In our contemporary world, we face different types of elections regularly. But have you ever thought that different types of voting systems can lead to different winners? In this article, we will use a simple example to analyze the types of vote counts.
Let's imagine that we live in a small town with a population of 100 people. In order to choose the head of the city, a vote was held. The following results were obtained:
If you look at this table, you will notice that candidate C received the most votes, so does it mean that he won? According to the “relative majority” method, yes. However, this is not entirely fair, since the vast majority (65 people) are dissatisfied.
In this case, we need at least a majority (50%) of residents to be for the chosen candidate. This approach is called the absolute majority method (or runoff method). To do this, we need to have a prioritization vote (alternative votes). Each voter ranks candidates according to the 1st, 2nd, 3rd, and 4th choice principle:
Now we take only 2 of the most popular candidates: A and C. Votes of B and D voters go to A or B depending on their alternative choice.
According to the ‘absolute majority’ method, candidate A wins. This is one of the most common methods since a lot of countries use it for presidential elections.
But what if we eliminate the least popular candidates instead? This is called “sequential elimination voting”. Only for 10 voters candidate D is the first choice, so we eliminate this candidate, and his votes go to 2nd choice candidate - B. Now we have the following situation:
Num. of 1st choice votes:
Still no one of candidates got more than half of votes, so we eliminate choice A:
Here, candidate B got 65 votes which is the absolute majority, so in this selection method he wins.
Now let's look at another counting method, in which we will compare candidates with each other. Similarly to the previous method, we use voters’ alternative choices and count votes between two candidates. Whoever wins the most comparisons wins. This is called the Condorset method.
As we can see, candidate A won 1 time, candidate B won 3 times and candidate D - 2 times. In compliance with the Condorset method, candidate B wins. Candidate C in this situation is called a Condorset loser, because he lost a runoff between all other winners.
The last method that we are going to use in the article is a “point based” method. Voters will give 4 points to their 1st choice, 3 points to their 2nd choice, 2 points to a 3rd choice, and 1 point to a 4th choice. Candidate with the highest number of points wins.
Candidate A
4 * 31 + 3 * 20 + 2 * 34 + 1 * 15 = 267 (points)
Candidate B
4 * 24 + 3 * 41 + 2 * 15 + 1 * 0 = 289 (points)
Candidate C
4 * 35 + 3 * 0 + 2 * 0 + 1 * 65 = 205 (points)
Candidate D
4 * 10 + 3 * 39 + 2 * 31 + 1 * 20 = 239 (points)
Thus, candidate B won since he got 289 points.
Conclusion
We counted votes with 5 different methods, did we get the same result for all of them?
Method | Winner |
relative majority | candidate C |
absolute majority method | candidate A |
sequential elimination voting | candidate B |
Condorset method | candidate B |
point based | candidate B |
As we can see, candidate B won 3 times, but candidate D didn’t win even 1 time. Perhaps some other election method would lead to candidate D winning. Understanding these methods is important, because they affect fairness and representation in elections. By comparing them, we can better understand the challenges of ensuring election integrity and the importance of choosing the right voting system for different types of elections.
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