The students of your school choose a movie for a movie night among three possibilities:
Movie A: All for love (a romantic comedy)
Movie B: Boulevard police (action movie)
Movie C: Creepy night (horror movie).
The students vote by ordering the movies in their order of preference (first choice, second choice, third choice). For example, they write $B>C>A$ to mean that $B$ is the first choice, $C$ the second choice, and $A$ the third choice. Suppose that the result of the students' movie ranking is as follows:
A>B>C
38%
A>C>B
2%
B>C>A
18%
B>A>C
7%
C>A>B
3%
C>B>A
32%
In your opinion, which movie should be selected?
Movie A could be selected because it's the most common first choice:
40% of the students have A as first choice
25% have B as first choice
35% have C as first choice.
Movie B could be selected because it wins in head-to-head comparison over Movie A and over Movie C:
57% of the students prefer B to A, so B wins over A;
63% of the students prefer B to C, so B wins over C.
Movie C could be selected, if we discard the students' least favorite first choice and reconsider the ranking. In our case, Movie B is the least favorite first option: removing B from the rankings we see that
47% of the students have A as first choice
53% of the students have C as first choice.
Movie B is the compromise solution because it is the second choice for 70% of the students. Since 95% of the students rank movie B as first choice or second choice, it would be reasonable to suggest to select movie B.
Conclusion:The outcome of an election depends on the voting rule that is applied. Indeed, as we see in the above example, according to the chosen rule, it’s either movie $A$ or $B$ or $C$ that gets selected. For this reason, the voting rule must be established before the voting (and before the polls). The voting rule may depend, for example, on whether compromise solutions are well-accepted or not.
For example, do we want to:
Pick the movie with the most first-place votes?
Choose the movie that most people are okay with, even if it’s not their favorite?
Avoid the movie that many people really don’t like?
Different rules can lead to different winners!
A different example:
Replace B by a movie that is very similar to A (say, B is the movie Best friends in love).
In this case, the fans of romantic comedies split their votes between A and B. That could make Movie C (the horror movie) win.
Imagine 64 % of students love A or B and dislike horror movie C.
If those 64 % divide their votes evenly (32 % for A, 32 % for B), while 36 % vote for C, then C becomes the most common first choice.
This example shows that similar choices can split supporters’ votes and allow a different choice to win. It’s something to keep in mind when voting or designing a fair election.