Later-No-Harm Criterion

Consider the following preferences for a few groups of voters, with candidates labeled X to Z.

% of voters      Their ranking
36%                   X > Y > Z
29%                   Y > X > Z
35%                   Z > Y > X

This is an instant runoff voting election. Y gets eliminated with the least first-choice votes and gets its ballots transferred to X. The winner would be X, with 65% of the vote. Because IRV satisfies the later-no-harm criterion, there is no way that either of the losing candidates (Y or Z) could be helped by the removal of a less preferred candidate.

For instance, the 35% of voters who preferred Z (last row, highlighted text) cannot possibly cause Z to win by removing X or Y from their rankings, since those rankings for Y will only be considered if Z is eliminated. And their rankings for X would only be considered if Y was then eliminated, and so on. In a nutshell, Z’s supporters didn’t hurt Z by also ranking Y and X further down the list.

One might understandably take this to mean that it’s safe to rank as many choices as possible. But that would be wrong. Here’s a simple example (meant only for demonstration).

# of voters       Their ranking
2                        W > X > Y
3                        X > Y
4                        Y > Z
5                        Z

Again, this is an IRV election. W is eliminated, transfering its two votes to X, and then Y’s votes are transferred to Z. The winner is Z, with a 9-to-5 victory against X.

But if the first two voters only rank W (or if they don’t even vote at all), then Y (their 3rd choice) has a 7-to-5 victory against Z (their last choice). That is, X’s votes would go to Y, so Y would not have gotten eliminated.

So those two voters get a better result by limiting the number of candidates they rank. That is, sincerely ranking candidates after W hurt them.

It’s almost as though we need to have two different criteria: voter later-no-harm, and candidate later-no-harm. The “later-no-harm” criterion is actually the latter. IRV ensures that a voter can’t harm a candidate by ranking additional less preferred candidates further down the list. But voters can still hurt themselves by doing so.

This begs the question of whether the later-no-harm criterion actually has value. Also, passing this criterion says nothing about whether a method allows voters to support their favorite without harming their ballot.

When you have a voting method both allows expressions on multiple candidates and acknowledges all of a voter’s ballot simultaneously, passing the later-no-harm criterion is virtually impossible. As such, both approval voting and score voting do not pass this criterion.

Proponents of instant runoff voting commonly argue that satisfaction of later-no-harm means IRV will encourage voters to provide a full ranking of the candidates, rather than just “bullet voting” for their favorite candidate. Additionally, they criticize systems such as score voting and approval voting for not satisfying later-no-harm. Specifically, they argue that voters will nearly all bullet vote, causing these systems to degenerate into ordinary plurality voting. Yet, a closer analysis of bullet voting shows this not to be the case.