This example was created by professor Donald G. Saari and is from his 2001 book Decisions and Elections.
Let there be 30 voters and four candidates named A, B, C, and D. We display both the first and second choices of each voter.
| #voters | their vote |
|---|---|
| 6 | A>D |
| 3 | A>C |
| 5 | B>D |
| 3 | B>C |
| 5 | C>D |
| 2 | C>B |
| 4 | D>C |
| 2 | D>B |
With plurality voting, A wins this election with 9 votes (shown pink), followed by B=8, C=7, D=6.
But now suppose the losingest candidate D drops out. Of course, that'll make no difference, right? Wrong. Now the results are completely reversed: C wins with 11, followed by B=10, A=9.
In fact, no matter which candidate drops out, the result-order among the others gets totally reversed.
The point of this example is that plurality voting is totally self-contradictory. It can say somebody is the best candidate, then turn around and say that same person is the worst. It must have been wrong at least one of those times. And the consequence can be that we elect the worst instead of the best candidate, which is very bad news for your country.
You might want to consider range voting instead.