In voting theory, monotonicity is the axiom that an improvement in the ranking of a candidate by voters cannot cause a candidate who would otherwise win to lose. The participation axiom states that the sincere report of a voter’s preferences cannot cause an outcome that the voter regards as less attractive than the one that would result from the voter’s non-participation. This article identifies three binary distinctions in the types of circumstances in which failures of monotonicity or participation can occur. (...) Two of the three distinctions apply to monotonicity, while one of those and the third apply to participation. The distinction that is unique to monotonicity is whether the voters whose changed rankings demonstrate non-monotonicity are better off or worse off. The distinction that is unique to participation is whether the marginally participating voter causes his first choice to lose or his last choice to win. The overlapping distinction is whether the profile of voters’ rankings has a Condorcet winner or a cycle at the top. This article traces the occurrence of all of the resulting combination of characteristics in the voting methods that can exhibit failures of monotonicity. (shrink)

In this account, we explain the meaning of a priori voting power and outline how it is measured. We distinguish two intuitive notions as to what voting power means, leading to two approaches to measuring it. We discuss some philosophical and pragmatic objections, according to which a priori (as distinct from actual) voting power is worthless or inapplicable.

If K is an index of relative voting power for simple voting games, the bicameral postulate requires that the distribution of K -power within a voting assembly, as measured by the ratios of the powers of the voters, be independent of whether the assembly is viewed as a separate legislature or as one chamber of a bicameral system, provided that there are no voters common to both chambers. We argue that a reasonable index – if it is to be used (...) as a tool for analysing abstract, ‘uninhabited’ decision rules – should satisfy this postulate. We show that, among known indices, only the Banzhaf measure does so. Moreover, the Shapley–Shubik, Deegan–Packel and Johnston indices sometimes witness a reversal under these circumstances, with voter x ‘less powerful’ than y when measured in the simple voting game G1 , but ‘more powerful’ than y when G1 is ‘bicamerally joined’ with a second chamber G2 . Thus these three indices violate a weaker, and correspondingly more compelling, form of the bicameral postulate. It is also shown that these indices are not always co-monotonic with the Banzhaf index and that as a result they infringe another intuitively plausible condition – the price monotonicity condition. We discuss implications of these findings, in light of recent work showing that only the Shapley–Shubik index, among known measures, satisfies another compelling principle known as the bloc postulate. We also propose a distinction between two separate aspects of voting power: power as share in a fixed purse (P-power) and power as influence (I-power). (shrink)

This book provides an evaluation of 18 voting procedures in terms of the most important monotonicity-related criteria in fixed and variable electorates. All voting procedures studied aim at electing one out of several candidates given the voters' preferences over the candidates. In addition to (strict) monotonicity failures, the vulnerability of the procedures to variation of the no-show paradoxes is discussed. All vulnerabilities are exemplified and explained. The occurrence of the no-show paradoxes is related to the presence or absence of a (...) Condorcet winner. The primary readership of this book are scholars and students in the area of social choice. (shrink)

We consider a singular event of the following form: in a simple voting game, a particular division of the voters resulted in a positive outcome. We propose a plausible measure that quantifies the causal contribution of any given voter to the outcome. This measure is based on a conceptual analysis due to Braham [1], but differs from his solution to the problem of measuring causality of singular events.

In the voting-power literature the rules of decision of the US Congress and the UN Security Council are widely misreported as though abstention amounts to a `no' vote. The hypothesis (proposed elsewhere) that this is due to a specific cause, theory-laden observation, is tested here by examining accounts of these rules in introductory textbooks on American Government and International Relations, where that putative cause does not apply. Our examination does not lead to a conclusive outcome regarding the hypothesis, but reveals (...) that the rules in question are also widely misreported in these textbooks. A second hypothesis---that the widespread misreporting is explicable by the relative rarity and unimportance of abstention in the two bodies concerned---is also tested and found to be untenable. (shrink)

We analyse and evaluate the qualified majority (QM) decision rules for the Council of Ministers of the EU that are included in the Draft Constitution for Europe proposed by the European Convention [5]. We use a method similar to the one we used in [9] for the QM prescriptions made in the Treaty of Nice.

We analyse and evaluate the qualified majority (QM) decision rule for the Council of Ministers of the EU adopted at the EU Inter-Governmental Conference, Brussels, 18 June 2004 [1]. We compare this rule with the QM rule prescribed in the Treaty of Nice, and the rule included in the original draft Constitution proposed by the European Convention in July 2003. We use a method similar to the one we used in [3] and [4].

We analyse and assess the qualified majority (QM) decision rule for the Council of Ministers of the EU, adopted at the Council of the European Union, Brussels, 23 June 2007. This rule is essentially the same as that adopted at the Inter-Governmental Conference, Brussels, 18 June 2004. We compare this rule with the QM rule prescribed in the Treaty of Nice, and the scientifically-based rule known as the ‘Jagelonian Compromise’.

This book deals with 18 voting procedures used or proposed for use in elections resulting in the choice of a single winner. These procedures are evaluated in terms of their ability to avoid paradoxical outcomes. Together with a companion volume by the same authors, Monotonicity Failures Afflicting Procedures for Electing a Single Candidate, published by Springer in 2017, this book aims at giving a comprehensive overview of the most important advantages and disadvantages of procedures thereby assisting decision makers in the (...) choice of a voting procedure that would best suit their purposes. (shrink)

This book deals with 20 voting procedures used or proposed for use in elections resulting in the choice of a single winner. These procedures are evaluated in terms of their ability to avoid five important paradoxes in a restricted domain, viz., when a Condorcet winner exists and is elected in the initial profile. Together with the two companion volumes by the same authors, published by Springer in 2017 and 2018, this book aims at giving a comprehensive overview of the most (...) important advantages and disadvantages of voting procedures thereby assisting decision makers in the choice of a voting procedure that would best suit their purposes. (shrink)