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In the frame of social choice, in the aggregation of preferences and more particularly in voting theory, we present two approaches of mathematical modelisation towards political representation. Together they lead, in Section 4, to a sketch of what is, in our sense, the nature, the ideal shape and the most common misuses of real-world modelisation, in particular, its mathematical modelisation. ; info:eu-repo/semantics/published

Abstract. In this note we study different methods of aggregation of preferences met on the occasion of elections. Through a simple geometrical representation, we analyse several of their properties, in particular those linked to Arrow's theorem for ordinal rankings; we pursue this discussion in the case of cardinal rankings, the qualities of which convince us of the usefulness of experiencing their introduction in real ballots.

Comparative political analysis at the macrolevel of political systems can reduce the inevitably high complexity of such comparisons by the systematic matching or contrasting of cases, depending on the particular problem. Such "most similar systems" or "most different systems" designs, in Przeworski and Teune's terminology, thus constitute one of the major ways out of the usual "small N—many variables" dilemma. This article proposes a detailed and comprehensive method to establish such similarities and dissimilarities in a systematic and, at all stages, transparent way. The examples chosen refer to an analysis of the conditions of survival or breakdown of democratic systems in the interwar period in Europe.

The problem of fair representation is studied in the case of cleavage according to one or two criteria. In the latter case we show that with minimal requirements of equity, a solution exists only if the two criteria are binary. This might explain an observed tendency to political bipolarization. ; SCOPUS: ar.j ; FLWNA ; info:eu-repo/semantics/published