Informational requirements of social choice rules

The required amount of information to make a social choice is the cost of information processing, and it is a practically important feature of social choice rules. We introduce informational aspects into the analysis of social choice rules and prove that (i) if an anonymous, neutral, and monotonic social choice rule operates on minimal informational requirements, then it is a supercorrespondence of either the plurality rule or the antiplurality rule, and (ii) if the social choice rule is furthermore Pareto efficient, then it is a supercorrespondence of the plurality rule.     

Assessing the Level of Compromise in Real Choice Models

We analyze the plurality runoff rule often used in national elections and prove that the corresponding choice function is Borda-rational. The compromise level attained in real voting systems is defined. The corresponding measures are calculated for the case of plurality runoff with three main candidates. We investigate the influence of the axiom of independence of irrelevant alternatives on the rationality type of choice functions realized in multicriterion choice systems.     

Information aggregation in multicandidate elections under plurality rule and runoff voting

I consider a model in which imperfectly informed voters with common interests participate in a multicandidate election decided by either plurality rule or a runoff. Prior to the election, each voter receives a private signal corresponding to the candidate the voter thinks is best. Voters are relatively more likely to think a given candidate is best if the candidate is a relatively better candidate. I show that there is a sequence of equilibrium strategies for the voters such that, as the number of voters goes to infinity, the probability that the best candidate is elected goes to 1. I further show that all candidates receive significant vote shares in any equilibrium in which information fully aggregates under plurality rule and that voters do at least as well when the election is decided by a runoff as they do when the election is decided by plurality rule.     

Strong and coalition-proof political equilibria under plurality and runoff rule

We analyze the effects of voter coordination on the equilibrium of voting games. Specifically, we analyze the concepts of strong equilibrium and coalition-proof equilibrium for plurality rule and runoff rule elections. We characterize these equilibria in the three candidate case, and provide results for important special cases in the general multicandidate case.      

A distance-based comparison of basic voting rules

In this paper we provide a comparison of different voting rules in a distance-based framework with the help of computer simulations. Taking into account the informational requirements to operate such voting rules and the outcomes of two well-known reference rules, we identify the Copeland rule as a good compromise between these two reference rules. It will be shown that the outcome of the Copeland rule is “close” to the outcomes of the reference rules, but it requires less informational input and has lower computational complexity.     

Generalized best choice problem based on the information economics approach

We consider the problem of choosing the ‘best choice’ among a certain number of objects that are presented to a decision-maker in sequential order. Such a sequential selection problem is commonly referred to as the ‘best choice problem’, and its optimal stopping rule has been obtained either via the dynamic programming approach or via the Markovian approach. Based on the theory of information economics, we propose in the paper the third approach to a generalized version of the best choice problem that is intuitively more appealing. Various types of the best choice problem, such as (1) the classical secretary problem, (2) no information group interview problem, and (3) full information best choice problem with a random walk process, are shown to be special cases of the generalized best choice problem. The modelling framework of information economics has potential for building theory that ultimately would produce practical stopping rules.     

Performance evaluation of some special classes of weighted majority rules

The main concern of this paper is the performance evaluation of four classes of decision rules: the expert rule, the balanced expert rules, the simple majority rule, and the restricted simple majority rules. Employing the uncertain dichotomous choice model we first establish the necessary and sufficient conditions for the optimality of these four types of decision rules.For small groups consisting of less than six members the optimality conditions cover all the potentially optimal decision rules. Consequently, we are able to pursue a complete analysis of the small group cases. The analysis of the special (small group) cases as well as that of the general (n-member group) cases is based on the assumption that individual decisional skills are uniformly distributed. In evaluating the quality of a decision rule we resort to four alternative criteria: the expected optimality likelihood of the rule, the expected probability of yielding a correct collective decision given complete information on decisional skills, the expected probability of yielding a correct collective judgement given complete inability of skills verification, and, finally, the sensitivity of the rule to skills verifiability.     

Subgroup additivity in the queueing problem

Subgroup additivity requires that a rule assigns the same expected ‘relative’ utility to each agent whether an agent’s expected relative utility is calculated from the problem involving all agents or from its sub-problems with a smaller number of agents. In this paper, we investigate its implications for the queueing problem. As a result, we present characterizations of five important rules: the minimal transfer rule, the maximal transfer rule, the pivotal rule, the reward based pivotal rule, and the symmetrically balanced VCG rule. In addition to some basic axioms and subgroup additivity, the characterization results can be obtained by additionally imposing either a strategic axiom or an equity axiom.     

Generalized evaluation in decision analysis

The paper presents a discussion on evaluation methods in decision analysis. The presentation begins with the discussion of the expected value rule for selection amongst a number of available courses of action. Then a number of other evaluation rules to either replace or supplement the expected value are presented. They are discussed from a choice rather than preference view. To improve the expected value rule (or any other similar rule), it is suggested that it should be supplemented with other, qualitative rules rather than engaging in further modifications in pursuit of the perfect rule. A characteristic of qualitative rules is that they do not rely on multiplying probabilities and values but treat them as separate numeric entities. Once a rule has been agreed upon, it can be applied to all the alternatives, provided there is a computational procedure for evaluating the alternatives under that rule. Delta dominance is introduced as a unifying concept for many of the dominance rules in current use. Dominance and threshold methods are discussed and the kinship between them is pointed out.     

Equilibrium and effectiveness of two-parameter scoring rules

We study a cardinal model of voting with three alternatives where voters’ von Neumann Morgenstern utilities are private information. We consider voting protocols given by two-parameter scoring rules, as introduced by Myerson (2002). For these voting rules, we show that all symmetric Bayes Nash equilibria are sincere, and have a very specific form. These equilibria are unique for a wide range of model parameters, and we can therefore compare the equilibrium performance of different rules. Computational results regarding the effectiveness of different scoring rules (where effectiveness is captured by a modification of the effectiveness measure proposed in Weber, 1978) suggest that those which most effectively represent voters’ preferences allow for the expression of preference intensity, in contrast to more commonly used rules such as the plurality rule, and the Borda Count. While approval voting allows for the expression of preference intensity, it does not maximize effectiveness as it fails to unambiguously convey voters’ ordinal preference rankings.     

An experimental study of voting rules and polls in three-candidate elections

We report the results of elections conducted in a laboratory setting, modelled on a threecandidate example due to Borda. By paying subjects conditionally on election outcomes, we create electorates with (publicly) known preferences. We compare the results of experiments with and without non-binding pre-election polls under plurality rule, approval voting, and Borda rule. We also refer to a theory of voting “equilibria,” which makes sharp predictions concerning individual voter behavior and election outcomes. We find that Condorcet losers occasionally win regardless of the voting rule or presence of polls. Duverger's law (which asserts the predominance of two candidates) appears to hold under plurality rule, but close three-way races often arise under approval voting and Borda rule. Voters appear to poll and vote strategically. In elections, voters usually cast votes that are consistent with some strategic equilibrium. By the end of an election series, most votes are consistent with a single equilibrium, although that equilibrium varies by experimental group and voting rule.     

Connecting pairwise and positional election outcomes

General conclusions relating pairwise tallies with positional (e.g., plurality, antiplurality (“vote-for-two”)) election outcomes were previously known only for the Borda Count. While it has been known since the eighteenth century that the Borda and Condorcet winners need not agree, it had not been known, for instance, in which settings the Condorcet and plurality winners can disagree, or must agree. Results of this type are developed here for all three-alternative positional rules. These relationships are based on an easily used method that connects pairwise tallies with admissible positional outcomes; e.g., a special case provides the first necessary and sufficient conditions ensuring that the Condorcet winner is the plurality winner; another case identifies when there must be a profile whereby each candidate is the “winner” with some positional rule.     

多元Lanchester方程在装备战损量预计中的应用

在战时装备保障中,装备战损量预计是一难点问题.本文从分析影响装备战损的因素出发,采用多元Lanchester方程寻求解决方案.提出了基于指数多元Lanchester方程的装备战损量预计模型和模型中毁伤系数的确定方法.据此,建立了一种新的装备战损量预计方法,并举例验证.该方法较好的满足了未来信息化条件下作战装备保障的需要,具有重要的参考价值.     

Potential variability of decisional skills in uncertain dichotomous choice situations

The main concern of this paper is the selection of optimal decision rules for groups of individuals with identical preferences but diverse and potentially variable independent decisional skills. Employing the uncertain dichotomous choice model the main results illustrate how optimality and sensitivity analysis can be pursued while explicitly recognizing decision-making costs associated with potential variability of decisional skills. For panels of experts consisting of three members our analysis focuses on three special cases of potential variability in individual skills. The extended optimality problem is analyzed resolving the dilemma which of the two common rules, the simple majority rule or the expert rule, is the better selection for the group. The sensitivity of the two rules to variability of decisional skills is also investigated.     

Some Generalizations of the Pinwheel Tiling

We introduce a new family of nonperiodic tilings, based on a substitution rule that generalizes the pinwheel tiling of Conway and Radin. In each tiling the tiles are similar to a single triangular prototile. In a countable number of cases, the tiles appear in a finite number of sizes and an infinite number of orientations. These tilings generally do not meet full-edge to full-edge, but can be forced through local matching rules. In a countable number of cases, the tiles appear in a finite number of orientations but an infinite number of sizes, all within a set range, while in an uncountable number of cases both the number of sizes and the number of orientations is infinite. Received April 9, 1996, and in revised form September 16, 1996.     

Asymptotic vulnerability of positional voting rules to coalitional manipulation

Voting rule performances are sometimes evaluated according to their respective resistances to allow profitable misrepresentation of individual preferences. This seems to be a hard task when scoring systems with possibly non integer weights are involved. In this paper, it is shown how one can still obtain asymptotic results in these settings. Our analysis for three-candidate elections provides a characterization of unstable voting situations at which a positional voting rule is manipulable by some coalition not larger than an arbitrary proportion of the electorate. This allows us to address a conjecture by Pritchard and Wilson (2007). That is, under the Impartial Anonymous Culture (IAC), the plurality rule asymptotically minimizes the vulnerability to coalitional manipulation when the size of the manipulating coalition is unrestricted. This later result is no longer valid when only manipulation by small coalitions is considered: now, the Borda rule tends to outperform other rules. Furthermore, the vulnerability of a positional voting rule to coalitional manipulation is not affected by increasing the size of the manipulating coalition from 0.5 to 1.     

Rough set theory: a novel approach for extraction of robust decision rules based on incremental attributes

Rough set theory is a new data mining approach to manage vagueness. It is capable to discover important facts hidden in the data. Literature indicate the current rough set based approaches can’t guarantee that classification of a decision table is credible and it is not able to generate robust decision rules when new attributes are incrementally added in. In this study, an incremental attribute oriented rule-extraction algorithm is proposed to solve this deficiency commonly observed in the literature related to decision rule induction. The proposed approach considers incremental attributes based on the alternative rule extraction algorithm (AREA), which was presented for discovering preference-based rules according to the reducts with the maximum of strength index (SI), specifically the case that the desired reducts are not necessarily unique since several reducts could include the same value of SI. Using the AREA, an alternative rule can be defined as the rule which holds identical preference to the original decision rule and may be more attractive to a decision-maker than the original one. Through implementing the proposed approach, it can be effectively operating with new attributes to be added in the database/information systems. It is not required to re-compute the updated data set similar to the first step at the initial stage. The proposed algorithm also excludes these repetitive rules during the solution search stage since most of the rule induction approaches generate the repetitive rules. The proposed approach is capable to efficiently and effectively generate the complete, robust and non-repetitive decision rules. The rules derived from the data set provide an indication of how to effectively study this problem in further investigations.     

On the quasi-optimal rules for the choice of the regularization parameter in case of a noisy operator

A usual way to characterize the quality of different a posteriori parameter choices is to prove their order-optimality on the different sets of solutions. In paper by Raus and H?marik (J Inverse Ill-Posed Probl 15(4):419–439, 2007) we introduced the property of the quasi-optimality to characterize the quality of the rule of the a posteriori choice of the regularization parameter for concrete problem Au = f in case of exact operator and discussed the quasi-optimality of different well-known rules for the a posteriori parameter choice as the discrepancy principle, the modification of the discrepancy principle, balancing principle and monotone error rule. In this paper we generalize the concept of the quasi-optimality for the case of a noisy operator and concretize results for the mentioned parameter choice rules.     

A family of rules for parameter choice in Tikhonov regularization of ill-posed problems with inexact noise level

We consider Tikhonov regularization of linear ill-posed problems with noisy data. The choice of the regularization parameter by classical rules, such as discrepancy principle, needs exact noise level information: these rules fail in the case of an underestimated noise level and give large error of the regularized solution in the case of very moderate overestimation of the noise level. We propose a general family of parameter choice rules, which includes many known rules and guarantees convergence of approximations. Quasi-optimality is proved for a sub-family of rules. Many rules from this family work well also in the case of many times under- or overestimated noise level. In the case of exact or overestimated noise level we propose to take the regularization parameter as the minimum of parameters from the post-estimated monotone error rule and a certain new rule from the proposed family. The advantages of the new rules are demonstrated in extensive numerical experiments.     

Reconsideration of the present value method

In investment decision-making, the net present value method is widely used as one of the best decision rules (techniques or criteria). At the same time, it is also used to evaluate decision alternatives for a long range period of time, in economics or even in control theory. Its theoretical validation as the best method for investment decision-making has been based on a basis such that the best technique (investment decision rule) will maximize shareholders' wealth which is measured by the present value of cash flows discounted at the opportunity cost of capital. Such a theoretical requirement as maximizing shareholders' wealth is very important for investment decision-makings. This requirement implies that an ordering relation of projects determined by the best investment rule must be order-isomorphic to that determined by the measure of shareholders' wealth. This order-isomorphism can be represented by necessary and sufficient conditions (or separate criteria). However, they are not suitable for comparing investment decision rules, because they are designed for selecting the best investment decision rule. At the same time, the other dominance of the net present value method over other investment rules is also found in its decision-theoretical aspects. Formulating the net present value method, internal rate of return method and simple sum method in an axiomatic fashion, the net present value method is compared with the other rules, and is shown to have enough clarity and simplicity in theory and practice.