The paradox of multiple elections

Assume that voters must choose between voting yes (Y) and voting no (N) on three propositions on a referendum. If the winning combination is NYY on the first, second, and third propositions, respectively, the paradox of multiple elections is that NYY can receive the fewest votes of the 2³ = 8 combinations. Several variants of this paradox are illustrated, and necessary and sufficient conditions for its occurrence, related to the “incoherence” of support, are given. The paradox is shown, via an isomorphism, to be a generalization of the well-known paradox of voting. One real-life example of the paradox involving voting on propositions in California, in which not a single voter voted on the winning side of all the propositions, is given. Several empirical examples of variants of the paradox that manifested themselves in federal elections – one of which led to divided government – and legislative votes in the US House of Representatives, are also analyzed. Possible normative implications of the paradox, such as allowing voters to vote directly for combinations using approval voting or the Borda count, are discussed. Received: 31 July 1996 / Accepted: 1 October 1996     

Jury theorems with multiple alternatives

I consider a game in which imperfectly informed jurors vote to select one of several possible choices when there is a natural ordering of the possibilities. Each juror votes for the largest alternative the juror would like to implement, and the alternative that is selected is the largest alternative supported by a given number of jurors. For non-unanimous voting rules, the probability of a mistaken judgment goes to zero as the number of jurors goes to infinity. I also give necessary and sufficient conditions to obtain asymptotic efficiency under unanimous voting rules, and show that unanimous rules may lead to a bias in which moderate outcomes are never chosen.     

A basic model for multiple self

Standard economic theory represents the individual in a unique preferential order, which is complete and transitive. Such a vision of the person is extremely reductionist. The present paper is an attempt to explore possibilities of constructing a multi-dimensional representation of man. We shall define modes of identity so as to better understand human personality. The multiplicity of modes of identity gives way to tensions between various forms of identities, which the individual has to manage.     

Strategy-proof allocation of multiple public goods

This paper characterizes strategy-proof social choice functions (SCFs), the outcome of which are multiple public goods. Feasible alternatives belong to subsets of a product set . The SCFs are not necessarily “onto”, but the weaker requirement, that every element in each category of public goods A _k is attained at some preference profile, is imposed instead. Admissible preferences are arbitrary rankings of the goods in the various categories, while a separability restriction concerning preferences among the various categories is assumed. It is found that the range of the SCF is uniquely decomposed into a product set in general coarser than the original product set, and that the SCF must be dictatorial on each component B _l . If the range cannot be decomposed, a form of the Gibbard–Satterthwaite theorem with a restricted preference domain is obtained.     

A strong paradox of multiple elections

We consider a stronger version of the paradox of multiple elections and show that it is possible that not only the winning combination of propositions, but also all the combinations sufficiently close to it, receive zero votes. Received: 8 April 1997/Accepted: 18 April 1997     

Systematic analysis of multiple voting rules

For a class of voting rules, which includes Approval and Cumulative Voting, it is shown how to find and analyze all possible outcomes that arise with a specified profile, and, conversely, how to start with a potential region and determine whether there exist supporting profiles. The geometry of these regions is determined by the “Reversal symmetry” portion of a profile; i.e., components of the A\succ B\succ C, C\succ B\succ A{A\succ B\succ C, C\succ B\succ A} type.     

A majority-rule characterization with multiple extensions

When May's necessary and sufficient conditions for majority rule as a binary voting rule are extended in a natural way to decisions over more than two options, the resulting conditions are consistent with the Borda and Black voting rules, but not with a variety of other voting rules for more than two options. This paper presents an alternative set of necessary and sufficient conditions for binary majority rule, which permits the plurality, Condorcet and (simplified) Dodgson rules, as well as the Borda and Black rules, but not the Copeland or Nanson rules, to be classified as extensions of binary majority rule to decisions over more than two options.I am indebted to Amartya Sen and anonymous referees for helpful suggestions     

Introduction: Cultural production under multiple colonialisms

ABSTRACT

In this introduction to the special journal issue, we elaborate a multiple colonialisms framework that allows us to examine the complex relationalities of multiple and converging colonial relations in historical and contemporary contexts within which cultural production does its work. Through examples of cultural production from the Americas and Asia, Special Issue contributors analyse rarely-recognized sites of colonialism that bear a palimpsestic relationship to other articulations that are more commonly legible as colonialism. Such an approach makes new analytical connections and gives greater depth to conventional theorizations of coloniality and decolonization. We also illustrate the centrality of the scholarship of Indigenous, Black, and Dalit-Bahujan scholars to the framework, especially the ways in which their work challenges our collective and accumulated racialized and colonial unknowings and illuminates what often remains unthinkable in conventional analyses of cultural production and the colonial contexts of their making. Overall, rather than analytically imply pluralism and equivalence among varied colonialisms, we argue that a multiple colonialisms framework enables cultural studies scholarship to dwell on the relationality, contradictions, and incommensurabilities generated within converging structures and multiple articulations of colonial and racialized violence across spaces. Weaving the various contributions into the framework, we invite readers to consider what histories, structures, and relationships help to explain why actually existing colonialities remain illegible as such in the particular context of each paper, and what that implies for solidarity and decolonization struggles. We hope that highlighting the specific creative methodological practices and significant spatial and temporal rethinking that a multiple colonialisms approach can generate incites conversations about how we might enrich theorizations of coloniality and decolonization.     

Relationships across multiple settings: an overview

It is not the method of interaction but the quality of the interaction between patient and therapist, student and teacher, mentee and mentor, or youth and youth worker that is the most critical determinant of success in a myriad of fields.     

A multiple indicator approach to blockmodeling signed networks

Regardless of whether the focus is on algebraic structures, elaborating role structures or the simple delineation of concrete social structures, generalized blockmodeling faces a pair of vulnerabilities. One is sensitivity to poor quality of the relational data and the other is a risk of over fitting blockmodels to the details of specific networks. Over fitting blockmodels can lead to multiple equally well fitting partitions where choices cannot be made between them on a principled basis. This paper presents a method of tackling these problems by viewing (when possible) observed social relations as multiple indicators of an underlying affect dimension. Quadratic assignment methods using matching coefficients, product moment correlations and Goodman and Kruskal's gamma are used to assess the appropriateness of using the sum of observed relations as input for applying generalized blockmodeling. Data for four groups are used to show the value of this approach within which multiple equally well fitting blockmodels for single relations are replaced by unique (or near-unique) partitions of the summed data. This strategy is located also within a broader problem of blockmodeling three-dimensional networks data and suggestions are made for future work.     

Pioneering partnerships: Resident involvement from multiple perspectives

Resident involvement in residential care homes is a challenge due to shortcomings of consumerist and formal approaches such as resident councils. The PARTNER approach aims to involve residents through collective action to improve their community life and wellbeing. The purpose of this article is to provide insights into the process of resident involvement by the PARTNER approach from the perspectives of multiple stakeholders, including residents, volunteers and staff members. A responsive evaluation was conducted, using participant observations, semi-structured interviews with residents, volunteers and professionals (n = 16), and three focus groups. The findings show that critical elements in this process of resident involvement were the agenda-setting by residents, the formation of a cohesive resident group, the sharing of experiences and stories, the development of collective action, and the development of partnerships between residents and professionals and other stakeholder groups. Residents developed actions (gallery parties and a buddy project) to strengthen social interactions and realized these with the help of volunteers and professionals. We conclude that bringing residents together around a shared topic creates room for activism and leads to empowerment, feelings of social belonging and learning processes. We argue that it is a worthwhile enterprise to further develop structural partnership relations between residents, volunteers and staff in residential care homes.     

A behavioral portfolio approach to multiple job holdings

In this paper we present an alternative explanation of multiple job holdings. It is based on a behavioral portfolio approach using prospect theory. Multiple job holdings is often a result of economic hardship but also because of peer comparisons. Workers may decide to take on a risky job like self-employment and engage into new ventures but also hold on to a safe employment in order to stay as close as possible to their reference level. While multiple job holdings might be the case for some, many others might decide to keep on working only at a safe job and do not engage into new risky ventures. This paper presents a behavioral economics model to explain such decisions. We find that the decision to hold multiple jobs depends on the degree of loss aversion, the value of the reference level and on the expected return in the risky venture. The worker will not seek for a risky job if she has an income reference level equal to what she can earn from a safe job. At any other reference level, the worker will seek new ventures provided she is compensated with a higher expected wage and is sufficiently loss averse.     

Criticality in games with multiple levels of approval

In this article, criticality within a voting game is rigorously defined and examined. Criticality forms the basis of the traditional voting power measures frequently employed to analyse voting games; therefore understanding criticality is a pre-requisite to understanding any such analysis. The concept of criticality is extended to encompass games in which players are allowed to express multiple levels of approval. This seemingly innocuous extension raises some important questions, forcing us to re-evaluate exactly what it means to be critical. These issues have been largely side-stepped by the main body of research as they focus almost exclusively on ‘yes/no’ voting games, the so called single level approval voting games. The generalisation to multilevel approval voting games is much more than just a theoretical extension, as any single level approval game in which a player can abstain is in effect a multilevel approval voting game.     

Repeat rape and multiple offending among undetected rapists

Pooling data from four samples in which 1,882 men were assessed for acts of interpersonal violence, we report on 120 men whose self-reported acts met legal definitions of rape or attempted rape, but who were never prosecuted by criminal justice authorities. A majority of these undetected rapists were repeat rapists, and a majority also committed other acts of interpersonal violence. The repeat rapists averaged 5.8 rapes each. The 120 rapists were responsible for 1,225 separate acts of interpersonal violence, including rape, battery, and child physical and sexual abuse. These findings mirror those from studies of incarcerated sex offenders (Abel, Becker, Mittelman, Cunningham-Rathner, Rouleau, & Murphy, 1987; Weinrott and Saylor, 1991), indicating high rates of both repeat rape and multiple types of offending. Implications for the investigation and prosecution of this so-called "hidden" rape are discussed.     

Work accommodation for people with multiple chemical sensitivity

Multiple chemical sensitivity (MCS) is a term used to describe allergic-like reactions to chemicals that represent everyday exposures in industrialized countries. It is sometimes associated with electromagnetic sensitivity, and both conditions are most likely engendered by environmental exposures. Prevalence studies suggest that chemical sensitivity affects 12-15% of the US population and that it crosses age, socio-economic status and racial lines. Electromagnetic sensitivity is less understood, but affects a portion of those with chemical sensitivity. Persons with these environmental sensitivities often experience difficulties with health care, housing and work. Workplace barriers result in significant disability, with ensuing financial loss and isolation for the worker. We examined work accommodations for 100 persons with self-reported MCS and its relation to life satisfaction. Results are discussed in terms of accommodating invisible disabilities that challenge industrial capitalism.