Journal of Applied Mathematics and Computation

ISSN Print: 2576-0645 Downloads: 87909 Total View: 1370286
Frequency: quarterly ISSN Online: 2576-0653 CODEN: JAMCEZ

Towards a Perfect Voting System

Elena Karachaliou*, Alex Brekoulakis, John Stratoulias

The Moraitis School, GR-15452, Athens, Greece.

*Corresponding author: Elena Karachaliou

Published: December 18,2020


Choosing a voting system may seem a simple-looking procedure, however, it has to take into account many different social and political parameters as well as some mathematical contradictions. Thus, whether a voting system is considered fair or not is a debate that has been concerning researchers for decades. In this paper, we examine what makes a voting system fair, successful and effective. In order to achieve this, we present some of the most well-known voting systems and explain their mechanisms. Then, we present some basic mathematical properties-criteria of social choice procedures. After all, the satisfaction or not of such properties is what determines the fairness of a voting system. The question that arises is: “Can a voting system fulfill all these properties?” We show that all voting systems fail to satisfy some of the properties and we finally mention the impossibility theorems that prove that there is no social choice procedure that satisfies all properties, for example, the Gibbard-Satterthwaite theorem which can be practically applied. However, by examining the legitimacy of such claims, we discover voting paradoxes that arise in many hypothetical election scenarios, such as contradictions between some of the set criteria, and also scenarios in which it is impossible to fulfill some of these criteria, the existence of which seems to dictate that there is no perfect voting system. Or is there?



[2] The Math Forum, Condorcet Criterion.


[4] Alan D. Taylor, & Allison M. Pacelli. (2008). Mathematics and Politics, Springer, USA. 

[5] Hannu Nurmi. (1999). Voting Paradoxes and How to Deal with Them, Springer, Berlin.

[6] Mathias Risse. (2005). Why the count de Borda cannot beat the Marquis de Condorcet, Springer-Verlag.

[7] Ace Project, The Single Transferable Vote (STV).

[8] Arrow’s “impossibility” theorem—how can range voting accomplish the impossible?

[9] The Gibbard-Satterthwaite theorem about honest & strategic voting.

[10] The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1972. nobel_prizes/economic-sciences/laureates/1972/.

How to cite this paper

Towards a Perfect Voting System

How to cite this paper: Elena Karachaliou, Alex Brekoulakis, John Stratoulias. (2020) Towards a Perfect Voting System. Journal of Applied Mathematics and Computation, 4(4), 241-248.