Skip to main content
SpringerLink
Log in

An improved model of alliances between political parties

  • Published:
Ricerche di Matematica Aims and scope Submit manuscript

Abstract

We consider an operatorial model of alliances between three political parties which interact with their electors, with the undecided voters, and with the electors of the other parties. This extends what was done in a previous paper, where this last type of interactions was not considered. Of course, taking them into account makes the system closer to real life. To produce an exactly solvable model, we restrict here to quadratic Hamiltonians, so that the equations of motion turn out to be linear. The dynamics of the so-called decision functions are deduced, and some explicit situations are considered in details.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Notes

  1. In [12] an extra term has also been added to H, to get the full Hamiltonian of the system. However, the nature of the term added in [12] is completely different from that of \(H_{mix}\), since this still produces an analytically solvable set of differential equations.

  2. Notice that, to simplify the notation, in \(M_j\) and \(R_j\) we are making explicit only the dependence on t.

References

  1. Khrennikov, A.: Ubiquitous Quantum Structure: From Psychology to Finances. Springer, Berlin (2010)

    Book  MATH  Google Scholar 

  2. Haven, E., Khrennikov, A.: Quantum Social Science. Cambridge University Press, New York (2013)

    Book  MATH  Google Scholar 

  3. Busemeyer, J.R., Bruza, P.D.: Quantum Models of Cognition and Decision. Cambridge University Press, Cambridge (2012)

    Book  Google Scholar 

  4. Asano, M., Ohya, M., Tanaka, Y., Basieva, I., Khrennikov, A.: Quantum-like model of brain’s functioning: decision making from decoherence. J. Theor. Biol. 281, 56–64 (2011)

    Article  MathSciNet  Google Scholar 

  5. Asano, M., Ohya, M., Tanaka, Y., Basieva, I., Khrennikov, A.: Quantum-like dynamics of decision-making. Phys. A 391, 2083–2099 (2012)

    Article  MATH  Google Scholar 

  6. Khrennikova, P., Haven, E., Khrennikov, A.: An application of the theory of open quantum systems to model the dynamics of party governance in the US Political System. Int. J. Theor. Phys. (2013). doi:10.1007/s10773-013-1931-6

    MathSciNet  Google Scholar 

  7. Davis, O.A., Hinich, M.J., Ordeshook, P.: An expository development of a mathematical model of the electoral process. Am. Political Sci. Rev. 64(2), 426–448 (1970)

    Article  Google Scholar 

  8. Buonomo, B., d’Onofrio, A.: Modeling the influence of public’s memory on the corruption-popularity dilemma in politics. J. Optim. Theory Appl. 158, 554–575 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Makowski, Marcin, Piotrowski, Edward W.: Decisions in elections-transitive or intransitive quantum preferences. J. Phys. A Math. Theor. 44(21), 215303 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Galam, S.: Sociophysics, A Physicist’s Modeling of Psycho-political Phenomena. Springer, Berlin (2012)

    Google Scholar 

  11. Bagarello, F.: An operator view on alliances in politics. SIAM J. Appl. Math. (SIAP) 75(2), 564–584 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. Bagarello, F., Haven, E.: First results on applying a non-linear effect formalism to alliances between political parties and buy and sell dynamics. Phys. A (In press)

  13. Bagarello, F., Gargano F.: The role of nonlinear interactions in modeling political alliances. Accademia Peloritana dei Pericolanti (In press)

  14. Bagarello, F.: Quantum Dynamics for Classical Systems: With Applications of the Number Operator. Wiley, New York (2012)

    Book  Google Scholar 

Download references

Acknowledgments

The author acknowledges partial support from Palermo University and from G.N.F.M. of the INdAM. The author also wishes to thank the organizers of the XVIII Wascom Conference for their financial and logistic support during the conference.

Author information

Authors and Affiliations

  1. Dipartimento di Energia, Ingegneria dell’Informazione e Modelli Matematici, Scuola Politecnica Ingegneria, Università di Palermo, I-90128, Palermo, Italy

    F. Bagarello

  2. I.N.F.N., Sezione di Torino, Torino, Italy

    F. Bagarello

Authors
  1. F. Bagarello
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. Bagarello.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bagarello, F. An improved model of alliances between political parties. Ricerche mat 65, 399–412 (2016). https://doi.org/10.1007/s11587-016-0261-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11587-016-0261-4

Keywords

Mathematics Subject Classification

Search

Navigation