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Using the Nash product (Nash Social Welfare Function) as a micro foundation, we create a decomposable index to evaluate the unfairness of representation in electoral districts. Using this index, we decompose the factors of such unfairness into apportionment and districting. We explore the situations of New Zealand, the United States, Australia, the...
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Existing studies on legislative malapportionment often conceptualize and measure this phenomenon with little regard to intertemporal variations and the malapportionment-generating process (MGP). Our conceptualization leads us to introduce a measure called α-divergence that can identify the vote inequality derived from various stages of MGP. Using an originally created database that covers 440 elections in 112 countries, we decompose the overall degree of malapportionment into three stages: malapportionment that arises at the stages of interstate apportionment, intrastate districting, and allotment of seats to special districts. We also provide analyses that can decompose the demographic and political factors contributing to the trends of the overall degree of malapportionment for selected countries.
A pesar del tiempo transcurrido desde que se pro-clamara la Independencia y se fundara la República, las elecciones han estado plagadas de vicios y exclusiones, y han originado interrupciones constitucionales; en una palabra, las elecciones no han cumplido enteramente con su cometido.En este sentido, Elecciones presidenciales en el Perú,1931-2016 es una valiosa contribución del Jurado Nacional de Elecciones para la comprensión de los problemas políticos relacionados con las elecciones, de los dilemas que enfrentan los actores para resolverlos, de las decisiones que adoptan y de sus resultados.A este respecto, este libro tiene una importancia excepcional, en principio porque aporta una abundante información que ayuda a profundizar el conocimiento que se tiene de la evolución de la representación política del país. En segundo lugar, porque contribuye a conocer el funcionamiento del sistema electoral y evaluar su desempeño, lo que favorece el proceso de democratización del Estado y la sociedad, en curso. En tercer lugar, este libro tiene precisamente esa importancia, porque el análisis de los datos que proporciona es indispensable para formular un diagnóstico de las actuales mediaciones políticas del país, en vista del eclipse de los partidos políticos, y de las medidas que deberían adoptarse para solucionar la crisis de representación y del (des)orden imperante.
Using optimization to minimize the maximum vote-value disparity and enumeration for the districting problem, we can obtain a lot of candidates of the electoral district. However, it is difficult to choose a good constituency among them. Because there is no indication of other except the gap in the value of votes. The Supreme Court accepts the discretionary authority of the Diet while assuming one vote of difference the most important matter. However, it is difficult to judge whether the exercise of any such discretionary power of the Diet was appropriate. The purpose of this research is to propose a closeness and a degree of divergence as a new index for the decision making and evaluation. The closeness is an indicator to estimate the intimacy level between the municipal districts constituting an electoral district. The degree of divergence is an indicator to measure the degree of estrangement with the current electoral district. In addition, it shows that these indexes are useful in decision-making and evaluation of the validity.
Apportionment of representatives is a basic rule of everyday politics. By definition, this basic rule is a constitutional stage problem and should be decided behind the veil of uncertainty. To bring apportionment closer to quotas, we introduce f-divergence for utilitarianism and Bregman divergence for consistent optimization. Even in our less restricted condition, we find that we must use α-divergence for optimization and show that the minimization of α-divergence induces the same divisor methods that correspond to the maximization of the Kolm–Atkinson social welfare function (or the expected utility function), which is bounded by constant relative risk aversion.
This paper links Stolarsky mean apportionment methods, which include the US House of Representatives, the Saint-Lague, and the d’Hondt methods, to Kolm–Atkinson social welfare maximization and to generalized entropy minimization. Within this class, the logarithmic mean apportionment method is the most unbiased one that assigns at least one seat to each state.
