Later-no-harm Criterion

Definition

A voting method satisfies the Later-no-harm Criterion if a voter cannot cause a more preferred candidate to lose by giving an additional ranking or positive rating to a less preferred candidate.

[Source]

Examples

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
 
Example 1

If this election were held using Instant Runoff Voting, 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 could be helped by the removal of a less preferred candidate. For instance, the 35% of voters who preferred Z (last row, bolded 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.

Misleading naming

One might take this to mean that it’s safe to rank as many choices as possible. But that’s wrong! Here’s a simple example (meant to be easy to understand, not to be realistic).
# of voters
Their ranking
2 W > X > Y
3 X > Y
4 Y > Z
5 Z
The winner of this IRV election 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). 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 the voter can hurt himself by doing so.
 
This begs the question, of what value is the Later-no-harm Criterion? It is our view that it is of little value, or even negative value.
 

Significance to comparative analysis of voting systems

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 LNH. Specifically, they argue that voters will nearly all bullet vote, causing these systems to degenerate into ordinary Plurality Voting.

Our response

There are obvious cases in which Score Voting and Approval Voting do not encourage bullet voting behavior. For instance, if you prefer the Green over the Democrat over the Republican, your best bet is probably going to be to vote for the Green and the Democrat. It would be irrational to worry that voting for the Democrat might cause the Democrat to defeat the Green. Your bigger concern is that not voting for the Democrat could cause the Republican to win. We explore this issue in much greater detail, including data from real elections and exit polls here. (Plot spoiler: bullet voting is a bigger problem for IRV than it is for Score Voting or Approval Voting.) 

We already discussed why the Later-no-harm Criterion has a very misleading name. But it’s actually even worse. If you look back to Example 1, you’ll see that the bottom row of voters could have gotten Y instead of X if some of them had tactically ranked Y ahead of Z. In that case, it wouldn’t matter that they couldn’t harm Z by also ranking Y and X further down the list. Their real problem is that they are harmed by ranking Z in first place. We explore this incentive for tactical voting in much greater detail here.
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