The drastic outcomes from voting alliances in three-party bottom-up democratic voting (1990 $\rightarrow$ 2013)

Abstract

The drastic effect of local alliances in three-party competition is investigated in democratic hierarchical bottom-up voting. The results are obtained analytically using a model which extends a sociophysics frame introduced in 1986 \cite{psy} and 1990 \cite{lebo} to study two-party systems and the spontaneous formation of democratic dictatorship. It is worth stressing that the 1990 paper was published in the Journal of Statistical Physics, the first paper of its kind in the journal. It was shown how a minority in power can preserve its leadership using bottom-up democratic elections. However such a bias holds only down to some critical value of minimum support. The results were used latter to explain the sudden collapse of European communist parties in the nineties. The extension to three-party competition reveals the mechanisms by which a very small minority party can get a substantial representation at higher levels of the hierarchy when the other two competing parties are big. Additional surprising results are obtained, which enlighten the complexity of three-party democratic bottom-up voting. In particular, the unexpected outcomes of local voting alliances are singled out. Unbalanced democratic situations are exhibited with strong asymmetries between the actual bottom support of a party and its associated share of power at the top leadership. Subtle strategies are identified for a party to maximize its hold on the top leadership. The results are also valid to describe opinion dynamics with three competing opinions.