On the selection of the same winner by all scoring rules

Different scoring rules can result in the selection of any of the k competing candidates, given the same preference profile, (Saari DG 2001, Chaotic elections! A mathematician looks at voting. American Mathematical Society, Providence, R.I.). It is also possible that a candidate, and even a Condorcet winning candidate, cannot be selected by any scoring rule, (Saari DG 2000 Econ Theory 15:55–101). These findings are balanced by Saari’s result (Saari DG 1992 Soc Choice Welf 9(4):277–306) that specifies the necessary and sufficient condition for the selection of the same candidate by all scoring rules. This condition is, however, indirect. We provide a sufficient condition that is stated directly in terms of the preference profile; therefore, its testability does not require the verdict of any voting rule.     

EFFECTS OF WELFARE REFORM ON WOMEN'S VOTING PARTICIPATION

This study investigates the effects of welfare reform in the United States in the 1990s on voting among low‐income women. Using the November Current Population Surveys with the added Voting and Registration Supplement for the years 1990 through 2004 and exploiting changes in welfare policy across states and over time, we estimate the causal effects of welfare reform on women's voting registration and voting participation during the period in which welfare reform unfolded. During this time period, voter turnout was decreasing in the United States. We find robust evidence that welfare reform led to smaller declines in voting (about 3 to 4 percentage points, which translates to about 10% relative to the baseline mean) for women who were exposed to welfare reform compared to several different comparison groups of similar women who were much less exposed. The robust findings suggest that welfare reform had prosocial effects on civic participation, as characterized by voting. The effects were largely confined to presidential elections, were stronger in Democratic than Republican states, were stronger in states with stronger work incentive policies, and appeared to operate through employment, education, and income. (JEL D72, H53, I38, J21)     

Subgame perfect implementation of voting rules via randomized mechanisms

We characterize completely ordinal and onto choice rules that are subgame perfect of Nash equilibrium (SPE) implementable via randomized mechanisms under strict preferences. The characterization is very operationalizable, and allows us to analyse SPE implementability of voting rules. We show that no scoring rule is SPE implementable. However, the top-cycle and the uncovered correspondences as well as plurality with runoff and any strongly Condorcet consistent voting rule can be SPE implemented. Therefore our results are favourable to majority based voting rules over scoring rules. Nevertheless, we show that many interesting Condorcet consistent but not strongly Condorcet consistent rules, such as the Copeland rule, the Kramer rule and the Simpson rule, cannot be SPE implemented.     

How the size of a coalition affects its chances to influence an election

Since voting rules are prototypes for many aggregation procedures, they also illuminate problems faced by economics and decision sciences. In this paper we are trying to answer the question: How large should a coalition be to have a chance to influence an election? We answer this question for all scoring rules and multistage elimination rules, under the Impartial Anonymous Culture assumption. We show that, when the number of participating agents n tends to infinity, the ratio of voting situations that can be influenced by a coalition of k voters to all voting situations is no greater than $D_{m} \frac{k}{n}Since voting rules are prototypes for many aggregation procedures, they also illuminate problems faced by economics and decision sciences. In this paper we are trying to answer the question: How large should a coalition be to have a chance to influence an election? We answer this question for all scoring rules and multistage elimination rules, under the Impartial Anonymous Culture assumption. We show that, when the number of participating agents n tends to infinity, the ratio of voting situations that can be influenced by a coalition of k voters to all voting situations is no greater than , where D _m is a constant which depends only on the number m of alternatives but not on k and n. Recent results on individual manipulability in three alternative elections show that this estimate is exact for k=1 and m=3.

Arkadii SlinkoEmail:

     

Scoring rule voting games and dominance solvability

This article studies the dominance solvability (by iterated deletion of weakly dominated strategies) of general scoring rule voting games when there are three alternatives. The scoring rules we study include Plurality rule, Approval voting, Borda rule, and Relative Utilitarianism. We provide sufficient conditions for dominance solvability of general scoring rule voting games. The sufficient conditions that we provide for dominance solvability are in terms of one statistic of the game: sufficient agreement on the best alternative or on the worst alternative. We also show that the solutions coincide with the set of Condorcet Winners whenever the sufficient conditions for dominance solvability are satisfied. Approval Voting performs the best in terms of our criteria.     

Approval voting and positional voting methods: Inference,relationship, examples

Approval voting is the voting method recently adopted by the Society for Social Choice and Welfare. Positional voting methods include the famous plurality, antiplurality, and Borda methods. We extend the inference framework of Tsetlin and Regenwetter (2003) from majority rule to approval voting and all positional voting methods. We also establish a link between approval voting and positional voting methods whenever Falmagne et al.s (1996) size-independent model of approval voting holds: In all such cases, approval voting mimics some positional voting method. We illustrate our inference framework by analyzing approval voting and ranking data, with and without the assumption of the size-independent model. For many of the existing data, including the Society for Social Choice and Welfare election analyzed by Brams and Fishburn (2001) and Saari (2001), low turnout implies that inferences drawn from such elections carry low (statistical) confidence. Whenever solid inferences are possible, we find that, under certain statistical assumptions, approval voting tends to agree with positional voting methods, and with Borda, in particular.Michel Regenwetter thanks the National Science Foundation for funding this research through NSF grant SBR 97-30076. Both authors thank the Fuqua School of Business for financially supporting their collaboration. Most of this research was done while Regenwetter was a faculty member at Fuqua. We thank Prof. Steven Brams for his valuable comments as a discussant of a previous version of this paper, given at the 2002 Public Choice meeting, and Prof. Donald Saari for his helpful comments in conversations and on another draft. We also thank the editor in charge and a referee for their valuable comments. Tsetlin acknowledges the support of the Centre for Decision Making and Risk Analysis at INSEAD.     

On the Average Minimum Size of a Manipulating Coalition

We study the asymptotic average minimum manipulating coalition size as a characteristic of quality of a voting rule and show its serious drawback. We suggest using the asymptotic average threshold coalition size instead. We prove that, in large electorates, the asymptotic average threshold coalition size is maximised among all scoring rules by the Borda rule when the number m of alternatives is 3 or 4, and by -approval voting when m ≥ 5.     

General Feelings Toward Unions and Employers as Predictors of Union Voting Intent

The union voting intention literature shows that many nonunion employees who indicate that they think unions are instrumental in increasing wages, benefits, and working conditions would vote against forming a union. Although American workers have often been characterized as pragmatic with regard to their support for unions, the “disconnect” between union beliefs and union voting intentions just described suggests that more subtle forces are at work. In this paper, it is shown empirically that union instrumentality is a limited predictor of union voting intentions for a recent national cross-section of workers. Rather, more general feelings toward unions and employers are primary. These accounted for a large portion of the variance in union voting intentions, with general feelings towards unions by far the most critical predictor. A concluding section discusses whether the results may reflect changes in union power and changes in employee views of unions. Areas for future research are discussed.     

Robustness against inefficient manipulation

This paper identifies a family of scoring rules that are robust against coalitional manipulations that result in inefficient outcomes. We discuss the robustness of a number of Condorcet consistent and “point runoff” voting rules against such inefficient manipulation and classify voting rules according to their potential vulnerability to inefficient manipulation.     

Voting here and there: political integration and transnational political engagement among immigrants in Europe

In this article, I examine voting patterns in origin and receiving country national elections among immigrants in Europe. The existing scholarship on transnational political engagement offers two competing interpretations of the relationship between immigrant integration and transnational engagement, which I classify as the resocialization and complementarity perspectives. The resocialization perspective assumes that transnational political engagement gradually declines as immigrants become socialized into the new receiving society. Conversely, the complementarity perspective assumes that immigrant integration increases transnational political engagement. I test these competing perspectives with survey data collected between 2004 and 2008 for 12 different immigrant groups residing in seven European cities. The analysis examines how immigrant political and civic participation in receiving countries affect their proclivities to vote in homeland elections. I also analyse the effects of receiving and origin country contexts on immigrant voting behaviour in homeland elections. While my findings support both the resocialization and complementarity perspectives, they also highlight the ways in which a set of origin‐country contexts shape immigrant propensities to engage in transnational electoral politics. I observe a degree of complementarity among immigrants with resources who are motivated and eligible to participate in both receiving and origin‐country elections.     

The Willingness to State an Opinion: Inequality,Don't Know Responses,and Political Participation

Most explanations of inequality in political participation focus on costs or other barriers for those with fewer economic, educational, and “cognitive” resources. I argue, drawing on Pierre Bourdieu's work on “political competence,” that social position in the form of income also structures political participation through differences in the sense that one is a legitimate producer of political opinions. I test whether income differences in participation persist net of costs by examining nonparticipation in a setting in which barriers to participation are low: answering political survey questions. Lower‐income people are more likely than others to withhold political opinions by saying “don't know” net of differences in education, “cognitive ability,” or engagement with the survey exercise. Further, political “don't know” rates predict voting rates, net of other predictors. Efforts to democratize participation in American politics must attend not only to the costs of involvement but also to class‐based differences in individuals' relationship to political expression itself.     

Power indices and minimal winning coalitions

The Penrose–Banzhaf index and the Shapley–Shubik index are the best-known and the most used tools to measure political power of voters in simple voting games. Most methods to calculate these power indices are based on counting winning coalitions, in particular those coalitions a voter is decisive for. We present a new combinatorial formula how to calculate both indices solely using the set of minimal winning coalitions.     

Analyzing Roll-Call Voting Tools for Content

Abstract

The roll-call voting tools most frequently used by legislative scholars are not equally useful for all. Roll-call votes selected for traditional measurement tools systematically exclude issues determined to be important to women legislators. Those who study women in politics are unable to employ roll-call voting tools with the assurance that they are using valid measures for their research. After analyzing the content of widely used voting tools and discovering that votes from controversial bills of interest to women were often excluded, I outline suggestions for employing alternative methodological approaches. Further, I add to a growing criticism of roll-call voting statistics by identifying another limitation to their use.     

National Politics,Neighborly Politics: How Trump’s Election Impacted a Black and White Detroit Community

Most research on right-wing populism has tried to explain the rise of populist movements and parties. While some have studied how neighborhood contexts and histories shape voting patterns, few have examined what happens locally after votes are cast. This article draws on three years of ethnographic research while the author lived in Brightmoor, a majority black, minority white poor depopulated Detroit neighborhood, to show how Trump’s politics shaped local expressions and experiences of racism. First, I show how white Trump supporters expressed distinct approaches to xenophobic ethnonationalism and racial politics. Trump’s surge empowered many to broadcast anti-immigrant sentiments, while they continued to put interactional and discursive work into not being seen as racist. Many also applied a “Trump lens” to local interactions and geographies and rendered minorities salient under Trump politics hypervisible. Second, I show how black residents equated xenophobic ethnonationalism with antiblack racism: seeing through pro-Trump whites’ attempts to separate these. Some also applied a new “Trump lens” to interactions and geographies, using the category of Trump voter and a sense of the voting map to anticipate and make sense of racist interactions. This article offers new insights into the local impacts of a national surge in right-wing populism.     

Characterizing best–worst voting systems in the scoring context

An increasing body of theoretical and empirical work on discrete choice considers a choice design in which a person is asked to select both the best and the worst alternative in an available set of alternatives, in contrast to more traditional tasks, such as where the person is asked to: select the best alternative; select the worst alternative; rank the alternatives. Here we consider voting systems motivated by such “best–worst” choice; characterize a class of “best–worst” voting systems in terms of a set of axioms in the context of scoring rules; and discuss briefly possible extensions to approval–disapproval systems.     

Intransitivities in multidimensional spatial voting: period three implies chaos

It is well known that multidimensional spatial voting can involve intransitivity and cycles, resulting in outcomes anywhere in the policy space. These results are typically referred to as the chaos theorems. In this paper, I show that the connection between non-equilibrium spatial voting and chaos is not merely semantic, but is theoretic. Using symbolic dynamics, I show that if a three-cycle intransitivity among social choices exists, then cycles of all lengths greater than three are possible. This result is then used to establish the three conditions of sensitive dependence on initial conditions, topological transitivity, and dense periodic points, demonstrating the formal connection between multidimensional spatial voting and chaotic nonlinear dynamics.     

Proportional representation in variable-size legislatures

This paper examines a method to achieve proportional representation (PR) for parties in a legislature that allows the size of the legislature to vary as a function of voting results. The legislature's base consists of one elected candidate from each voting district. Seats are then added to underrepresented parties to approximate their nationwide vote proportions. Additions are governed by rules designed to honor the single-member district concept, to keep the increase manageable, and to satisfy other desirable criteria.These rules work well in the two-party case although they limit the extent to which true PR is achieved. When there are three or more parties, it is necessary to relax the rules if reasonable moves toward PR are to occur.     

Black and Farquharson on order-of-voting effects: an extension

This paper, by using the known algorithms for calculating the oucomes under the amendment procedure and under the successive procedure, extends the statements of Black and Farquharson about order-of-voting effects: if alternativex, in thej-th position in an agenda, is the sincere (sophisticated) voting outcome with that agenda, then x is also the sincere (sophisticated) voting outcome with any agenda that is the same as the initial agenda with respect to the alternatives in positions from the first to the (j – 1)-th (from the (j + 1)-th to the last, respectively).I am grateful to David Austen-Smith and two anonymous referees for helpful suggestions and comments. The responsibility for any remaining errors is entirely mine.     

Borda’s Paradox with weighted scoring rules

Representations are obtained for the probabilities that a Strict Borda Paradox and a Strong Borda Paradox are observed for large electorates with three candidates under the standard assumptions of Impartial Culture and Impartial Anonymous Culture. These representations are obtained for general weighted scoring rules (WSRs), and the probabilities are found to be maximized for voting rules like plurality rule and negative plurality rule. It is found that these paradox probabilities are not reduced for every scoring rule with the introduction of some degree of dependence among voters’ preferences with IAC. It is concluded that actual observances of a Strict Borda Paradox should be extremely rare, and that while observances of a Strong Borda Paradox should also be rare, they might occasionally be witnessed.