Proportionality and Party Success in Europe

This thesis consists of four articles and an introductory section. The main research questions in all the articles are about proportionality and party success in Europe, at European, national or district levels. Proportionality in this thesis denotes the proximity of seat shares parties receive compared to their respective vote shares, after the electoral system’s allocation process. This proportionality can be measured through numerous indices that illustrate either the overall proportionality of an electoral system or a particular election. The correspondence of a single party’s seat shares to its vote shares can also be measured. The overall proportionality is essential in three of the articles (1, 2 and 4), where the system’s performance is studied by means of plots. In article 3, minority party success is measured by advantage-ratios that reveal single party’s winnings or losses in the votes to seat allocation process. The first article asks how proportional are the European parliamentary (EP) electoral systems, how do they compare with results gained from earlier studies and how do the EP electoral systems treat different sized parties. The reasons for different outcomes are looked for in explanations given by traditional electoral studies i.e. electoral system variables. The countries studied (EU15) apply electoral systems that vary in many important aspects, even though a certain amount of uniformity has been aspired to for decades. Since the electoral systems of the EP elections closely resemble the national elections, the same kinds of profiles emerge as in the national elections. The electoral systems indeed treat the parties differentially and six different profile types can be found. The counting method seems to somewhat determine the profile group, but the strongest variables determining the shape of a countries’ profile appears to be the average district magnitude and number of seats allocated to each country. The second article also focuses on overall proportionality performance of an electoral system, but here the focus is on the impact of electoral system changes. I have developed a new method of visualizing some previously used indices and some new indices for this purpose. The aim is to draw a comparable picture of these electoral systems’ changes and their effects. The cases, which illustrate this method, are four elections systems, where a change has occurred in one of the system variables, while the rest remained unchanged. The studied cases include the French, Greek and British European parliamentary systems and the Swedish national parliamentary system. The changed variables are electoral type (plurality changed to PR in the UK), magnitude (France splitting the nationwide district into eight smaller districts), legal threshold (Greece introducing a three percent threshold) and counting method (d’Hondt was changed to modified Sainte-Laguë in Sweden). The radar plots from elections after and before the changes are drawn for all country cases. When quantifying the change, the change in the plots area that is created has also been calculated. Using these radar plots we can observe that the change in electoral system type, magnitude, and also to some extent legal threshold had an effect on overall proportionality and accessibility for small parties, while the change between the two highest averages counting method had none. The third article studies the success minority parties have had in nine electoral systems in European heterogeneous countries. This article aims to add more motivation as to why we should care how different sized parties are treated by the electoral systems. Since many of the parties that aspire to represent minorities in European countries are small, the possibilities for small parties are highlighted. The theory of consociational (or power-sharing) democracy suggests that, in heterogeneous societies, a proportional electoral system will provide the fairest treatment of minority parties. The OSCE Lund Recommendations propose a number of electoral system features, which would improve minority representation. In this article some party variables, namely the unity of the minority parties and the geographical concentration of the minorities were included among possible explanations. The conclusions are that the central points affecting minority success were indeed these non-electoral system variables rather than the electoral system itself. Moreover, the size of the party was a major factor governing success in all the systems investigated; large parties benefited in all the studied electoral systems. In the fourth article the proportionality profiles are again applied, but this time to district level results in Finnish parliamentary elections. The level of proportionality distortion is also studied by way of indices. The average magnitudes during the studied periodrange from 7.5 to 26.2 in the Finnish electoral districts and this opens up unequal opportunities for parties in different districts and affects the shape of the profiles. The intra-country case allows the focus to be placed on the effect of district magnitude, since all other electoral systems are kept constant in an intra-country study. The time span in the study is from 1962 to 2007, i.e. the time that the districts have largely been the same geographically. The plots and indices tell the same story, district magnitude and electoral alliances matter. The district magnitude is connected to the overall proportionality of the electoral districts according to both indices, and the profiles are, as expected, also closer to perfect proportionality in large districts. Alliances have helped some small parties to gain a much higher seat share than their respective vote share and these successes affect some of the profiles. The profiles also show a consistent pattern of benefits for the small parties who ally with the larger parties.

A quantitative view on fuzzy numbers

Since its introduction, fuzzy set theory has become a useful tool in the mathematical modelling of problems in Operations Research and many other fields. The number of applications is growing continuously. In this thesis we investigate a special type of fuzzy set, namely fuzzy numbers. Fuzzy numbers (which will be considered in the thesis as possibility distributions) have been widely used in quantitative analysis in recent decades. In this work two measures of interactivity are defined for fuzzy numbers, the possibilistic correlation and correlation ratio. We focus on both the theoretical and practical applications of these new indices. The approach is based on the level-sets of the fuzzy numbers and on the concept of the joint distribution of marginal possibility distributions. The measures possess similar properties to the corresponding probabilistic correlation and correlation ratio. The connections to real life decision making problems are emphasized focusing on the financial applications. We extend the definitions of possibilistic mean value, variance, covariance and correlation to quasi fuzzy numbers and prove necessary and sufficient conditions for the finiteness of possibilistic mean value and variance. The connection between the concepts of probabilistic and possibilistic correlation is investigated using an exponential distribution. The use of fuzzy numbers in practical applications is demonstrated by the Fuzzy Pay-Off method. This model for real option valuation is based on findings from earlier real option valuation models. We illustrate the use of number of different types of fuzzy numbers and mean value concepts with the method and provide a real life application.

New directions in Stochastic Multicriteria Acceptability Analysis

Decisions taken in modern organizations are often multi-dimensional, involving multiple decision makers and several criteria measured on different scales. Multiple Criteria Decision Making (MCDM) methods are designed to analyze and to give recommendations in this kind of situations. Among the numerous MCDM methods, two large families of methods are the multi-attribute utility theory based methods and the outranking methods. Traditionally both method families require exact values for technical parameters and criteria measurements, as well as for preferences expressed as weights. Often it is hard, if not impossible, to obtain exact values. Stochastic Multicriteria Acceptability Analysis (SMAA) is a family of methods designed to help in this type of situations where exact values are not available. Different variants of SMAA allow handling all types of MCDM problems. They support defining the model through uncertain, imprecise, or completely missing values. The methods are based on simulation that is applied to obtain descriptive indices characterizing the problem. In this thesis we present new advances in the SMAA methodology. We present and analyze algorithms for the SMAA-2 method and its extension to handle ordinal preferences. We then present an application of SMAA-2 to an area where MCDM models have not been applied before: planning elevator groups for high-rise buildings. Following this, we introduce two new methods to the family: SMAA-TRI that extends ELECTRE TRI for sorting problems with uncertain parameter values, and SMAA-III that extends ELECTRE III in a similar way. An efficient software implementing these two methods has been developed in conjunction with this work, and is briefly presented in this thesis. The thesis is closed with a comprehensive survey of SMAA methodology including a definition of a unified framework.