First results on applying a non-linear effect formalism to alliances between political parties and buy and sell dynamics

TL;DR

This paper introduces a non-linear operator-based model for political alliances and financial asset dynamics, capturing complex interactions and decision processes influenced by internal and external factors.

Contribution

It presents a novel non-linear extension of a political alliance model using Hamiltonian formalism applicable to both politics and financial markets.

Findings

The model captures the influence of parties on each other's decisions.

It demonstrates how the same formalism applies to financial asset dynamics.

Preliminary results show the model's potential to describe complex interaction effects.

Abstract

We discuss a non linear extension of a model of alliances in politics, recently proposed by one of us. The model is constructed in terms of operators, describing the \emph{interest} of three parties to form, or not, some political alliance with the other parties. The time evolution of what we call \emph{the decision functions} is deduced by introducing a suitable hamiltonian, which describes the main effects of the interactions of the parties amongst themselves and with their \emph{environments}, {which are }generated by their electors and by people who still have no clear {idea }for which party to vote (or even if to vote). The hamiltonian contains some non-linear effects, which takes into account the role of a party in the decision process of the other two parties. Moreover, we show how the same hamiltonian can also be used to construct a formal structure which can describe the dynamics of buying and selling financial assets (without however implying a specific price setting mechanism).