DefinitionA 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]
Example
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 |
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 (LNH), 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 in the last row, who preferred Z, cannot possibly cause Z to win by removing X or Y from their rankings. Their rankings for Y will only be counted if Z is eliminated. And their rankings for X will only be considered if Y is eliminated, and so on.
Tactical voting 101
Before treading into the implications of LNH, it's helpful to establish some basic principles of tactical voting, depending on whether we're using ranking, rating (aka scores), or approvals. The following chart contrasts honesty with generalized tactical behavior of "polarizing" the frontrunners. It is not comprehensive, but is meant to illustrate some things that newcomers to voting theory often overlook.
| Green | Democrat | Republican | Libertarian | |
| Honest Ranking | 1 | 2 | 3 | 4 |
| Tactical Ranking | 2 | 1 | 4 | 3 |
| Honest Score | 5 | 3 | 2 | 0 |
| Tactical Score | 5 | 5 | 0 | 0 |
| Honest Approval 1 | X | |||
| Honest Approval 2 | X | X | ||
| Honest Approval 3 | X | X | X | |
| Tactical Approval | X | X | ||
| Tactical Plurality | X |
Proponents of certain ranked voting systems may have some skepticism about the second row in particular. For instance, a supporter of Instant Runoff Voting (IRV) would probably object that she would rank her favorite candidate in first place regardless of viability, thinking that if her favorite didn't win, her vote would simply transfer to her second favorite in this case. We will now refute that.
Favorite betrayal
Despite what many believe, IRV can actually hurt you for supporting your favorite candidate. Here's a brief layman-friendly animated video explanation of this phenomenon, by Andy Jennings, a co-founder of the Center for Election Science who did his math PhD thesis on voting methods.
We can see the same effect in slow motion if we look again at the opening example where X wins. But this time, imagine the bottom-row voters insincerely rank Y (their second choice) in first place instead of their true favorite Z.
| % of voters | Their ranking |
| 36% | X > Y > Z |
| 29% | Y > X > Z |
| 35% | Y |
Now Y wins an outright 64% majority (second and third rows added together), which causes those tactical voters in the last row to get their second choice (Y) instead of their third choice (X). In other words, sincerely ranking Z as their favorite candidate hurts them.
Is this realistic?
Now maybe you think this is a contrived fluke scenario that couldn't possibly affect real life voter behavior. If so, note that mathematical analysis shows this "favorite betrayal" is a generally advisable strategy whenever your favorite appears unlikely to win with IRV. In a nutshell, unlikely candidates are by definition more likely to to be spoilers than winners (as Z above just demonstrated).
The science of voting systems includes numerous criteria aside from LNH. For instance, Score Voting and Approval Voting satisfy the Independence of Irrelevant Alternatives criterion, the monotonicity criterion criterion, and the Favorite Betrayal Criterion—all of which IRV fails. So why the focus on LNH?
LNH is generally regarded by proponents of IRV, who argue that it incentives voters to provide a complete and sincere ordering of the candidates rather than simply bullet voting for their favorite candidate. They contrast this with systems such as Score Voting and Approval Voting, where showing support for one's second choice can lead to the defeat of one's first choice, which they argue will lead to mass bullet voting. They often even go so far as to claim Score/Approval will thus degenerate into ordinary Plurality Voting in practice, leaving us right back where we started.
On the surface, these arguments seem to make some intuitive sense. But as we just saw, the situation is almost the complete opposite. The general strategy with any voting system is to push your favorite frontrunner to first place, and only consider less viable candidates as an afterthought. With a ranked system that doesn't allow equal rankings, such as IRV, that means you cannot rank your true favorite in first place if she isn't a frontrunner. Thus you get a strategic behavior that is very similar to the choose-one Plurality Voting system we already have, aka First-past-the-post. This is what voting theorists mean when they say that IRV fails the Favorite Betrayal Criterion (FBC).
But with Score Voting or Approval Voting, which pass the FBC, you have absolutely no reason to abandon your true favorite. As we showed in our voting strategy table at the top, the Green Party voter who gives the more electable Democrat a strategic top score cannot possibly be harmed by also giving a max score to her sincere favorite Green Party candidate. It is this behavior that makes Score Voting and Approval Voting so resistant to the negative impact of tactical voting, even though this is precisely the opposite of what initial intuition often leads us to believe.
And that also counters the frequent claim that Score Voting and Approval Voting would degenerate right back into what we already have. One need only look at the last two rows of our tactical voting table to see the drastic difference between the tactical Approval Voting ballot, which approves two candidates, and the tactical Plurality Voting ballot, which "approves" only one.
Misleading naming
LNH is misleading because it's about ranking additional candidates after you've already decided to start with your sincere favorite. But as these examples have just shown, you may not want to rank your favorite candidate first to begin with. But it's even worse than that. Chances are you took IRV's passage of Later-no-harm to mean that it's at least safe to rank additional candidates given you've already taken the plunge at started out with a sincere ordering. But that's also wrong! Here's a simple example (meant to be easy to understand, not 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. That means the two voters in the first row get their last choice.
But if they only rank W (or if they stay home and don't even vote at all), then Y has a 7-to-5 victory against Z. So those two voters get their third favorite instead of their least/fourth favorite. In other words, sincerely ranking additional candidates after W hurt them (see those additional candidates X and Y in the first row, highlighted with lighter bolded text).
How did this happen? What happened to LNH? Simple. Later-no-harm is a misleading name. Your later rankings can't harm your earlier rankings—but they can harm you, the voter! And of course that is what matters most. After all, we just discussed how voters are generally perfectly happy to harm their favorite candidate if it benefits them personally. Again, the cliche is Green Party supporters voting Democrat when they're worried about getting a Republican, but there are many other examples.
Ignoring your opinions
Hopefully by now you've come to see the weakness with Later-no-harm as a quality measure. But there's an even deeper dimension that has nothing to do with strategy. Simply put, obeying LNH forces a voting system to ignore a great deal of voter preference information. Imagine preferences like these:
35% LRC
34% RCL
16% CLR
15% CRL
C is eliminated first with 31%, and L wins with 51%.
But suppose just 2%, from the CLR faction, swap their LR preference (a sincere change of preference, not a strategy), creating:
35% LRC
34% RCL
14% CLR
17% CRL
C is still eliminated, but now R wins with 51%.
A tiny change in preferences changes the winner from L to R.
But now suppose a huge change in preferences occurs going the other way. The LRC voters (first row) find out something terrible about R, causing them to lower R to 2rd place. And the RCL voters (second row) find out something super positive about L, causing them to elevate L to 2nd place.
35% LCR
34% RLC
14% CLR
17% CRL
This massive shift in public opinion is positive for L and harmful for R. But that doesn't change the winner back from R to L, even though a tiny change of preferences moved the winner from L to R in the first place. This is because satisfying Later-no-harm means a system simply cannot acknowledge any change in preference between two candidates, X and Y, until their order swaps. Only that tiny boundary-crossing change can be detected, and any movement before or after it goes completely unregistered.
Thus IRV essentially lies to voters. It gives them a fairly expressive ranked ballot, promising them that it will dutifully respect their wishes. And then it simply discards a great deal of the voters' expressed intentions.