The power of voting and corruption cycles

ABSTRACT

We introduce an evolutionary dynamical model for corruption in a democratic state describing the interactions between citizens, government and officials, where the voting power of the citizens is the main mechanism to control corruption. Three main scenarios for the evolution of corruption emerge depending on the efficiency of the institutions and the social, political, and economic characteristics of the State. Efficient institutions can create a corruption intolerant self-reinforcing mechanism. The lack of political choices, weaknesses of institutions and vote buying can create a self-reinforcing mechanism of corruption. The ambition of the rulers can induce high levels of corruption that can be fought by the voting power of the citizens creating corruption cycles.

KEYWORDS:

• Corruption
• democracy
• evolutionary game theory
• replicator dynamics
• heteroclinic cycles
• social traps

Acknowledgments

The authors would like to thank an anonymous reviewer for the very useful suggestion which vastly improved the paper. The authors would like to thank Laura Gardini and Elisabetta Michetti for the fruitful discussions regarding this work.

This work is partially financed by National Funds through the Portuguese funding agency, FCT – Fundação para a Ciência e a Tecnologia – within project: UID/EEA/50014/2019; the project “Dynamics, optimization and Modeling”, with reference PTDC/MAT-NAN/6890/2014 and the project “Modeling, Dynamics and Games” – MDG – with the reference PTDC/MAT-APL/31753/2017.

Elvio Accinelli wishes to thank the dean of the Faculty of Economic Sciences of the UASLP for the support provided for the academic stay at the Faculty of Sciences of the University of Porto, where much of this work was elaborated and also the Department of Mathematics of University of Porto for their hospitality. Part of this work was done during Filipe Martins PhD research, who thanks FCT for a PhD scholarship with reference PD/BD/105726/2014. Atefeh Afsar would like to thank the financial support of FCT through a PhD grant of the MAP-PDMA program with reference PD/BD/142886/2018.

Notes

¹ The European Union published its first ever anti-corruption report in February 2014, where it concluded that bribery, embezzlement, financial and tax fraud, money laundering, cronyism, etc., “(…) cost the EU economy 120 billion euros per year, just a little less than the annual budget of the European Union’’.

² A paradigmatic episode of vote buying occurred in XVIII century England in the “Spendthrift election’’ in Northamptonshire Grego (1886), when three earls spent over $100,000$ pounds each to win a seat.

³ An heteroclinic cycle is a path in the phase/state space of a dynamical system connecting different equilibrium points and eventually ending in the first equilibrium, hence making a cycle. As is the case with fixed points and periodic orbits, such cycles may be stable or unstable.

⁴ For instance it is well documented that in some countries some distribution of benefits and/or payments by some politicians occurs for instance in the context of electoral campaigns (see Brusco, Nazareno, and Stokes (2004)). In these cases it is often reported that even if people acknowledge these as corrupt practices, they do not explicitly condemn them, and indeed accept such payments, therefore acting in a compliant way. Another example would be using fake news to denigrate the image of the political opposition and, by comparison, to make the government appear as less corrupt which may have an effect on citizens.

Additional information

Funding

This work is partially financed by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia - within project: UID/EEA/50014/2019; the project ``Dynamics, optimization and modelling'', with reference PTDC/MAT-NAN/6890/2014 and the project ``Modelling, Dynamics and Games'' - MDG - with the reference PTDC/MAT-APL/31753/2017.