Strict proportional power in voting bodies

It is a widely known fact among game theorists as well as political scientists that the distribution of voting weights in a voting body is generally a poor proxy for the distribution of voting power within the body. It has been proposed to equate the distribution of a priori voting power and actual seat distribution by randomizing the decision rule of the voting body over various majority rules. In this paper, some implications of this procedure will be discussed.     

Condorcet vs. Borda in light of a dual majoritarian approach

Many voting rules and, in particular, the plurality rule and Condorcet-consistent voting rules satisfy the simple-majority decisiveness property. The problem implied by such decisiveness, namely, the universal disregard of the preferences of the minority, can be ameliorated by applying unbiased scoring rules such as the classical Borda rule, but such amelioration has a price; it implies erosion in the implementation of the widely accepted “majority principle”. Furthermore, the problems of majority decisiveness and of the erosion in the majority principle are not necessarily severe when one takes into account the likelihood of their occurrence. This paper focuses on the evaluation of the severity of the two problems, comparing simple-majoritarian voting rules that allow the decisiveness of the smallest majority larger than 1/2 and the classical Borda method of counts. Our analysis culminates in the derivation of the conditions that determine, in terms of the number of alternatives k, the number of voters n, and the relative (subjective) weight assigned to the severity of the two problems, which of these rules is superior in light of the dual majoritarian approach.     

The significance of independent decisions 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 dependent decisional skills. The main result establishes that within the uncertain dichotomous choice situation independent voting is always weakly superior to any pattern of interdependence among individual decisions. For the special class of total interdependence patterns the optimal rule is explicitly identified.     

On The Meaning Of Owen–Banzhaf Coalitional Value In Voting Situations

In this paper we discuss the meaning of Owen's coalitional extension of the Banzhaf index in the context of voting situations. It is discussed the possibility of accommodating this index within the following model: in order to evaluate the likelihood of a voter to be crucial in making a decision by means of a voting rule a second input (apart from the rule itself) is necessary: an estimate of the probability of different vote configurations. It is shown how Owen's coalitional extension can be seen as three different normative variations of this model.     

A characterization of majority voting rules with quorums

We give a characterization of majority voting rules with quorums in the framework of May (Econometrica 20:680–684, 1952)’s seminal article. According to these voting rules, an alternative is socially chosen if and only if it obtains the relative majority of votes and the total number of voters not abstaining reaches the quorum.     

Calculable Power: A Case Study of IMF Quotas and Voting Rights Reform*

Voting procedure is an important mechanism for public choice in collective bodies such as international organizations. This paper measures and compares IMF member countries’ voting power before the 2008 reform and after the 2010 reform on the basis of datasets on IMF quotas and voting rights distribution provided by IMF. Our study verifies that IMF’s quotas and voting rights reforms do help to reduce the voting power gap among member countries. The 2008 and 2010 reforms produce a greater improvement in emerging members’ voting power under the 70 percent majority rule than the 85 percent rule; the 70 percent majority rule means the United States would lose its absolute veto. Moreover, the paper disproves the underlying assumption that regards a member’s voting power as proportional to its voting rights. Countries with different amounts of voting rights can still have the same voting power.     

A characterization of the maximin rule in the context of voting

In a voting context, when the preferences of voters are described by linear orderings over a finite set of alternatives, the Maximin rule orders the alternatives according to their minimal rank in the voters’ preferences. It is equivalent to the Fallback bargaining process described by Brams and Kilgour (Group Decision and Negotiation 10:287–316, 2001). This article proposes a characterization of the Maximin rule as a social welfare function (SWF) based upon five conditions: Neutrality, Duplication, Unanimity, Top Invariance, and Weak Separability. In a similar way, we obtain a characterization for the Maximax SWF by using Bottom Invariance instead of Top Invariance. Then, these results are compared to the axiomatic characterizations of two famous scoring rules, the Plurality rule and the Antiplurality rule.     

Committee Decisions with Partisans and Side-Transfers

A dichotomous decision-making context in committees is considered where potential partisan members with predetermined votes can generate inefficient decisions and buy neutral votes. The optimal voting rule minimizing the expected costs of inefficient decisions for the case of a three-member committee is analyzed. It is shown that the optimal voting rule can be non-monotonic with respect to side-transfers: in the symmetric case, majority voting is optimal under either zero, mild or full side-transfer possibilities, whereas unanimity voting may be optimal under an intermediate side-transfer possibility. The side-transfer possibilities depend on the power of partisans (their ability or willingness to pay for neutral votes) relative to the corruptibility of neutral members (personal cost of deliberately casting a `wrong' vote).     

Intensity of preference and related uncertainty in non-compensatory aggregation rules

Non-compensatory aggregation rules are applied in a variety of problems such as voting theory, multi-criteria analysis, composite indicators, web ranking algorithms and so on. A major open problem is the fact that non-compensability implies the analytical cost of loosing all available information about intensity of preference, i.e. if some variables are measured on interval or ratio scales, they have to be treated as measured on an ordinal scale. Here this problem has been tackled in its most general formulation, that is when mixed measurement scales (interval, ratio and ordinal) are used and both stochastic and fuzzy uncertainties are present. Objectives of this article are first to present a comprehensive review of useful solutions already proposed in the literature and second to advance the state of the art mainly in the theoretical guarantee that weights have the meaning of importance coefficients and they can be summarized in a voting matrix. This is a key result for using non-compensatory Condorcet consistent rules. A proof on the probability of existence of ties in the voting matrix is also developed.     

Rules Trump Desires in Preschoolers’ Predictions of Group Behavior

The objective of this article is to investigate the way children weigh conventional rules against desires when considering how a group will behave. To do so, two experiments involving a prediction task in which desires were pitted against conventional rules were presented to three‐ to five‐year‐old children. In Experiment 1, four scenarios were established as classroom scenes in which either one protagonist or three protagonists had a desire that went against an explicit conventional rule. In the individual control condition, the choices linked to the rules were at chance whereas, in the group condition, the participants predicted that all the protagonists would end up following the rule. Given that both conditions in Experiment 1 implied four rule followers in the design, Experiment 2 staged not three but seven potential rule transgressors to see whether the desire of the majority might undermine the rule. Results showed no majority effect: participants expected protagonists to act counter to their desire and to follow the rule. Such results suggest that children as young as three‐year‐old favor rules over desires when they have to predict the behavior of a group, whether it be the majority or not. Possible implications of these intriguing findings are discussed.     

Optimal jury design for homogeneous juries with correlated votes

In a homogeneous jury, in which each vote is correct with the same probability, and each pair of votes correlates with the same correlation coefficient, there exists a correlation-robust voting quota, such that the probability of a correct verdict is independent of the correlation coefficient. For positive correlation, an increase in the correlation coefficient decreases the probability of a correct verdict for any voting rule below the correlation-robust quota, and increases that probability for any above the correlation-robust quota. The jury may be less competent under the correlation-robust rule than under simple majority rule and less competent under simple majority rule than a single juror alone. The jury is always less competent than a single juror under unanimity rule.     

Sophisticated voting under the plurality procedure: A test of a new definition

The Niemi-Frank definition of sophisticated voting can now be evaluated on two grounds. First, we can compare our definition to Farquharson's. For the most part, the two definitions yield identical outcomes. Both pickCondorcet winners a very high proportion of the time and prevent the selection of Condorcet losers. The major differences are in the logic underlying the two definitions and in the rate of determinacy of outcomes. Here there is a tradeoff. The logic underlying the Farquharson model is especially persuasive, although it is our feeling that the Niemi-Frank definition comes closer to mirroring the way in which voters might actually analyze a plurality situation. In any case, the price paid by the Farquharson definition for its ironclad logic is a much higher rate of indeterminacy. In over half of the cases, the Farquharson logic fails to lead to any conclusion whatsoever. The Niemi-Frank definition yields many more determinate situations, with mostly Condorcet winners and with strategies that make good, if not completely unassailable sense. A second way of evaluating the Niemi-Frank definition is in comparison with sincere voting. A commonly-cited shortcoming of plurality voting is that often fails to choose a Condorcet winner. As we notedearlier, sophisticated plurality voting, unlike binary voting, is imperfect in this respect. Nonetheless, even taking account of the indeterminacy thatremains in the Niemi-Frank definition, sophisticated voting picked a Condorcet winner about 10 percent more frequently than did sincere voting as well as eliminating the possibility of a Condorcet loser being chosen. By this measure, the Niemi-Frank definition is not only acceptable but suggests that this form of strategic behavior actually leads tobetter outcomes. By proposing and now by testing a new definition of sophisticated voting under plurality rule, we have begun to make some headway on understanding strategic behavior and its effects in an outwardly simple yet deceptively complex voting system. We are, of course, far from finished. Most significantly, our definition applies to only three alternatives, and Farquharson's (even if one is willing to live with its high indeterminacy) becomes extraordinarily cumbersome with more than three alternatives? In any event, the results of this foray into sophisticated nonbinary voting suggests once again that strategic behavior, rather than making things worse, improves the chances that the outcome will be the one most favored by the majority criterion.     

A note on manipulability of large voting schemes

A voting system is a rule which assigns to every possible combination of votes (by any number of individuals) an alternative. We define the notion of asymptotic nonmanipulability for voting systems, and prove that every representable positionalist voting system is asymptotically nonmanipulable. Various aspects of manipulation of large voting schemes and several examples are also discussed.     

Resolute majority rules

We investigate resolute voting rules that always rank two alternatives strictly and avoid social indecision. Resolute majority rules differ from the standard majority rule in that whenever both alternatives win the same number of votes, a tie-breaking function is used to determine the outcome. We provide axiomatic characterizations of resolute majority rules or resolute majority rules with a quorum. Resoluteness axiom is used in all these results. The other axioms are weaker than those considered in the characterization of the majority rule by May (1952 Econometrica, 20:680–684). In particular, instead of May’s positive responsiveness, we consider a much weaker monotonicity axiom.     

On the inference rules in legal logic

推论规则是逻辑学研究的核心内容。法律逻辑是一门应用逻辑,但它并不是形式逻辑的推论规则在法律领域中的简单运用,而是形式逻辑的推论规则加上法律领域中的特殊推论规则的结果。因此,法律逻辑中的推论规则与形式逻辑中的推论规则相比,既有共性的一面,又有个性的一面。其共性表现为形式逻辑的基本推论规则是构成法律逻辑中的推论规则必不可少的组成部分,其个性表现为法律逻辑中有着与形式逻辑中的推论规则所不具有的特殊推论规则——证明责任规则。     

A Legal Structure for Limiting the Agency Cost of Stock Rights Transfer

The unilateral disposition of stock rights’ voting rights detracts from the welfare of the other shareholders. Contractual arrangements restricting or prohibiting the transfer of stock rights under the capital majority rule may infringe upon shareholders’ right of withdrawal, further weakening stock market constraints on senior management and indirectly raising the agency cost of management abuse of power for private ends. In creating a legal structure for stock rights transfer, we need to find an appropriate balance between freedom of contract, capital majority rule and reduction of agency costs. Judges should determine that the transfer of voting rights is invalid in order to ensure that voting rights match residual claim rights and maintain the constraints on senior management represented by shareholder voting rights. The general prohibition of stock rights transfer in the articles of association blocks shareholders’ right of withdrawal; this is not conducive to restraining potential abuses of power on the part of senior management and should be made invalid. Judges must differentiate between long- and short-term contracts and the initial and revised clauses of the articles of association in order to distinguish between the efficacy of different arrangements limiting transfer of stock rights as laid down in the articles of association.     

A Legal Structure for Limiting the Agency Cost of Stock Rights Transfer

股权表决权能的单独处分会减损其他股东的福利，资本多数决之下限制或者禁止股权转让的合约安排可能会侵害股东的退出权，进而减损股权市场对高管的制约力量，间接推高管理层滥权谋私的代理成小。在创设股权转让的法律结构时，必须任合约自由、资本多数决与降低代理成本之间求取妥当的平衡。法官应认定投票权转让行为无效，以保证投票权与剩余索取权匹配，并保持股东投票权之于高管的约束功能。章程概括性地禁止股权转让，阻塞了股东退出权，不利于遏制控股股东与高管潜在的滥权行为，当属无效。法官必须本着长期契约与短期契约、章程初始条款及修订条款的差异化视角，区分各类限制股权转让的章程约定的效力。     

Partial information on decisional competences and the desirability of the expert rule in uncertain dichotomous choice situations

The paper analyzes the expert resolution problem by employing extended versions of the uncertain dichotomous choice model. The main purpose of this study is to illustrate how the analysis of optimal decision rules can be carried out while dispensing with the common restrictive assumption of full information regarding individual decisional competences. In contrast to most previous studies in this field we here evaluate the expert rule under alternative assumptions regarding the available partial information on judgmental competences rather than compare it in an ad hoc manner to some common alternative rules, such as simple majority rule. A fuller optimality analysis allowing the evaluation of all relevant decision rules, and not merely the expert rule, is attempted for a five-member panel of experts assuming a uniform distribution of individual competences. For three-member groups the optimality issue is resolved by assuming no information on individual competences and interpreting the expert rule as an even-chance lottery on skills.     

Expected frequency and mean size of the paradox of new members

The paradox of new members occurs when the addition of one or more new members to a weighted voting body increases, rather than decreases, the voting power of some of the old members. Extending the computational work of Brams and Affuso (1976), the mean size of the paradox and the relative frequency of its occurrence are presented for small and moderate-size weighted voting bodies. Computational results are presented and conclusions are drawn for the two power indices of Shapley-Shubik and Banzhaf, three different decision rules, and voting bodies with or without dictator. Although the paradox cannot be dismissed as either contrived or improbable, its mean size in moderatesize voting bodies is sufficiently small to question its practical significance.     

Comparison of the Polar Decision Rules for Various Types of Distributions

We focus on the dichotomous choice model, which goes back as far as Condorcet (1785; Essai sur l'application de l'analyse a la probabilité des décisions rendues a la pluralité des voix, Paris). A group of experts is required to select one of two alternatives, of which exactly one is regarded as correct. The alternatives may be related to a wide variety of areas. A decision rule translates the individual opinions of the members into a group decision. A decision rule is optimal if it maximizes the probability of the group to make a correct choice. In this paper we assume the correctness probabilities of the experts to be independent random variables, selected from some given distribution. Moreover, the ranking of the members in the team is (at least partly) known. Thus, one can follow rules based on this ranking. The polar different rules are the expert and the majority rules. The probabilities of the two polar rules being optimal were compared in a series of papers. The main purpose of this paper is to outline the results, providing exact formulas or estimates for these probabilities. We consider a variety of distributions and show that for all of these distributions the asymptotic behaviour of the probabilities of the two polar rules follows the same patterns.