A Qualitative Theory of Conflict Resolution and Political Compromise

Abstract

We view political activity as an interaction between forces seeking to achieve a political agenda. The viability of a situation depends on the compatibility of such agendas. However even in a conflictual situation a compromise may be possible. Mathematically a political structure is modeled as a simplicial complex and a viable configuration as a simplex. A represented compromise is a viable configuration obtained by the withdrawal of some agents in favor of some friendly representatives. A delegated compromise is a sophisticated version of a compromise obtained by the iteration of the withdrawal process. Existence of such solutions depends on the discrete topology of the simplicial complex. In particular we prove that the existence of a delegated compromise is equivalent to the strong contractibility of the simplicial complex.