On logical quantitative methods in politics
2021
The first chapter introduces the methodology of logical quantitative
models and its applications to political sciences. The second chapter
explains the conversion of votes to seats. I use the law of minority
attrition, expanding its form into a final model which is applicable from
single member district to several electoral systems. The third chapter
introduces the estimation of party seats from the previous elections using
a weighted regression with independent variables jointly: 1) the product
of the assembly size and the district magnitude, 2) the past values of the
biggest party shares, and 3) the number of Effective parties and simply
considered. Chapter four develops a probability density function with
five inflection points which describes any party system. It better catches
the asymmetries among the party seats distribution at nationwide level.
Chapter five implements the Downsian (or positional) competition
model that describes the left-right space occupied by each party through
Beta functions that I have tested on the Italian elections from 1992 to 2018.
Chapter six presents an in-depth qualitative analysis of the hypothesis
that the more proportional an electoral system, the more the parties tend
to centripetal competition, thus connecting ideological terms, effective
number of parties and electoral system. In chapter seven, I suggest an
alternative logical method to aggregate electoral flows, which resolves
Goodman’s problematics and provides a simpler solution than that of G.
King. Chapter eight provides tools to more accurately calculate the
optimal value of S (Taagepera and Shugart, 1989, p. 175), and
unprecedently, the optimal value of other institutional variables such as:
the district magnitude, the Gallagher’s index of dis-representation, and
the dis-representation index attributable to an electoral system (De), originally developed in this thesis. Chapter nine wants to determine an
equilibrium between parties’ and voters’ “electoral utility”, which is the
quantity of dis-representation which benefits a group of parties and
voters in the system, producing disutility for the others; this chapter
enriches the law of minority attrition including thresholds and majority
premiums (MJPs) and strategic vote, using a primary game theory
approach and the "Maximin" Rawlsian theory (1971) as a benchmark for
equality. Chapter ten provides an overview of links among the new tools
and knowledge developed in this thesis, with the final aim of the
normative building of an optimal electoral system, which can warrant
both logical coherence and social equity as categorized by Arrow (1951).
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