July 11, 2019

About polls

Countries in the world use very different electoral systems, but which one is best? The series of videos Politics In The Animal Kingdom by CGP Grey is a great introduction on this topic, which has also been studied by mathematicians, sociologists and economists.

Things can be very simple, for example in the countries which chose the pragmatic solution of having no elections, only one candidate or only one voter. But in countries where power is intended to be fairly held by the people, it quickly gets complicated. Already from 3 candidates, serious problems may start to arise since collective preferences can be cyclic (see Condorcet paradox). In the following example from the mathematician Michel Balinski, each of the 5 candidates a, b, c, d and e is the winner of the vote with one of these 5 voting systems used in the real world: plurality, Borda's rule sequential majority comparisons (a,b,c,d,e), instant-runoff, plurality with runoff. (The array must be read as "33% of voters would rank candidates in the order a then b then c then d then e")

33%16%3%8%18%22%
abccde
bddeec
ccbbcb
deadbd
eaeaaa

He proposed another voting system majority judgement in which voters have to grade candidates into categories (excellent, very good, good, acceptable, poor, or reject)


Some fairness criteria

There are specific criteria that can be defined to determine if a voting system is good. Let's list some of them.

Non-dictatorship

The result of the election cannot be chosen by a single voter, ignoring the others

Monotonicity

If some voters modify their preferences by ranking candidate A higher in their list, then the election result should not place A lower than before. An individual should not be able to hurt an option by ranking it higher.

Pareto efficiency

If every individual prefers a certain option to another, then so must be reflected the resulting societal preference order.

Resistance to tactical voting

A voter can vote tactically by lying about his or her preferences in order to get a more favourable outcome. A voting system is resistant to tactical voting if that scenario cannot occur.


Arrow's impossibility theorem shows that a rank-order voting system cannot satisfy the first 3 criteria, which means that we have to make some compromises.

Voting application

This application allows users to create polls using their favorite method. So next time you have to make a decision in a group, feel free to come here.

Happy voting!