# Clarification on Ranked Choice Voting Tie Breaker Algorithm

Suppose we are running a Ranked Choice vote between 6 candidates:

1. Harrison Ford
2. Carrie Fisher
3. Mark Hammill
4. James Earl Jones
5. Frank Oz
6. George Lucas

There are a lot of website that propose the rules - I've chosen at random:

http://electowiki.org/wiki/Instant-runoff_voting

But really, they're all pretty similar. The basic algorithm is:

First choices are tallied. If no candidate has the support of a majority of voters, the candidate with the least support is eliminated. A second round of counting takes place, with the votes of supporters of the eliminated candidate now counting for their second choice candidate. After a candidate is eliminated, he or she may not receive any more votes.

This process of counting and eliminating is repeated until one candidate has over half the votes. This is equivalent to continuing until there is only one candidate left. However it is possible, with voter truncation, for the process to continue until there is only one candidate left, who does not end up with more than half the votes.

The tie breaking rules, however, are less consistent. One option (from the above site) is:

LOGIC: If the tied candidates combined have fewer [first place] votes than the next highest candidate, the entire tied set can be eliminated at once. Logically deterministic, but may not apply

There are other options, but from the reading I've done, they tend to be based on the first place votes. Whoever has the fewest first place votes is eliminated, if there are multiple, one is either chosen at random, or potentially they are all eliminated.

So, what happens in the following scenario? This is a bit contrived, but actually came up in a small vote.

Voter A 1. Harrison Ford 2. Mark Hammill 3. Frank Oz

Voter B 1. Carrie Fisher 2. Mark Hammill 3. James Earl Jones

Voter C 1. George Lucas 2. Mark Hammill 3. James Earl Jones

Just eyeballing the results, it seems like Mark Hammill should win, since there was no consensus for first place. However, following the rules specified above, I believe he would be eliminated, and the winner would randomly be George, Harrison, or Carrie.

So, a few questions - am I interpreting the rules correctly? Is this a non-issue, because in the larger elections that this was designed for, you don't tend to run into this problem? Was ranked choice voting in fact designed to favor someone who got at least 1 first place vote over someone who got all the 2nd place votes? And finally, is there a better tie breaking algorithm covered to handle this issue?

• Now you know how Palpatine got voted chancellor :)
– Philipp
Jan 19, 2016 at 9:02
• @Philipp - technically, he was voted chancellor because he promised to deal with Senatorial gridlock and had a sympathy vote upswing from Naboo issues. There's about 5 other reasons but geeking out on SW/EU is probably offtopic here :) Jan 22, 2016 at 2:59
• In other words, there are a variety of different tie-breaking rules, but none of them will give the result you want, because the problem you're noticing is inherent to IRV itself, not the tie-breaking rules. Most people who study voting reform recognize that IRV is not very good, but it's unfortunately still the most popularly-proposed reform. Apr 3, 2019 at 17:13

After the first round, Frank Oz is eliminated.

After the second round, James Earl Jones is eliminated.

After the third round, yes, Mark Hamill is eliminated.

Note that this is much less likely to happen in reality, as more voters make odd results like this less likely. But this is the problem with IRV. It eliminates second choice votes even if they are generally preferred.

If you instead chose a Condorcet-compliant voting method, you could get a different result:

Mark Hamill beats Harrison Ford, Carrie Fisher, and George Lucas two to one. Hamill beats Frank Oz and James Earl Jones unanimously. Hamill wins without processing any eliminations.

Robert's rules state that the tied candidates should be eliminated at the same time in the same round no matter what. (source) This makes sense because if candidates with the lowest votes should be removed no tied candidate should have the chance to pass any of the others just because they were someone's second choice and that added to their score, does that make sense?

Round 1: All candidates who had no first place votes are eliminated, including Hammill. Round 2: Ford, Fisher, and Lucas are all eliminated because they are all tied.

Technically I guess Ford, Fisher, and Lucas are tied for first place and if I held this election I would probably have a run-off using only these three which would not be necessary if voters could vote for as many options as are allowed though that wouldn't work either because everyone would rank these all as their first choices again anyway.

IRL I don't think this is a problem, mainly because it is so unlikely that all candidates get eliminated and in a real scenario you probably have more people voting than are running. If it did by some miracle happen with a larger sample size I'd say probably have another election with a non-ranked system that isn't first past the post (because with these votes you have the same problem) but again it probably wouldn't happen.

• Note that the mention in Robert's Rules is just an example, not prescriptive. "Preferential voting has many variations. One method is described here by way of illustration" Apr 11, 2019 at 19:40

Seems like the rounds should be like this:

Round 1: 3 way tie. Harrison Ford, Carrie Fisher, George Lucas all eliminated.

Round 2: Mark Hammill wins with 3 votes.

If the voting is done with a stack of post-it notes like a RCV demo video I have seen, it works great.

• But that isn't how IRV works. It eliminates the bottom candidates, not the top. There are of course systems where Hamill wins, as he is the Condorcet winner. So any Condorcet-compliant system will have him winning. But any later-no-harm system will have him losing. Mar 2, 2018 at 0:21
• @Brythan, I've read many descriptions of IRV and to me it seems like this should be how it happens. IRV does eliminate bottom candidates, but by round. Least favorite candidate in the first round gets eliminated... This seems consistent with mutual majority condition, If the mutual majority like a candidate which does not appear in the first round, that should not matter. If an eliminated person comes back in the 3rd round I don't see why, logically, that would be a problem. Nov 5, 2020 at 13:11