An operator view on alliances in politics

TL;DR

This paper introduces an operator decision-making framework to analyze coalition formation among three political parties, considering voter groups and interaction types, providing dynamic decision functions and their long-term outcomes.

Contribution

It presents a novel operator-based approach to model political coalition decisions, incorporating voter group dynamics and interaction effects, with explicit decision functions and asymptotic analysis.

Findings

Derived time-dependent decision functions for each party.

Identified asymptotic coalition formation outcomes.

Analyzed effects of party interactions on decision stability.

Abstract

We introduce the concept of an {\em operator decision making technique} and apply it to a concrete political problem: should a given political party form a coalition or not? We focus on the situation of three political parties, and divide the electorate into four groups: partisan supporters of each party and a group of undecided voters. We consider party-party interactions of two forms: shared or differing alliance attitudes. Our main results consist of time-dependent decision functions for each of the three parties, and their asymptotic values, i.e., their final decisions on whether or not to form a coalition.