A previous work by Friedman et al. (Theory and Decision, 61:305–318, 2006) introduces the concept of a hierarchy of a simple voting game and characterizes which hierarchies, induced by the desirability relation, are achievable in linear games. In this paper, we consider the problem of determining all hierarchies, conserving the ordinal equivalence between the Shapley–Shubik and the Penrose–Banzhaf–Coleman power indices, achievable in simple games. It is proved that only four hierarchies are non-achievable in simple games. Moreover, it is also proved (...) that all achievable hierarchies are already obtainable in the class of weakly linear games. Our results prove that given an arbitrary complete pre-ordering defined on a finite set with more than five elements, it is possible to construct a simple game such that the pre-ordering induced by the Shapley–Shubik and the Penrose–Banzhaf–Coleman power indices coincides with the given pre-ordering. (shrink)

Many bodies around the world make their decisions through voting systems in which voters have several options and the collective result also has several options. Many of these voting systems are anonymous, i.e., all voters have an identical role in voting. Anonymous simple voting games, a binary vote for voters and a binary collective decision, can be represented by an easy weighted game, i.e., by means of a quota and an identical weight for the voters. Widely used voting systems of (...) this type are the majority and the unanimity decision rules. In this article, we analyze the case in which voters have two or more voting options and the collective result of the vote has also two or more options. We prove that anonymity implies being representable through a weighted game if and only if the voting options for voters are binary. As a consequence of this result, several significant enumerations are obtained. (shrink)

The doctor-patient relationship is a crucial aspect of primary-care practice Research on associations between quality of care provision and burnout and empathy in a primary care setting could improve this relationship. Cross-sectional study of family physicians and nurses of twenty-two primary care centers in the health district of Lleida, Spain. Empathy and burnout were measured using the Jefferson Physician Empathy Scale and the Maslach Burnout Inventory, while quality of care delivery was evaluated using Quality Standard Indicator scores. JPSE and MBI (...) results were grouped into low, medium, and high scores to analyze associations with QSI scores and sociodemographic variables. The mean QSI score recorded for the family physicians and nurses was 665. Higher, albeit insignificant, QSI scores were observed for practitioners with high burnout. No differences were observed according to level of empathy. The differences with respect to sex, age, and area of practice were not significant. Practitioners with low empathy had higher QSI scores than those with high empathy while those with high burnout had higher scores than those with low burnout. Burnout and empathy did not significantly influence quality of care delivery scores in 22 primary care centers. More studies, however, are needed to investigate the unexpected trend observed that suggests that physicians and nurses with higher levels of burnout provide higher quality care. (shrink)