Exhausted Ballots

Another common criticism of RCV is how it handles ballots that do not include preferences for all candidates.

For example, suppose a group is planning a vacation and asks everyone to rank their preferred destinations. You might list your top choices without bothering to rank every place you would be willing to visit. You may have preferences beyond your top choices, or you may be indifferent. For example, you might list Playa del Carmen as your preferred destination but leave Cancun and Hawaii unranked. You have expressed a preference for Playa del Carmen, but no preference between Cancun and Hawaii.

Ranked ballots work the same way. If a ballot does not express a preference between the remaining candidates, there is no information about which candidate the voter would prefer. How unranked candidates are handled depends on the voting method. In Instant Runoff Voting, a ballot becomes exhausted when none of its ranked candidates remain in the race. This effect can be seen in the following example.

Returning to the wilderness example, suppose there is one Forester candidate (the Bear) and two Feline candidates (the Tiger and the Cheetah).

The Foresters make it clear they prefer the Bear, but express no preference between the Tiger and the Cheetah. The Jungle Group makes it clear they prefer the Tiger, and list the Cheetah second because they do not like the Bear. The Plains Group only votes for the Cheetah and provides no information about whether they have any preference between the Bear and the Tiger.

Instant Runoff Voting

Now, suppose Instant Runoff Voting (IRV) is used. We start by comparing the first-choice preferences:

The Cheetah with the fewest first-choice preferences is eliminated. The 25 ballots with the Cheetah ranked first do not rank either remaining candidate, so they do not continue. The process continues between the Bear and the Tiger:

And the Bear wins with a majority of the final votes, but not with a majority of the total votes. Members of the Feline community may be outraged by these results, because Feline candidates combined for more total votes than the Bear. They may call Ranked Choice Voting a partisan plot by Foresters to rig elections, and argue that the Felines as a whole were disenfranchised by having their ballots thrown in the garbage or set on fire.

It may be that the Plains Group did not fully understand the ballot. Or it may be that they simply chose not to express a preference between the Tiger and the Bear. It is impossible to know whether they would have shown up if the race had been only between the Tiger and the Bear, or if there had been a runoff election.

Critics of IRV would describe the Tiger as a spoiler candidate. If the Tiger had not run, the Jungle group indicated they would have supported the Cheetah over the Bear to reach their best achievable outcome. This gives the Felines an incentive not to run the Tiger, because doing so could cause the Bear to win instead of the Cheetah.

Head-to-Head Record

Now consider how the same example would play out using Head-to-Head Record. The results would be:

All three candidates would have the same head-to-head record, creating a preference cycle of Bear > Tiger > Cheetah > Bear. The winner would therefore depend on the cycle-resolution method. If first-choice preferences were used as the tiebreaker:

The Bear would win. But if worst loss differential were used as the tiebreaker:

With Head-to-Head and Worst Loss Differential cycle-resolution, the Tiger would win, while under Instant Runoff Voting or Head-to-Head with First-Choice Preferences cycle-resolution, the Jungle Group is incentivized not even to run the Tiger at all. Many would argue this is a strength of Worst Loss Differential as a cycle-resolution method.

Exhausted ballots are not the result of a mistake in counting, but of voters choosing not to express preferences among all of the candidates. This could be because voters are indifferent, or because they simply choose not to list them in their order of preference.