Monotonicity of power in games with a priori unions

Power indices are commonly required to assign at least as much power to a player endowed with some given voting weight as to any player of the same game with smaller weight. This local monotonicity and a related global property however are frequently and for good reasons violated when indices take account of a priori unions amongst subsets of players (reflecting, e.g., ideological proximity). This paper introduces adaptations of the conventional monotonicity notions that are suitable for voting games with an exogenous coalition structure. A taxonomy of old and new monotonicity concepts is provided, and different coalitional versions of the Banzhaf and Shapley–Shubik power indices are compared accordingly.      

How far does the gender gap extend?: Decision making on state Supreme Courts in Fourth Amendment Cases, 1980–2000

The importance of women on the bench and the influence of gender on judicial decision making has garnered much scholarly attention. We examine the voting behavior of male and female justices in 718 Fourth Amendment search and seizure votes cast on state Supreme Courts between 1980 and 2000. We find that women justices, controlling for institutional, political, and legal constraints, are more likely to rule in favor of the criminal defendant than their male brethren in cases decided after 1991 but not before. We also find women justices serving with female colleagues are more inclined to render liberal votes. We conclude the influence of gender may be evident in a wider variety of cases than those dealing with women's lives but that this influence is dependent upon the existence of a critical mass of women on the state court benches.     

Oligarchy for Social Choice Correspondences and Strategy-Proofness

We study the existence of a group of individuals which has some decisive power for social choice correspondences that satisfy a monotonicity property which we call modified monotonicity. And we examine the relation between modified monotonicity and strategy-proofness of social choice correspondences according to the definition by Duggan and Schwartz (2000). We will show mainly the following two results. (1) Modified monotonicity implies the existence of an oligarchy. An oligarchy is a group of individuals such that it has some decisive power (semi-decisiveness), and at least one of the most preferred alternatives of every its member is always chosen by any social choice correspondence. (2) Strategy-proofness of social choice correspondences is equivalent to modified monotonicity.     

A new monotonicity condition for tournament solutions

We identify a new monotonicity condition (called cover monotonicity) for tournament solutions which allows a discrimination among main tournament solutions: The top-cycle, the iterated uncovered set, the minimal covering set, and the bipartisan set are cover monotonic while the uncovered set, Banks set, the Copeland rule, and the Slater rule fail to be so. As cover monotonic tournament solutions induce social choice rules which are Nash implementable in certain non-standard frameworks (such as those set by Bochet and Maniquet (CORE Discussion Paper No. 2006/84, 2006) or Özkal-Sanver and Sanver (Social Choice and Welfare, 26(3), 607–623, 2006), the discrimination generated by cover monotonicity becomes particularly notable when implementability is a concern.     

Monotonicity of power and power measures

Monotonicity is commonly considered an essential requirement for power measures; violation of local monotonicity or related postulates supposedly disqualifies an index as a valid yardstick for measuring power. This paper questions if such claims are really warranted. In the light of features of real-world collective decision making such as coalition formation processes, ideological affinities, a priori unions, and strategic interaction, standard notions of monotonicity are too narrowly defined. A power measure should be able to indicate that power is non-monotonic in a given dimension of players' resources if – given a decision environment and plausible assumptions about behaviour – itis non-monotonic.     

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).     

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.     

A note on the median voter theory and voter alienation

This note explores the consequences of movement of candidates toward the center of the political distribution. Uniform and normal distributions are considered. Movement toward the center of the political distribution can increase or decrease the number of votes received by a candidate. However, even if the candidate loses votes by such a move, as long as the distribution is denser in the center than in the tails, the candidate will benefit relative to his/her opponent. If both the candidate and his/her opponent move toward the center, the individual who makes the greater move benefits at the expense of the other individual.     

Third‐Party Candidates and the 2000 Presidential Election*

Objective. This article examines how third‐party candidates influenced the 2000 presidential election. Methods. Two surveys provide information on a hypothetical election between only George Bush and Al Gore. The determinants of voting behavior in this election are then used to estimate how votes cast for third‐party candidates would have been partitioned between Bush, Gore, and abstentions had the other candidates dropped out of the race. Results. The estimates suggest that the Ralph Nader votes would have gone primarily to Gore (giving him the win in Florida) while Bush would have received more of the Pat Buchanan votes. The results also show that Nader's presence in the race gave Gore an incentive to position himself farther to the left ideologically. Bush's ideological position was not affected by Buchanan's participation. Conclusion. The third‐party candidates' participation was a critical factor in George Bush's Electoral College victory over Al Gore.     

A Meta‐Analysis of Campaign Contributions' Impact on Roll Call Voting*

Objectives. Conventional wisdom about the link between campaign contributions and roll call votes is that contributions rarely matter because groups tend to give to like‐minded legislators. This meta‐analysis examines the conventional wisdom by analyzing published research on this topic. Methods. More than 30 studies are pooled to produce more than 350 individual tests of the contributions‐roll call link. Extending meta‐regression ( Stanley and Jarrell, 1989 ), a logit meta‐analysis is conducted to summarize the literature and assess the importance of various modeling choices. Results. We find that some, but not all, model specifications have an impact on whether significant results are present. Models that control for friendly giving by including a measure of legislators' ideology and that include more than one contributions variable are less likely to produce significant results. Conclusions. After considering the impact of model choice on study results, we conclude that one‐third of roll call votes exhibit the impact of campaign contributions.     

Varieties of failure of monotonicity and participation under five voting methods

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.     

The potential of iterative voting to solve the separability problem in referendum elections

In referendum elections, voters are often required to register simultaneous votes on multiple proposals. The separability problem occurs when a voter’s preferred outcome on one proposal depends on the outcomes of other proposals. This type of interdependence can lead to unsatisfactory or even paradoxical election outcomes, such as a winning outcome that is the last choice of every voter. Here we propose an iterative voting scheme that allows voters to revise their voting strategies based on the outcomes of previous iterations. Using a robust computer simulation, we investigate the potential of this approach to solve the separability problem.     

A Matter of Conscience? The Democratic Significance of 'Conscience Votes' in Legislating Bioethics in Australia

In Australia, members of a political party are expected to vote as a block on the instructions of their party. Occasionally a ‘conscience vote’ (or ‘free vote’) is allowed, which releases parliamentarians from the obligation to maintain party discipline and permits them to vote according to their ‘conscience.’ In recent years Australia has had a number of conscience votes in federal Parliament, many of which have focused on bioethical issues (e.g., euthanasia, abortion, RU486, and embryonic/stem cell research and cloning). This paper examines the use of conscience votes in six key case studies in these contested areas of policy‐making, with particular attention to their implications for promoting democratic values and the significance of women's Parliamentary participation.     

Determinants of presidential position taking in Congress, 1949–1995

In this paper we seek to explain the activity presidential position taking on roll call votes in the House. Position taking may help presidents pursue their policy agendas, but time and available resources constrain their ability to take positions. Even though position taking is a discretionary presidential action, it occurs in the legislative arena and, thus, presidents must consider elements in both institutions as well as outside conditions when making this decision. Accordingly, we posit a multiple perspectives approach to explain the number of presidential positions on votes in the House. Our multivariate two-stage least squares regression reveals that variables from all three environments (executive, legislative and exogenous) within our multiple perspectives approach are necessary to adequately explain presidential position taking overall and when divided according to domestic and foreign policy positions.     

What Are the Determinants of Open‐Space Ballot Measures? An Extension of the Research*

Objective. This article comments on the findings of Romero and Liserio's “Saving Open Spaces.” Their primary claim is that open‐space ballots are not related in any way to actual land‐use patterns. Methods. First, I present a number of methodological problems with their approach and demonstrate a sample selection bias using their original data. Second, I present some alternate models using data from 350 municipalities in the greater Philadelphia area. Results. I demonstrate that the sample selection bias in Romero and Liserio's model is so acute that all their parameter estimates are jointly zero. With other data, I find that sprawl votes are related to land‐use patterns using a number of different measures. Conclusions. I conclude that open‐space votes are related to land‐use patterns and that this may be explained as a rational response to sprawl by community planning bureaucracies.     

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.     

Is more health always better for society? Exploring public preferences that violate monotonicity

There has recently been some literature on the properties of a Health-Related Social Welfare Function (HRSWF). The aim of this article is to contribute to the analysis of the different properties of a HRSWF, paying particular attention to the monotonicity principle. For monotonicity to be fulfilled, any increase in individual health—other things equal—should result in an increase in social welfare. We elicit public preferences concerning trade-offs between the total level of health (concern for efficiency) and its distribution (concern for equality), under different hypothetical scenarios through face-to-face interviews. Of key interests are: the distinction between non-monotonic preferences and Rawlsian preferences; symmetry of HRSWF; and the extent of inequality neutral preferences. The results indicate strong support for non-monotonic preferences, over Rawlsian preferences. Furthermore, the majority of those surveyed had preferences that were consistent with a symmetric and inequality averse HRSWF.     

A No-Trade Theorem under Knightian Uncertainty with General Preferences

This paper derives a no-trade theorem under Knightian uncertainty, which generalizes the theorem of Milgrom and Stokey (1982, Journal of Economic Theory 26, 17) by allowing general preference relations. It is shown that the no-trade theorem holds true as long as agents' preferences are dynamically consistent in the sense of Machina and Schmeidler (1991, Econometrica 60, 745), and satisfies the so-called piece-wise monotonicity axiom. A preference satisfying the piece-wise monotonicity axiom does not necessarily imply the additive utility representation, nor is necessarily based on beliefs. This revised version was published online in June 2006 with corrections to the Cover Date.     

How Policy Conditions the Impact of Presidential Speeches on Legislative Success*

Objective. Although the impact of the president's rhetoric on public opinion remains unfound, it appears to increase the president's success in Congress. This article argues that instead of moving public opinion, presidential speeches act as informational cues for legislators and holds that the impact of the president's public speeches in Congress is conditional on the salience and complexity of the policy voted on by Congress. Method. I use probit methodology to examine the effect of presidential rhetoric on the likelihood of presidential success on House roll‐call votes from 1989–2000. An interactive model assesses the conditioning impact a policy's salience and complexity have on the relationship between presidential rhetoric and legislative success. Results. Presidential rhetoric increases the president's legislative success on votes pertaining to policies that are both salient and complex. Conclusion. Presidential rhetoric matters to the president's relationship with Congress, despite the limited impact it appears to have on public opinion.