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What’s the best voting method?

There is no best voting method.

You can always find a specific situation where a given voting method produces the wrong result. However, whereas in general there is no perfect voting method, in practice there are voting methods that can be worse or better for you and your organization.

Here are a few suggestions to guide you in the forest of voting methods. Take them with a grain of salt and judge for yourself, which is best in your specific situation.

Questions and answers to find the Best Voting Method

Q: I need to take a decision concerning a very small number of choices (2-3)
A: consider plain Single Preference voting

Q: I need to choose between a moderate number of choices and I want a simple and solid method…
A: consider Approval method

Q: I need to choose between a large number of choices; my voters have no reasons to be insincere…
A: consider Borda method

Q: My voters are familiar with Runoff method and would like to avoid voting twice…
A: consider Instant Runoff method

Q: I need to choose between a large number of choices; I want to be as robust as possible against insincere votes…
A: consider Condorcet method

In most situations the simplest voting methods are the best solution: so consider plain Single Preference voting and Multiple Preference approval before any other method. Sometimes you may want to use more than a single voting method, and may want to study the robustness of a result against different voting methods.

In the case of small committees with highly skilled voters, one may consider using sophisticated methods. In this case Condorcet is usually a good choice. It may easily produce ties, however, so it may be a good idea to confront the result with the Borda method results, which are much less likely to end up in a tie.

Condorcet voting

The Condorcet method is the most sophisticated voting method. Here, we will just give an informal description and a few examples. Condorcet method is a pairwise election method where each candidate runs against all the others separately, and one counts the “defeats” X/Y, i.e. the number of times candidates X beats candidates Y versus the number of times X is beaten by Y.

Defeats X/Y are ordered according their magnitude, the magnitude being the number of times candidates X beats candidates Y. For instance in this ballot with three candidates:

40: C
35: A B C
25: B A C

We have the following defeats:

B/C:60/40 (B beats C 60 times, C beats B 40 times, the magnitude is 60)
A/C:60/40 (A beats C 60 times, C beats A 40 times, the magnitude is 60)
A/B:35/25 (A beats B 35 times, B beats A 25 times, the magnitude is 35)

Since A beats all its opponents in separate races, it is the clear winner. In more complex situations, no candidate beats all the others. Then the counting proceeds by removing the weakest defeats until an unbeaten candidate is found, or we get a tie. For instance in this case:

40: C
35: A B C
25: B C

we get:

C/A: 65/35
B/C: 60/40
A/B: 35/25

and removing successively the weakest (smallest magnitude) defeat, we remain with the unbeaten candidate B which is the Condorcet winner. This is the algorithm describing the original Condorcet method, but actually PARTECS™ does not implement it (since it has some minor defects). PARTECS™ uses a state-of-the-art variation of Condorcet, the Cloneproof or Schwartz sequential dropping (SSD) Condorcet method.

Instant Runoff (a.k.a. Preferential voting)

Instant Runoff is an ordinal voting method, which may be a good choice for people familiar with runoff voting, i.e. voting in multiple turns, where weaker candidates are removed and their votes are transferred to the remaining candidates. It is simpler and less robust than Condorcet and more complicated but more robust than the Borda method. It is used in the real world in Australian elections under the name of Preferential voting (or Alternative voting).

Voters rank the candidates as first, second, third, etc. Table 1 illustrates the IRV tallying procedure for an example with four candidates (A, B, C, D) and 16 voters.

Table 1: An example ballot with four candidates A, B, C, D

3: B A C
2: B C A
1: B D
2: A B D
1: A B C
1: A
1: D C B
1: D C A
1: D
1: C A B
1: C D A

The first step is to count the first choices. Candidate B got 6 of the 16 first choices, while A got 5, D got 3, and C got 2. If one candidate had received a majority of first choices, that candidate would have won, but nobody did in this case. The counting procedure therefore goes to a second round.

The candidate with the fewest first choices, candidate C, is now eliminated. Each vote for C is transferred to the next candidate. Thus, all C entries are eliminated and the remaining choices are pushed left, if necessary, to fill in the empty cells. Table 2 shows the result (the third column is no longer needed).

Table 2: Ballot after the first round

5: B A
1: B D
4: A B
1: A D
1: A
1: D B
2: D A
1: D

The top choices are now counted again. Candidate A gained one new top choice (the second from last vote) for a total of 6. Still no candidate has a majority, so the counting procedure goes to a third round. Candidate D now has the fewest top choices and is therefore eliminated. Table 3 shows the result.

Table 3: Ballot after the first round

7: B
8: A

In the final round, the third from last vote has been exhausted; so only 15 active votes remain. Candidate A picked up two votes and now has 8 votes, which is a majority of the remaining votes, so candidate A wins. In this example, candidate A had fewer first choices than candidate B in the first round, but ultimately won the election.

The maximum number of rounds is always one less than the number of candidates. In the case of ties for the fewest top choices, the tied candidate with the fewest second choices is eliminated (if those are also tied, look at third choices, etc.). In the case of a tie in the final round, a coin toss can break the tie.

IRV has serious problems. It allows a sufficiently small minority of voters to safely register “protest” votes for minor-party candidates – but only as long as their candidate is sure to lose. As soon as their candidate threatens to actually win, they risk hurting their own cause by ranking their favourite first, just as they do under our current plurality system. IRV is therefore unlikely to be any more successful than plurality at solving the classic “lesser of two evils” problem.

A variation of IRV allows voters to rank groups of candidates equally. For example, a voter could rank candidates B and C equally for first choice, and D for second choice. For technical reasons that will not be discussed here, this equal-ranking option significantly mitigates the serious problems of IRV, but not enough to make it a good election method.

IRV does have one potential advantage over plurality. It requires the same voting equipment and the same voting mechanics (ranking candidates) as Condorcet voting. IRV could therefore possibly be transitional to Condorcet voting, a far superior alternative to IRV. However, IRV could also get entrenched and preclude Condorcet voting.

Shortcomings of Instant Runoff

Instant Runoff has serious technical problems, since it fails the monotonic criteria:

With the relative order or rating of the other candidates unchanged, voting a candidate
higher should never cause the candidate to lose, nor should voting a candidate lower ever cause the candidate to win.

This means that there are peculiar cases where the Instant Runoff method lets the “wrong” candidate win, even if the votes are all sincere. One example of such a case is the following votes count with four candidates “A, B, C, D”:

7: A,B,C
6: B,A,C
5: C,B,A
3: D,C,B

Applying the rules of IRV, candidate A wins. But suppose the three voters who voted (D, C, B) now promote A from last choice all the way up to first choice, without changing the relative order of the other candidates. Now B wins instead of A. So by promoting A from last to first choice, those voters caused A to lose instead of win!

Single Preference Voting (a.k.a. Plurality Voting)

This is the voting method everybody is familiar with: the voter just selects the option he/she likes the most. The final result is computed according to the number of votes received for each candidate and the results are displayed in terms of percentages.

The single preference voting method is clear, simple and easy to grasp: it is the best method when you need to decide between two candidates. However, in the case of decisions involving three or more candidates, it is unfair with respect to minority candidates. The problem is that votes given to minority candidates are “wasted”, so people tend to vote the “lesser of two evils” between the first two major candidates. In the case of political elections, the usage of single-preference voting naturally leads to a two-party system (Duverger’s Law) i.e. a duopoly regime. In the case of a decision making process this is less of an issue, but still one has the same undesirable effect: when there are two options, which are clearly favourites it becomes counter-productive to vote minority options and people are encouraged to vote insincerely.

Single-preference voting severely restricts the voter’s expressiveness. Since the voter is forced to select just one candidate between many, he/she has no way to express the fact that he/she equally likes two or more candidates. Also, he/she cannot express the order of his/her preferences. If you have many options to choose from and want to give more freedom to your electors, it is best if you switch to a multiple choice voting method.

Approval voting

Approval Voting is the simplest multiple preference voting method. The voter just lists the options he/she likes in any order. At the end, the number of preferences for each candidate is counted and displayed in terms of percentages.

Approval method is easy to explain and to grasp, but restricts the voter expressiveness in the sense that he/she has no way to express that he/she likes a candidate more that another, since all listed candidates are considered equally liked. If you have many options to choose from and want to give more freedom to your electors, it is best if you switch to an ordinal voting method.