Measuring disproportionality,volatility and malapportionment: axiomatization and solutions

The measurement of disproportionality, volatility and malapportionment often employ similar indices. Yet the debate on the issue of adequate measurement has remained open. We offer a formal and rigorous list of properties that roughly subsume those of Taagepera and Grofman (Party Polit 9(6):659–677, 2003). One of these properties, Dalton’s principle of transfers, is formalized in a manner that resolves the ambiguity associated with it in previous studies. We show that the cosine measure satisfies all the properties. We also show how the Gallagher index can be modified to satisfy all the properties. The cosine measure and the modified Gallagher measure are co-monotone.     

Voting power: an information theory approach

In recent years, there has been increasing awareness of the importance of formal measures of voting power and of the relevance of such measures to real life political issues. Nevertheless, existing measures have been criticized, especially because of their dependence on the unrealistic assumption that different coalitions have equal probabilities. In this paper we show that the classical problem of measuring voting power can be naturally embedded in information theory. This perspective on voting power allows us to extend measures of voting power to cases in which there are dependencies among voters. In doing so, we distinguish between two different notions of a given voter’s power—‘control’ and ‘informativeness’—corresponding, respectively, to the average uncertainty regarding the outcome of a vote that remains when all others have voted and the average uncertainty that is eliminated when only the given voter has voted. This distinction settles a number of well-known paradoxes and enables the study of voting power on the basis of actual political behavior at all levels.     

What Sociologists Do and Where They Do It—The NSF Survey on Sociologists's Work Activities and Workplaces

We present data from the National Science Foundation Survey of Doctoral Recipients that challenges the image of sociology as a classroom-based group of professionals. Our data reveal that only 45.8% of Ph.D. sociologists teach sociology. The anachronistic and false image of sociology, we argue, is profoundly consequential to the way sociologists interact with each other and with the larger society. As a discipline we tend to ignore or dismiss the doing of sociology in favor of the teaching of sociology or of theoretically focused research. We also present data on principal tasks and job classifications for those in academic and nonacademic settings.     

Beyond Condorcet: optimal aggregation rules using voting records

In certain judgmental situations where a “correct” decision is presumed to exist, optimal decision making requires evaluation of the decision-makers’ capabilities and the selection of the appropriate aggregation rule. The major and so far unresolved difficulty is the former necessity. This article presents the optimal aggregation rule that simultaneously satisfies these two interdependent necessary requirements. In our setting, some record of the voters’ past decisions is available, but the correct decisions are not known. We observe that any arbitrary evaluation of the decision-makers’ capabilities as probabilities yields some optimal aggregation rule that, in turn, yields a maximum-likelihood estimation of decisional skills. Thus, a skill-evaluation equilibrium can be defined as an evaluation of decisional skills that yields itself as a maximum-likelihood estimation of decisional skills. We show that such equilibrium exists and offer a procedure for finding one. The obtained equilibrium is locally optimal and is shown empirically to generally be globally optimal in terms of the correctness of the resulting collective decisions. Interestingly, under minimally competent (almost symmetric) skill distributions that allow unskilled decision makers, the optimal rule considerably outperforms the common simple majority rule (SMR). Furthermore, a sufficient record of past decisions ensures that the collective probability of making a correct decision converges to 1, as opposed to accuracy of about 0.7 under SMR. Our proposed optimal voting procedure relaxes the fundamental (and sometimes unrealistic) assumptions in Condorcet’s celebrated theorem and its extensions, such as sufficiently high decision-making quality, skill homogeneity or existence of a sufficiently large group of decision makers.