Mathematics and democracy. Recent advaces in voiting systems by Bruno Simeone, Friedrich Pukelsheim

By Bruno Simeone, Friedrich Pukelsheim

The learn of vote casting platforms and Collective selection lies on the crossroad of social and distinct sciences. the previous ones specialise in the improvement of electoral platforms within the context of the altering wishes of societies; the latter ones care for the formal learn of electoral mechanisms, whose underlying axioms replicate common rules similar to fairness, illustration, balance, and consistency. various quantitative ways to the research of electoral platforms were constructed: game-theoretic, decision-theoretic, statistical, probabilistic, combinatorial, geometric, and optimization ones. the entire authors are favourite students from those disciplines. Quantitative methods supply a robust device to observe inconsistencies or negative functionality in real platforms. functions to concrete settings equivalent to european, American Congress, neighborhood, and committee vote casting are mentioned.

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By Bruno Simeone, Friedrich Pukelsheim

The learn of vote casting platforms and Collective selection lies on the crossroad of social and distinct sciences. the previous ones specialise in the improvement of electoral platforms within the context of the altering wishes of societies; the latter ones care for the formal learn of electoral mechanisms, whose underlying axioms replicate common rules similar to fairness, illustration, balance, and consistency. various quantitative ways to the research of electoral platforms were constructed: game-theoretic, decision-theoretic, statistical, probabilistic, combinatorial, geometric, and optimization ones. the entire authors are favourite students from those disciplines. Quantitative methods supply a robust device to observe inconsistencies or negative functionality in real platforms. functions to concrete settings equivalent to european, American Congress, neighborhood, and committee vote casting are mentioned.

Show description

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Additional resources for Mathematics and democracy. Recent advaces in voiting systems

Sample text

A vote outcome is a bicoloring of the vertices that assigns to each vertex either the color blue or the color red: this means that all voters in the corresponding unit vote for the same party, blue or red, respectively. A vote outcome is balanced if the number of blue vertices is equal to the number of red ones. A balanced vote outcome corresponds to a situation in which the electoral population is perfectly split between two parties. 22 Nicola Apollonio et al. From now on, except for the last section, we shall consider only balanced vote outcomes.

Here we are obliged to adhere to reality and, in our case, we refer to the real vote distribution of Italian political elections of 1996. With respect to this vote, for any given district design, we are able to compute how many seats are assigned to the Pole and to the Olive party, respectively. The idea is that both Pole and Olive would like to win the election. To this purpose, if they each had the opportunity of designing their own political districts, they would try to find the district design that makes them win as many seats as possible (gerrymandering).

3, there are regions in which, for suitable district designs, the Pole or the Olive party gets the total number of seats. 3 Experimental Plan and Results Table 1 shows the main characteristics of the graphs representing the territories of three Italian regions considered in our experimental plan. As before, here PE means “Population Equality”, C means “Compactness” and AC means “Administrative Conformity”, while MT refers to the “Mixed Target” which is defined as the following convex combination of PE, C and The Sunfish Against the Octopus: Opposing Compactness to Gerrymandering 39 Table 1.

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