On logical quantitative methods in politics

The first chapter introduces the methodology of logical quantitativemodels and its applications to political sciences. The second chapterexplains the conversion of votes to seats. I use the law of minorityattrition, expanding its form into a final model which is applicable fromsingle member district to several electoral systems. The third chapterintroduces the estimation of party seats from the previous elections usinga weighted regression with independent variables jointly: 1) the productof the assembly size and the district magnitude, 2) the past values of thebiggest party shares, and 3) the number of Effective parties and simplyconsidered. Chapter four develops a probability density function withfive inflection points which describes any party system. It better catchesthe asymmetries among the party seats distribution at nationwide level.Chapter five implements the Downsian (or positional) competitionmodel that describes the left-right space occupied by each party throughBeta functions that I have tested on the Italian elections from 1992 to 2018.Chapter six presents an in-depth qualitative analysis of the hypothesisthat the more proportional an electoral system, the more the parties tendto centripetal competition, thus connecting ideological terms, effectivenumber of parties and electoral system. In chapter seven, I suggest analternative logical method to aggregate electoral flows, which resolvesGoodman’s problematics and provides a simpler solution than that of G.King. Chapter eight provides tools to more accurately calculate theoptimal value of S (Taagepera and Shugart, 1989, p. 175), andunprecedently, the optimal value of other institutional variables such as:the district magnitude, the Gallagher’s index of dis-representation, andthe dis-representation index attributable to an electoral system (De), originally developed in this thesis. Chapter nine wants to determine anequilibrium between parties’ and voters’ “electoral utility”, which is thequantity of dis-representation which benefits a group of parties andvoters in the system, producing disutility for the others; this chapterenriches the law of minority attrition including thresholds and majoritypremiums (MJPs) and strategic vote, using a primary game theoryapproach and the "Maximin" Rawlsian theory (1971) as a benchmark forequality. Chapter ten provides an overview of links among the new toolsand knowledge developed in this thesis, with the final aim of thenormative building of an optimal electoral system, which can warrantboth logical coherence and social equity as categorized by Arrow (1951).