The article investigates public choice models for the analysis of political cycles as efforts in refounding a genuine political economy. It classifies political cycles models according to two criteria: the "ends of government" and the rationality and information structure of voters. A closed review of the hypotheses guiding rational models reveals the heuristic limits of the approach. A genuine political economy should consider the consequences of processes governed by a political logic, which is intrinsically different from that of economic accumulation or utility maximisation. Rather than a re-foundation of political economy, in the case of public choice analysis one should speak of a widening of the realm of economics.