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According to the canonical model at the heart of the « economic » theory of (democratic) politics (or of « rational choice theory », the term preferred by political scientists), it is generally impossible to reach a determinate decision by using the majority rule in matters having two or more aspects. This problem, referred to as that of disequilibrium, or equilibrium instability, or even « chaos », was at first minimized, and later deemed ominous to the point of seriously undermining the prospects of the theory itself. The concern thus caused until the 1980s has recently given way to a recovery of serenity, thanks to the construction of solution-yielding models which admit an equilibrium, although the problem as initially formulated has not been really solved. This article presents the main lines of this theoretical two-way itinerary and a methodological interpretation of it, in the light of recent developments in the philosophy of science – in particular the legitimacy now assigned to research seeking to identify the main mechanisms at work in social systems rather than to discover universal empirical laws.