Majority rule: Second thoughts and refutations

The Evolution of Collective Choice Under Majority Rule

Critical strategies under approval voting: Who gets ruled in and ruled out

We consider the elections of a seat-posted committee, and investigate the propensity of seat-wise majority voting to choose a committee that fulfills the majority will with respect to preferences over committees. Voters have seat-wise preferences and preferences over committees are derived from seat-wise preferences by means of a neutral preference extension. Neutrality means that the names of candidates do not play any role. The majority committee paradox refers to a situation where a Condorcet winner exists for each seat, and a Condorcet winner committee also exists but does not coincide with the combination of seat-wise Condorcet winners. The majority committee weak paradox refers to a situation where the combination of seat-wise Condorcet winners is not a Condorcet winner among committees. We characterize the domains of preference extensions immune to each of the paradoxes.

Approval Voting is analyzed in a context of large elections with strategic voters: the Myerson’s Large Poisson Games. We first establish the Magnitude Equivalence Theorem which substantially reduces the complexity of computing the magnitudes of the pivot outcomes. Furthermore, we show that the Condorcet Winner need not be the Winner of the election in equilibrium under Approval Voting. Indeed, a ‘paradoxical’ example is provided where a candidate ranked first by more than half of the voters is not the Winner of the election.

Climate change, biodiversity losses, global health threats, changing recreation patterns are but a few of the many challenges that currently, and for some time to come, the world has to cope with. To address these challenges and to mitigate some of them, ecosystem and particularly conservation management increasingly have to adopt strategies never considered before. One such new possibility is crowdsourcing, a variant of public consultation, where a number of experts are invited and, for example, asked to mark trees that – in their opinion – should be removed in order to improve or restore a forest ecosystem. This type of crowdsourcing has recently been carried out in many European countries and overseas as part of what commonly is referred to as marteloscope. In this paper, we addressed the question of how the rating or voting of such a crowd of experts is best aggregated to obtain one final, consolidated list of trees to be evicted. Standard approval voting often leads to a domination by the majority of voters and important contributions by minority experts are largely ignored. To avoid this and to better represent the pluralism of expertise and opinions in matters, where currently no best-practice guidelines exist, we analysed the effects of three proportional multiwinner rules used in political science by applying them to 50 marteloscope experiments in Great Britain. Our results indicated that proportional rules – particularly in situations where the invited expert markers disagree – achieved a better representation of different opinions than standard approval voting. Proportional rules also act as a safety mechanism reducing risks when the majority decisions prove inappropriate and as a consequence forest development could completely go astray.

The paper introduces the concept of polar decision rules and establishes that majority rules are polar rules. We identify second best rules and penultimate rules in cases that majority rules are optimal or the most inferior, respectively. We especially specify the almost expert rule and the almost majority rule as the secondary rules of the expert and majority rules, respectively.

A sufficient condition is derived for a policy y to be a Condorcet winner, when the set of feasible policies is some subsety ofR N with non-empty interior. Voters are assumed to differ in some scalar characteristic w. The sufficient condition refers only to voters' preferences over the set of preferred policies (of the various other voters). This set is a one-dimensional curve inR N> . The condition is that the indifference curves of each typew through the preferred policyy* (v) of any typev all be collinear. If the condition holds, then the preferred policyy* (m) of the median type of voter will be a Condorcet winner. If there are only three types of voter, then the above condition is also necessary for the existence of a Condorcet winner.

On the model dependence of majority preference relations reconstructed from ballot or survey data

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.

Simple normative rules imply simple positive rules

Under approval voting (AV), each voter just distinguishes the candidates he approves of from those appearing as unacceptable. The preference approval voting (PAV) is a hybrid version of the approval voting first introduced by Brams and Sanver (in: Brams, Gehrlein, Roberts (eds) The mathematics of preference, choice and order. Springer, Berlin, pp 215–237, 2009). Under PAV, each voter ranks all the candidates and then indicates the ones he approves. In this paper, we provide an analytical representation of the limiting probability that PAV elects the Condorcet winner (resp. the Condorcet loser) when she exists in three-candidate elections. We perform our analysis by assuming the assumption of the Extended Impartial Culture. The aim is to measure at which extend PAV performs better than AV both on the propensity of electing the Condorcet winner and on that of the non-election of the Condorcet loser. For this purpose, we also provide an analytical representation of the limiting probability that AV elects the Condorcet winner (resp. the Condorcet loser) when she exists in three-candidate elections. Our representation of the limiting probability that AV elects the Condorcet winner is more general than that provided by Diss et al. (in: Laslier and Sanver (eds) Handbook on approval voting. Springer, Berlin, pp 255–283, 2010) and it leads to the same figures as the representation provided by Gehrlein and Lepelley (Group Decis Negot 24:243–269, 2015).

Previous research has indicated sex differences in style of interaction for members in small groups. It was assumed that some of these sex differences could be attributed to demand characteristics in relation to specific topics discussed by group members in earlier investigations. The purpose of the present study was to investigate the relative importance of two such demand characteristics, decision rule (consensus rule vs. majority rule), and decision consequence (high vs. low consequences), in addition to the sex composition of the group membership. Adherence to the group decision was also studied. On a topic previously rated as important, 16 four-person groups of males and the same number of female groups met and deliberated on a decision regarding an academic policy. Later these undergraduate students indicated their preference on the decision topic. The results showed male—female differences not accounted for by decision rule, decision consequence, or group decision post-test change. Explanation of the sex differences was offered in terms of varying academic aspiration levels and incongruency with attained academic achievement. The results also lend partial support for the importance of some operating demand characteristics, as yet unidentified.

In one-dimensional environments with single-peaked preferences we consider social welfare functions satisfying Arrow''s requirements, i.e. weak Pareto and independence of irrelevant alternatives. When the policy space is a one-dimensional continuum such a welfare function is determined by a collection of 2N strictly quasi-concave preferences and a tie-breaking rule. As a corollary we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voters preference is strictly quasi-concave.

A decision-making body may utilize a wide variety of different strategies when required to make a collective decision. In principle, we would like to use the most effective decision rule, that is, the rule yielding the highest probability of making the correct decision. However, in reality we often have to choose a decision rule out of some restricted family of rules. Therefore, it is important to be able to rank various families of rules. In this paper we consider three classes of decision rules: (i) balanced expert rules, (ii) the so-called single expert rules, and (iii) restricted majority rules. For the first two classes, we show that, as we deviate from the best rule in the family, the effectiveness of the decision rule decreases. For the last class, we obtain a very different phenomenon: any inner ranking is possible.

The purpose of economic decision rules is to guide decision makers who have competing goals or are uncertain about how their goals can be fulfilled. This chapter discusses the assumptions underlying major decision rules such as expected utility maximization, discounting of future events, maximin, and various types of efficiency criteria including cost effectiveness and Pareto efficiency. All of these decision rules impose restrictions on the information to be taken into account, and since these restrictions are value laden, so are the decision rules. However, in the process of applying decision rules, the value assumptions are often put out of sight instead of being brought forward and discussed.