Committee choice and the core under supramajority rule: Results from simulation of majority choice in 2-dimensional space

While simple-majority choice by committees is generally unstable, supramajority rule has been demonstrated to yield nonempty sets of stable outcomes: outcomes in the core. This paper reports results of a computer simulation of majority choice by committees under supramajority rule. The object is to explore the transition from unstable to stable committee choice with increasing supramajority rules. The findings are that supramajority rule limits the instability of committee choice; that stable committee choice is no more predictable than unstable committee choice; and that an optimal supramajority rule can be specified which minimizes instability and maximizes the predictability of committee choice. In all of the results, simple-majority rule plays virtually no role.     

Picking a loser? A social choice perspective on the Danish government formation of 1975

All democratic systems are theoretically open to so-called election inversions, i.e., instances wherein a majority of the decision makers prefer one alternative but where the actual outcome is another. The paper examines the complex 1975 Danish government formation process, which involved five rounds of negotiations and at least five competing alternatives. We demonstrate that in terms of party preferences the final outcome was not the Condorcet winner but rather one that could have been beaten by at least three other government alternatives in head-to-head comparisons. The Danish procedural system of “negative” parliamentarism combined with simple plurality rule to produce the electoral inversion.     

The economic significance of “insignificant” rules

We know relatively little about the economic effects of “insignificant” rules because they are not typically analyzed. Yet, these rules could be cumulatively important. We provide an economic analysis of one proposed rule to control hazardous air pollutants, which is not considered to be economically significant. This rule is of particular interest because it is one of the first in a long series of rules that Environmental Protection Agency (EPA) will consider for limiting hazardous air pollutant emissions. Our analysis suggests that the proposed controls that EPA has considered are not likely to pass a benefit–cost test. We recommend that an agency base its decision to allocate additional resources to benefit–cost analysis on the expected value of the improved information. In addition, agencies should consider applying a rule of thumb that would specify a threshold level of risk reduction that needs to be achieved before some kinds of regulation are considered.     

Measuring majority power and veto power of voting rules

We study voting rules with respect to how they allow or limit a majority from dominating minorities: whether a voting rule makes a majority powerful and whether minorities can veto the candidates they do not prefer. For a given voting rule, the minimal share of voters that guarantees a victory to one of the majority’s most preferred candidates is the measure of majority power; and the minimal share of voters that allows the minority to veto each of their least preferred candidates is the measure of veto power. We find tight bounds on such minimal shares for voting rules that are popular in the literature and used in real elections. We order the rules according to majority power and veto power. Instant-runoff voting has both the highest majority power and the highest veto power; plurality rule has the lowest. In general, the greater is the majority power of a voting rule, the greater its veto power. The three exceptions are: voting with proportional veto power, Black’s rule and Borda’s rule, which have relatively weak majority power and strong veto power, thus providing minority protection. Our results can shed light on how voting rules provide different incentives for voter participation and candidate nomination.

     

Optimal team and individual decision rules in uncertain dichotomous situations

In this paper, we consider the problem of determining the optimalteam decision rules in uncertain, binary (dichotomous) choice situations. We show that the Relative (Receiver) Operating Characteristic (ROC) curve plays a pivotal role in characterizing these rules. Specifically, the problem of finding the optimal aggregation rule involves finding a set ofcoupled operating points on the individual ROCs. Introducing the concept of a team ROC curve, we extend the method of characterizing decision capabilities of an individual decisionmaker (DM) to a team of DMs. Given the operating points of the individual DMs on their ROC curves, we show that the best aggregation rule is a likelihood ratio test. When the individual opinions are conditionally independent, the aggregation rule is a weighted majority rule, but with different asymmetric weights for the yes and no decisions. We show that the widely studied weighted majority rule with symmetric weights is a special case of the asymmetric weighted majority rule, wherein the competence level of each DM corresponds to the intersection of the main diagonal and the DM's ROC curve. Finally, we demonstrate that the performance of the team can be improved by jointly optimizing the aggregation rule and the individual decision rules, the latter possibly requiring a shift from the isolated (non-team) optimal operating point of each DM.Research supported by NSF grant #IRI-8902755 and ONR contract #N0014-90-J-1753.     

Two remarks on the effect of increased equalitarianism in decisional skills on the number of individuals that maximizes group judgmental competence

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.     

略论西方民主政治的理论基础

根据西方的民主理论,民主政治应当体现为多数人的统治。但是,如果多数的权力不受制约,多数人进行统治并不一定带来真正的民主政治,因为集体的智慧是有限的,多数的无限权威容易导致权力的滥用,多数的交易规则对少数人具有强制作用,这样常常会产生多数人忽视少数人权益的现象。因此,要使多数人的民主成为多数善政,要使民主政治具有适当的制度基础,就要对多数投票决定问题的范围加以限定,少教人应当被给予更大程度的自治,司法体系和社会力量要充分利用起来对多数的权力加以制衡。     

Do Group Decision Rules Affect Trust? A Laboratory Experiment on Group Decision Rules and Trust

Enhanced participation has been prescribed as the way forward for improving democratic decision making while generating positive attributes like trust. Yet we do not know the extent to which rules affect the outcome of decision making. This article investigates how different group decision rules affect group trust by testing three ideal types of decision rules (i.e., a Unilateral rule, a Representative rule and a ‘Non‐rule’) in a laboratory experiment. The article shows significant differences between the three decision rules on trust after deliberation. Interestingly, however, it finds that the Representative rule yields more trust than the Non‐rule and also significantly more trust than the Unilateral rule, when analysing the results at group level. These findings challenge the theoretical understanding by, for example, deliberative normative theorists that more inclusive, consensual and non‐hierarchical decision‐making procedures enhance trust vis‐à‐vis other more hierarchical decision‐making procedures.     

If you like the alternative vote (a.k.a. the instant runoff), then you ought to know about the Coombs rule

We consider four factors relevant to picking a voting rule to be used to select a single candidate from among a set of choices: (1) avoidance of Condorcet losers, (2) choice of Condorcet winners, (3) resistance to manipulability via strategic voting, (4) simplicity. However, we do not try to evaluate all voting rules that might be used to select a single alternative. Rather, our focus is restricted to a comparison between a rule which, under the name ‘instant runoff,’ has recently been pushed by electoral reformers in the US to replace plurality-based elections, and which has been advocated for use in plural societies as a means of mitigating ethnic conflict; and another similar rule, the ‘Coombs rule.’ In both rules, voters are required to rank order candidates. Using the instant runoff, the candidate with the fewest first place votes is eliminated; while under the Coombs rule, the candidate with the most last place votes is eliminated. The instant runoff is familiar to electoral system specialists under the name ‘alternative vote’ (i.e., the single transferable vote restricted to choice of a single candidate). The Coombs rule has gone virtually unmentioned in the electoral systems literature (see, however, Chamberlin et al., 1984). Rather than considering the properties of these two rules in the abstract, we evaluate them in the politically realistic situations where voters are posited to have (at least on balance) single-peaked preferences over alternatives. Evaluating the two rules under this assumption, we argue that the Coombs rule is directly comparable in that Coombs is always as good as AV with respect to two of our four criteria and it is clearly superior to AV with respect to one of the four criteria, namely criterion (2), and is potentially inferior only with respect to criterion (3). Key to this argument are two new propositions. The first new result shows that, under the posited assumption, for four alternatives or fewer, AV is always as likely or more likely to select the Condorcet winner than plurality. The second new result shows that, under the same assumptions, the Coombs rule will always select the Condorcet winner regardless of the number of alternatives.     

On collective goods,private wealth,and the core solution of simple games with sidepayments

This essay identifies consequences for the core solution in a class of social decision problems concerning the provision of collective goods (or bads) if the rules are modified to permit sidepayments. In these problems, a kind of formal decision procedure that includes any weighted or unweighted majority rule governs only the decision about collective goods. Each decision about collective goods, however, implies a vector of the agents' endowments of private wealth that can, but need not, vary across the alternatives. Any agent may offer to make sidepayments from this endowment that are contingent on the collective goods decision, but the agent holds preferences that, given any fixed decision about collective goods, strictly increase in the agent's own wealth. The results indicate that the core's response to introducing the possibility of sidepayments depends on whether any agent possesses a veto over the collective goods decision. If no one has a veto, then an outcome belongs to the core of the game with sidepayments only if no sidepayment is made and the same decision about collective goods belongs to the core of the associated game without sidepayments. In this case, introducing the possibility of sidepayments does not bring a new collective goods decision into the core. Indeed, merely adding the possibility of sidepayments can cause the core to vanish. On the other hand, if at least one agent possesses a veto, then introducing sidepayments can (but need not) lead to a new core solution concerning the decision about collective goods. In any such new solution, at least one agent who has a veto — but no one who lacks it — receives a sidepayment.     

Is Rule by Majorities Special?

One way of making decisions is for political associates or their representatives to vote on each issue separately in accordance with the majority principle and then take the cumulative outcomes of such majority decision making to define the collective choice for public policy. We call such a system one of majorities rule. Thought of in spatial terms, majorities rule is equivalent to the principle of making decisions according to the issue-by-issue median of voter preferences. If popular control and political equality are core democratic values, they can be rendered as requirements on a collective choice rule, involving resoluteness, anonymity, strategy-proofness and responsiveness. These requirements entail that the collective decision rule be a percentile method. If we then add a requirement of impartiality, as exhibited in a collective choice rule which would be chosen behind a veil of ignorance, then the issue-by-issue median is uniquely identified as a fair rule. Hence, majorities rule is special. Some objections to this line of reasoning are considered.     

The robustness of the optimal weighted majority rule to probability distortion

This study identifies the optimal collective decision rule in a dichotomous symmetric setting, allowing for probabilities distortion as originally assumed by Tversky and Kahneman (Journal of Risk and Uncertainty 5(4):297–323, 1992). We show that previous results that identified the weighted majority rule as the optimal one, and did not consider subjective probabilities, are robust to such distortion in the sense that neither the rule nor the weights are changed.     

Decision costs in legislative bargaining: an experimental analysis

We conduct an experiment to assess the effects of different decision rules on the costs of decision making in a multilateral bargaining situation. Specifically, we compare the amount of costly delay observed in an experimental bargaining game under majority and unanimity rule. Our main finding is that individual subjects are more likely to reject offers under unanimity rule. This higher rejection rate, as well as the requirement that all subjects agree, leads to more costly delay. This result provides empirical support for a classic argument in favor of less-than-unanimity decision rules put forth by Buchanan and Tullock (The calculus of consent: logical foundations of constitutional democracy, University of Michigan Press, Ann Arbor, 1962).     

Can democracy induce development? A constitutional perspective

We examine the constitutional design required for democratic societies to overcome poverty traps. Restricting agenda setting by ensuring subsistence levels of consumption and applying simple majority voting as a decision rule will not enable a society to overcome poverty. We show that a combination of suitable constitutional rules can, however, overcome poverty and induce economic well-being. Besides majority voting, these rules include rotating agenda setting, agenda repetition, and tax-protection rules. We thus highlight the crucial role of democratic institutions for economic development.     

Voting for Pareto optimality: a multidimensional analysis

We compare unanimity rule and majority rule in their abilities to produce Pareto superior and Pareto optimal alternatives in fixed number of rounds of voting using a two-dimensional spatial voting model with random proposals, sincere proposals, and strategic proposals. Our findings show that for random or sincere proposals, majority rule is at least as likely to select a Pareto optimal outcome as unanimity rule. For strategic proposals, the subgame perfect equilibrium under unanimity rule is Pareto optimal. For other k-majority rules, the outcome is Pareto optimal or very close to it. For outcomes that are both Pareto optimal and Pareto superior, unanimity rule outperforms majority rule.     

Optimal voting rules under uncertainty

The theory of ‘constitutional’ choice of voting rules developed by Buchanan and Tullock is an extended to an explicit decision-theoretic form. Voters in the ‘constitutional’ position choose what they believe will be their optimal share or majority rule for making social decisions, by maximizing their individual expected utility from the anticipated social decisions, under conditions of uncertainty. The rule that maximizes expected social benefits depends upon (1) the expected distribution and intensity of preferences on future issues, and (2) the decisionmaking procedures and costs. ‘Decisionmaking’ and ‘external’ costs are shown to be interrelated. Following this analysis, failure to pass laws imposes ‘external’ costs in the same way that passing them does, so that the optimal majority may be lower when desirable laws are viewed as changing over time. Decisionmaking costs depend upon the way in which voters are persuaded to support or oppose bills, upon the distribution of preferences on bills, and on vote-trading possibilities. If vote-trading is almost costless, a wide range of decision rules has nearly equal social benefits. Finally, the model is used to discuss optimal voting rules for several decisionmaking bodies.     

Communication in committees: who should listen?

In a parsimonious model of a collective decision problem with partially conflicting interests, we show that restricting communication may enhance decision quality. If disclosed information is observed by decision makers with different preferences, individuals may strategically withhold information. In this case, a committee member’s silence arouses the other members’ suspicions. As a consequence, in case of residual uncertainty, individual votes may react less to information that is publicly observed.     

The fairness of discounting: A majority rule approach

A model of majority rule is developed in which each of a finite number of generations votes on a redistribution of income between itself and the other generations. In voting, each generation expresses tastes for its own income and for the distribution of income across generations. The model is then used to derive the conditions under which discounting is justified — namely those conditions for which the majority rule exhibits a positive marginal rate of time preference. It is demonstrated that when each generation is wealthier than those preceding it, the parameters representing the taste for income equality must be relatively high for the majority rule to exhibit a positive marginal rate of time preference.     

Optimizing group judgmental accuracy in the presence of interdependencies

Consider a group of people confronted with a dichotomous choice (for example, a yes or no decision). Assume that we can characterize each person by a probability, p _i, of making the ‘better’ of the two choices open to the group, such that we define ‘better’ in terms of some linear ordering of the alternatives. If individual choices are independent, and if the a priori likelihood that either of the two choices is correct is one half, we show that the group decision procedure that maximizes the likelihood that the group will make the better of the two choices open to it is a weighted voting rule that assigns weights, w _i, such that $$w_i \propto \log \frac{{p_i }} {{1 - p_i }}.$$ We then examine the implications for optimal group choice of interdependencies among individual choices.     

Responsibility Attribution for Collective Decision Makers

We argue that individuals use responsibility attribution heuristics that apply to collective decisions made, for example, by families, teams within firms, boards in international organizations, or coalition governments. We conduct laboratory and online experiments to tease out the heuristics subjects use in their responsibility attribution for collective decision makers. The lab experiments comprise a collective dictator game in which decision makers have weighted votes and recipients can punish individual decision makers. Our results show that recipients punish unfair allocations and mainly target the decision maker with proposal power and with the largest vote share. We find weak evidence that decision makers with veto power are targeted or that recipients punish proportional to vote share. The online experiment demonstrates that subjects indeed believe that the decision maker with proposal power has the most influence on the collective decision outcome. We discuss the implications of our findings for theories of vote choice.