Mathematical ideas and tools are often used to describe aspects of large macroscopic systems. Examples abound in areas as varied as finance to psychology. In a paper published last month in the SIAM Journal on Applied Mathematics , author Fabio Bagarello proposes mathematical models to analyze political decision-making. Using a dynamical approach which accounts for interactions between political parties and their constituents, the model tries to deduce whether parties should form coalitions under various circumstances.
Bagarello uses a Hamiltonian operator, which can describe interactions among various constituents of a system. In the model, three parties in a system are considered. Each party can make one of two choices: forming a coalition or not. This gives rise to eight different possibilities that can change over time. The time behavior of "decision functions" of political parties is then determined, which describes the likelihood of a party forming a coalition. In order to make decisions, the parties need to interact with the voters or electors. This interaction is instrumental in their final decisions, and the model considers this via an open system which accounts for voter interaction.
"Several macroscopic systems have been analyzed using such operatorial techniques. I have adopted the same general framework in the description of 'love affairs', migrations, closed ecological systems and simplified stock markets," Bagarello continues. "Dealing with stock markets was my original interest, due to the fact that traders exchange discrete quantities which are well described by simple and well-known algebraic rules."
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Source Article: An Operator View on Alliances in Politics http://epubs.siam.org/doi/abs/10.1137/140990747 SIAM Journal on Applied Mathematics , 75(2), 564-584 (Online publish date: March 19, 2015)
About the author: Fabio Bagarello is a professor of mathematical physics at the University of Palermo, Department of Mathematical Models, Palermo, Italy.
SIAM Journal on Applied Mathematics