Measures of (a priori) power play a useful role in assessing the character of interpersonal interaction found in collective decision making bodies. We propose and axiomatically characterize an alternative power index to the familiar Shapley/Shubik and Banzhaf indices which can be used for such purposes. The index presented is shown to be unique for the class of simple n-person games. By subsequent generalization of the index and its axioms to the class of n-person games in characteristic function form we obtain an analog to the Shapley value.
Fair districting requires more than compact, contiguous equal-sized districts; namely, sets of districts should also possess certain features. Specifically, they should be neutral (treat all parties alike) and responsive to changes in votes. In order to establish the extent to which these goals can be achieved, we give a precise definition to the concept of neutrality and expand the notion of responsiveness into three characteristics: the range in actual votes over which a districting plan is responsive; the degree of responsiveness in the vicinity of the “normal vote” (i.e., competitiveness); and the constancy of the swing ratio (i.e., the rate at which vote changes yield seat changes) over a range of votes. We show that while all possible values for these features are readily attainable when considered individually, certain combinations of values cannot be achieved. Finally, we identify the nature of the compromises required and the properties that the compromises possess, and show the kinds of trade-offs that result in reasonably fair districting plans.
In ordinary least squares regression analysis the desired property of unbiasedness in estimated coefficients is contingent upon the correspondence of the fitted model with the true underlying data generating process. This paper focuses on developing a systematic characterization of the error forms resulting from model misspecification in single equation models. The consequences of model misspecification, for the error forms identified, are also evaluated.
In this probabilistic generalization of the Deegan-Packel power index, a new family of power indices based on the notions of minimal winning coalitions and equal division of payoffs is developed. The family of indices is parameterized by allowing minimal winning coalitions to form in accordance with varying probability functions. These indices are axiomatically characterized and compared to other similarly characterized indices. Additionally, a dual family of minimal blocking coalition indices and their characterization axioms is presented.
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