Decomposable Multi-Objective Optimization Problem

In this paper a committee decision-making process of a convex Lagrange decomposable multi-objective optimization problem, which has been decomposed into various subproblems, is studied. Each member of the committee controls only one subproblem and attempts to select the optimal solution of this subproblem most desirable to him, under the assumption that all the constraints of the total problem are satisfied. This procedure leads to a new solution concept of a Lagrange decomposable multi-objective optimization problem, called a preferred equilibrium set. A preferred equilibrium point of a problem, for a committee, may or may not be a Pareto optimal point of this problem. In some cases, a non-Pareto optimal preferred equilibrium point of a problem, for a committee, can be considered as a special type of Pareto optimal point of this problem. This fact leads to a generalization of the Pareto optimality concept in a problem.     

A successful algorithm for solving directed Hamiltonian path problems

In this paper we present a graph-theoretic polynomial algorithm which has positive probability of finding a Hamiltonian path in a given graph, if there is one; if the algorithm fails, it can be rerun with a randomly chosen starting solution, and there is again a positive probability it will find an answer. If there is no Hamiltonian path, the algorithm will always terminate with failure. We call this a Successful Algorithm because it has high (close to 1) empirical probability of success and it works in polynomial time. Some basic theoretical results concerning spanning arborescences of a graph are given. The concept of a ramification index is defined and it is shown that ramification index of a Hamiltonian path is zero. The algorithm starts with finding any spanning arborescence and by suitable pivots it endeavors to reduce the ramification index to zero. Probabilistic properties of the algorithm are discussed. Computational experience with graphs up to 30 000 nodes is included.     

The Condorcet criterion and committee selection

Recent studies have evaluated election procedures on their propensity to select committees that meet a Condorcet criterion. The Condorcet criterion has been defined to use majority agreement from voters' preferences to compare the selected committee to all other committees. This study uses a different definition of the Condorcet criterion as defined on committees. The focus of the new definition is on candidates. That is, we consider majority agreement on each candidate in the selected committee as compared to each candidate not in the selected committee.This new definition of the Condorcet criterion allows for the existence of majority cycles on candidates within the selected committee. However, no candidate in the non-selected group is able to defeat any candidate in the selected committee by majority rule. Of particular interest is the likelihood that a committee meeting this Condorcet criterion exists. Attention is also given to the likelihood that various simple voting procedures will select a committee meeting this Condorcet criterion when one does exist.     

Limit laws for the Randić index of random binary tree models

We investigate the Randić index of random binary trees under two standard probability models: the one induced by random permutations and the Catalan (uniform). In both cases the mean and variance are computed by recurrence methods and shown to be asymptotically linear in the size of the tree. The recursive nature of binary search trees lends itself in a natural way to application of the contraction method, by which a limit distribution (for a suitably normalized version of the index) is shown to be Gaussian. The Randić index (suitably normalized) is also shown to be normally distributed in binary Catalan trees, but the methodology we use for this derivation is singularity analysis of formal generating functions.     

A Power Index in Weighted Voting Systems

We examine the properties of a new method for constructing the power index in voting systems where voters have unequal influence. A system of equations derived in this study produces the sought index by optimal approximation of the original voting system with another system that allows for the weights of the voters. The new index is applied to analyze the known paradoxes of committee voting theory.     

A probabilistic approach to modelling uncertain logical arguments

Argumentation can be modelled at an abstract level using a directed graph where each node denotes an argument and each arc denotes an attack by one argument on another. Since arguments are often uncertain, it can be useful to quantify the uncertainty associated with each argument. Recently, there have been proposals to extend abstract argumentation to take this uncertainty into account. This assigns a probability value for each argument that represents the degree to which the argument is believed to hold, and this is then used to generate a probability distribution over the full subgraphs of the argument graph, which in turn can be used to determine the probability that a set of arguments is admissible or an extension. In order to more fully understand uncertainty in argumentation, in this paper, we extend this idea by considering logic-based argumentation with uncertain arguments. This is based on a probability distribution over models of the language, which can then be used to give a probability distribution over arguments that are constructed using classical logic. We show how this formalization of uncertainty of logical arguments relates to uncertainty of abstract arguments, and we consider a number of interesting classes of probability assignments.     

Nonlinear autoregressive models with heavy-tailed innovation

In this paper, we discuss the relationship between the stationary marginal tail probability and the innovation's tail probability of nonlinear autoregressive models. We show that under certain conditions that ensure the stationarity and ergodicity, one dimension stationary marginal distribution has the heavy-tailed probability property with the same index as that of the innovation's tail probability.     

On characterisation of Markov processes via martingale problems

It is well-known that well-posedness of a martingale problem in the class of continuous (or r.c.l.l.) solutions enables one to construct the associated transition probability functions. We extend this result to the case when the martingale problem is well-posed in the class of solutions which are continuous in probability. This extension is used to improve on a criterion for a probability measure to be invariant for the semigroup associated with the Markov process. We also give examples of martingale problems that are well-posed in the class of solutions which are continuous in probability but for which no r.c.l.l. solution exists.     

Likelihood Based Confidence Intervals for the Tail Index

For the estimation of the tail index of a heavy tailed distribution, one of the well-known estimators is the Hill estimator (Hill, 1975). One obvious way to construct a confidence interval for the tail index is via the normal approximation of the Hill estimator. In this paper we apply both the empirical likelihood method and the parametric likelihood method to obtaining confidence intervals for the tail index. Our limited simulation study indicates that the normal approximation method is worse than the other two methods in terms of coverage probability, and the empirical likelihood method and the parametric likelihood method are comparable.     

Ultrametricity indices for the Euclidean and Boolean hypercubes

Motivated by Murtagh’s experimental observation that sparse random samples of the hypercube become more and more ultrametric as the dimension increases, we consider a strict version of his ultrametricity coefficient, an index derived from Rammal’s degree of ultrametricity, and a topological ultrametricity index. First, we prove that the three ultrametricity indices converge in probability to one as dimension increases, if the sample size remains fixed. This is done for uniformly and normally distributed samples in the Euclidean hypercube, and for uniformly distributed samples in F₂ ^N with Hamming distance, as well as for very general probability distributions. Further, this holds true for random categorial data in complete disjunctive form. A second result is that the ultrametricity indices vanish in the limit for the full hypercube F₂ ^N as dimensionN increases,whereby Murtagh’s ultrametricity index is largest, and the topological ultrametricity index smallest, if N is large.     

Path critical index and activity critical index in PERT networks

The criticality index of an activity is the probability that the activity is on the critical path of the network. The criticality index of a path is the probability that the duration of the path is greater than or equal to the duration of every other path in the network. In this paper, a new exact formula is presented to compute the path critical index (PCI) and activity critical index (ACI) for the PERT network with any structure. It is assumed that each activity duration time is a discrete random variable. Numerical examples presented in this paper prove the method is highly efficient and has excellent results compared to Dodin and Elmaghraby's approach.     

Logic and probabilistic systems

Following some ideas of Roberto Magari, we propose trial and error probabilistic functions, i.e. probability measures on the sentences of arithmetic that evolve in time by trial and error. The set of the sentences that get limit probability 1 is a theory, in fact can be a complete set. We prove incompleteness results for this setting, by showing for instance that for every there are true sentences that get limit probability less than . No set as above can contain the set of all true sentences, although we exhibit some containing all the true sentences. We also consider an approach based on the notions of inner probability and outer probability, and we compare this approach with the one based on trial and error probabilistic functions. Although the two approaches are shown to be different, we single out an important case in which they are equivalent. Received March 20, 1995     

A novel approach for leveraging co-occurrence to improve the false positive error in signature files

Signature file is a well-studied method in information retrieval for indexing large text databases. Because of the small index size in this method, it is a good candidate for environments where memory is scarce. This small index size, however, comes at the cost of high false positive error rate. In this paper we address the problem of high false positive error rate of signature files by introducing COCA filters, a new variation of Bloom filters which exploits the co-occurrence probability of words in documents to reduce the false positive error. We show experimentally that by using this technique in real document collections we can reduce the false positive error by up to 21 times, for the same index size. It is also shown that in some extreme cases this technique is even able to completely eliminate the false positive error. COCA filters can be considered as a good replacement for Bloom filters wherever the co-occurrence of any two members of the universe is identifiable.     

A Critique of “Operational Research and Decision-Making” by Adelson and Norman

Several points mentioned by Adelson and Norman¹ in their paper "Operational Research and Decision-making" are discussed critically-the selection of the model and its implication on the decision by an individual or by a committee; the choice of objectives and the degree to which objectives can guide a decision-maker; subjective probability; the evolutionary process in management decision-making.     

A solution to the distribution problems arising in the studies of a two-sex population process

Given a population of two sexes, the birth rate of one sex of which depends upon the population size of the other, it is very difficult to find an explicit expression for the probability distribution of the former. In this paper we have explicitly found the probability generating function of the joint distribution from which individual probability distributions and, in particular, moments of all orders in each case can be obtained in principle. As an example, using this probability generating function we have worked out explicitly the first and second order moments of the male and female populations and the explicit expression for the distribution of the male population in a particular case. This method can be successfully applied for the same purpose in the studies of chemical and biological processes where the synthesis or production of one species depends upon the concentration of another species.     

Analysis and design of selection committees: a game theoretic secretary problem

Firms often delegate important decisions to committees which are set up specifically for that purpose; for example selection committees. We analyze the equilibrium behavior of a game in which committee members (the players) interview candidates sequentially, either hiring or going on to the next one. The players have differing evaluations of candidates (e.g. one cares about typing skills; the other about IT skills), which become their utilities if the candidate is hired. We then consider the optimal design (rules of the game) of such a committee, from the point of view of the firm. That is, which rules hire candidates which maximize the firm’s utility. Our committee game has a first round in which the members sequentially, by order of player number, say ‘yea’ or ‘nea’ to the candidate. If there are sufficient ‘yeas’ then she is tentatively hired; otherwise she is rejected. In the former case, members who said nea can veto the candidate in the second round. Thus the candidate is either hired, rejected, or vetoed. In the last case, the member casting a veto has one less to use on later candidates. We analyze equilibria where a player may say ‘yea’ to a candidate he would prefer not to hire, in order to force the other player to use up a valuable veto. We show that for the uniform candidate distribution there is a unique equilibrium and better candidates for the firm are hired when there are more vetoes. However we exhibit a candidate distribution where increasing the numbers of vetoes results in hiring worse candidates.     

具有随机风险的公司最优投资策略

本文讨论具有随机风险的公司的最优投资策略问题,公司投资选择是存款、贷款及股票交易、,因市场的不完备性,公司在任一时刻存在概率为正值的破产可能性,本文主要结果是：从贷款利率高于存款利率的实际出发,运用最优随机控制理论,得到使公司生存概率取得最大值的最优投资策略,以及相应的最大生存概率,并并对这些结果给出了严格证明。     

On the first time of ruin in the bivariate compound Poisson model

This paper considers a bivariate compound Poisson model for a book of two dependent classes of insurance business. We focus on the ruin probability that at least one class of business will get ruined. As expected, general explicit expressions for this bivariate ruin probability is very difficult to obtain. In view of this, we introduce the so-called bivariate compound binomial model which can be used to approximate the finite-time survival probability of the assumed model. We then study some simple bounds for the infinite-time ruin probability via the association properties of the bivariate compound Poisson model. We also investigate the impact of dependence on the infinite-time ruin probability by means of multivariate stochastic orders.