The structure of fuzzy preferences: Social choice implications

It has been shown that, with an alternative factorization of fuzzy weak preferences into symmetric and antisymmetric components, one can prove a fuzzy analogue of Arrow's Impossibility Theorem even when the transitivity requirements on individual and social preferences are very weak. It is demonstrated here that the use of this specification of strict preference, however, requires preferences to also be strongly connected. In the absence of strong connectedness, another factorization of fuzzy weak preferences is indicated, for which nondictatorial fuzzy aggregation rules satisfying the weak transitivity requirement can still be found. On the other hand, if strong connectedness is assumed, the fuzzy version of Arrow's Theorem still holds for a variety of weak preference factorizations, even if the transitivity condition is weakened to its absolute minimum. Since Arrow's Impossibility Theorem appeared nearly half a century ago, researchers have been attempting to avoid Arrow's negative result by relaxing various of his original assumptions. One approach has been to allow preferences – those of individuals and society or just those of society alone – to be “fuzzy.” In particular, Dutta [4] has shown that, to a limited extent, one can avoid the impossibility result (or, more precisely, the dictatorship result) by using fuzzy preferences, employing a particularly weak version of transitivity among the many plausible (but still distinct) definitions of transitivity that are available for fuzzy preferences. Another aspect of exact preferences for which the extension to the more general realm of fuzzy preferences is ambiguous is the factorization of a weak preference relation into a symmetric component (indifference) and an antisymmetric component (strict preference). There are several ways to do this for fuzzy weak preferences, all of them equivalent to the traditional factorization in the special case when preferences are exact, but quite different from each other when preferences are fuzzy (see, for example, [3]). A recent paper in this journal [1], by A. Banerjee, argues that the choice of definitions for indifference and strict preference, given a fuzzy weak preference, can also have “Arrovian” implications. In particular, [1] claims that Dutta's version of strict preference presents certain intuitive difficulties and recommends a different version, with its own axiomatic derivation, for which the dictatorship results reappear even with Dutta's weak version of transitivity. However, the conditions used to derive [1]'s version of strict preference imply a restriction on how fuzzy the original weak preference can be, namely, that the fuzzy weak preference relation must be strongly connected. Without this restriction, I will show that the rest of [1]'s conditions imply yet a third version of strict preference, for which Dutta's possibility result under weak transitivity still holds. On the other hand, if one accepts the strong connectedness required in order for it to be valid, I show that [1]'s dictatorship theorem can in fact be strengthened to cover any version of transitivity for fuzzy preferences, no matter how weak, and further, that this dictatorship result holds for any “regular” formulation of strict preference, including the one originally used by Dutta. Received: 13 May 1996 / Accepted: 13 January 1997     

The effects of gainsharing on grievance rates and absenteeism over time

We sought to better understand the long-term impact of gainsharing by analyzing longitudinal changes in two key indicators of workplace union-management relations: grievance rates and employee absenteeism. Using a seven and one-half year longitudinal data set and an interrupted time series design, we found that the introduction of a Scanlon-type gainsharing plan was followed by a gradual and permanent decline in both of these indicators. These results provide strong quantitative evidence for the ability of gainsharing to transform existing labor-management relations. Using qualitative data, we consider the relationship between labor relations outcomes and other plant-level performance improvements following the introduction of gainsharing in this case.     

Bandits,Militants, and Martyrs: Sub-state Violence as Claim to Authority in Late Antique North Africa

Fourth Century North Africa was a site of intense religious and political conflict. Emerging from a period of persecution and newly legitimized by the Roman state, the Christian Church immediately fractured into two competing camps. Now known as the Donatist schism, this fracture was the result of competing claims to religious authority between two camps of bishops, but the doctrinal debate at its core precipitated a specific form of violence: attacks on clergy and property perpetrated by roving groups of militant bandits. Known as circumcellions, these bands acquired a perverse reputation for religious zeal, a desire for martyrdom, and what their opponents described as the ‘madness’ and ‘insanity’ of their violence. Here I analyze sources produced by both Donatists and Catholics to trace patterns of circumcellion violence. I draw on borderland theory and research on non-state violence to argue that such acts were not mad, but rather the result of strategic efforts to consolidate religious and political power. In this, Donatism and the sectarian violence that accompanied it provide important insights into how banditry and peasant rebellions can serve as alternate sources of social and political power, avenues through which heterodox movements challenge the power state and religious hierarchies alike.     

Robust multivariate change point analysis based on data depth

Modern methods for detecting changes in the scale or covariance of multivariate distributions rely primarily on testing for the constancy of the covariance matrix. These depend on higher-order moment conditions, and also do not work well when the dimension of the data is large or even moderate relative to the sample size. In this paper, we propose a nonparametric change point test for multivariate data using rankings obtained from data depth measures. As the data depth of an observation measures its centrality relative to the sample, changes in data depth may signify a change of scale of the underlying distribution, and the proposed test is particularly responsive to detecting such changes. We provide a full asymptotic theory for the proposed test statistic under the null hypothesis that the observations are stable, and natural conditions under which the test is consistent. The finite sample properties are investigated by means of a Monte Carlo simulation, and these along with the theoretical results confirm that the test is robust to heavy tails, skewness and high dimensionality. The proposed methods are demonstrated with an application to structural break detection in the rate of change of pollutants linked to acid rain measured in Turkey lake, a lake in central Ontario, Canada. Our test suggests a change in the rate of acid rain in the late 1980s/early 1990s, which coincides with clean air legislation in Canada and the US. The Canadian Journal of Statistics 48: 417–446; 2020 © 2020 Statistical Society of Canada     

Knowledge Structures, Social Information Processing, and Children's Aggressive Behavior

Although a multitude of factors may be involved in the development of children's violent behavior, the actual aggressive act is preceded by a decision-making process that serves as the proximal control mechanism. The primary goal of this longitudinal study was to understand the nature of this proximal control mechanism involved in children's aggressive acts by focusing on two aspects of social cognitions: social information processing and stored knowledge (i.e., internal knowledge structures that are the latent memories of past events). It was hypothesized that: (1) children with hostile knowledge structures will display more biased patterns of aggressive social information processing than children whose knowledge structures are less hostile and negative; (2) children who display hostile knowledge structures will behave in chronically aggressive ways; and (3) the development of hostile knowledge structures and hostile patterns of social information processing contribute to the stability of aggressive behavior and thus partially mediate the relation between early and later aggressive behavior. 585 boys and girls (19% African-American) were followed from kindergarten through eighth grade. Results from this investigation support the hypotheses and are discussed in terms of the significance of the inclusion of knowledge structures in our theories of the mental processes involved in children's violent behaviour.     

Commentary on “Measuring Constructed Preferences: Towards a Building Code” by Payne,Bettman and Schkade

Journal of Risk and Uncertainty -