Failing Later-No-Harm doesn't mean cardinal systems suck


FairVote’s biggest issue with Approval Voting appears to be what they see as a vulnerability to bullet-voting, brought on by LNH failures. They use examples of bullet-voting in their articles (and I’d love to see your refutations!) to show how, with extremists running, a few naive moderate voters get the system repealed.

I think the key to understanding why this isn’t an issue in most high-stakes elections is to realize that cardinal systems don’t require voters to approve multiple candidates to work well. Yes, you heard me right. I think the biggest benefit in cardinal systems is that they give the voters total leverage over the candidates; no longer can one hog the nomination of an entire party and chain all that party’s voters to picking them; instead, just the simple threat of being able to switch to another candidate while also backing the old frontrunner does the trick. In fact, I suspect a great deal of bullet-voting will happen, for the simple reason that a voter doesn’t care enough to express their support for nonviable candidates. By changing the frontrunners and atmosphere, you already are eliminating the need to vote for more than one or two candidates as well. That’s the greatest thing cardinal systems have to offer.


The later-no-harm criterion is normally defined like “A voter giving an additional ranking or positive rating to a less-preferred candidate cannot cause a more-preferred candidate to lose.”
An equivalent statement would be “A voter giving an additional ranking or positive rating to a less-preferred candidate cannot cause a more generally appealing compromise candidate to win instead of the voters most preferred”

It is all in the phrasing. Also the name should be like “non-compramising” since it is a question of if the system allows for compromise or not. Compromise is good and later-no-harm is a worthless criteria. FairVote just tries to word it in a way that makes it seem otherwise.


Compromising is good, but it can’t come at the cost of what the voter wants and could’ve gotten. ^(the only reason I think it’s okay that cardinal systems fail LNH is that the only time they do in high-stakes elections is when voters hate a candidate so much they approve a bunch of others, where it doesn’t matter as much.)


Compromising is defined to come at the cost of what the voter wants and could’ve gotten. Each individual always wants their preferred candidate the most and could get it in a system where they had undue power. The question is not what each individual wants but what satisfies the wants to everybody the best. That is essentially the definition of Bayesian regret or average score


I agree, but the test a voting system has to pass is whether it makes all attempts at strategic voting less worth it than honest voting. The key to doing that imo is to, in most situations, have voters get what they want if they’re part of a strong majority, but otherwise have them compromise to better assure getting what they want. ^(It’s about probability, I think)


My arguments:

  1. What use is being able to honestly score your second choice, if you cannot always honestly score your first choice? With RCV, voting for your true favorite first can cause that favorite AND your second choice to lose.
  2. Under Approval Voting, voters will want to approve all but their absolute worst choice, so that that worst-case scenario does not happen. If they decided to disapprove additional candidates, that might cause the worst case to lose. - The entire “bullet voting” argument turned on its head. Both arguments are equally valid, but clearly, it cannot both be optimal to approve 1 candidate and approve N-1 candidates; the voter has to decide on a case-by-case basis.
  3. (similar to 2) You say that people may bullet vote, because voting for 1 and 2 can cause 2 to defeat 1. But by similar logic, one could argue that you should vote for 1 and 2 because otherwise 3 may beat 2. Ultimately, each voter will have to decide which of the N-1 defeats is most likely and most damaging, and vote accordingly.
  4. Bullet Voting in Approval may be a reasonable strategy for naive voters. But in Score Voting (say, 0-9 or 0-10) the voter has more options. For example, the second choice may be rated a 6 or 7, so that the favorite gets more support but the second also gets some boost. You might rate a third choice 3, 4, or 5. The point is, you have options to express your opinions. My honest ratings may be 10, 9, 7, 5, 4, 0. Yours of the same candidates may be 10, 6, 3, 1, 0, 0. Under IRV, both of us would (if we were honest) have to cast the same ballot. With Score, we could more accurately express our preferences.

Now I just have to remind myself this is not an IRV propagandist forum…


Is Score so much better than Approval in the long run? I think both systems converge to electing moderates; Score offers slightly more precision, but it could also backfire with people not scoring correctly. Ultimately, I think both systems are on equal footing, so I’m curious whether Score has any advantages over Approval.


Score is unbiased in the limit of large number of possible score and honest voters. Approval is always biased to moderates.


How is Score not equally biased to moderates? It still requires voters to support moderates somehow to get the most out of their vote.


The question is “biased relative to what”. When people talk about polarizing or moderate biased they are referring to the utility maximizing choice. Score for honest voters is a direct measure of utility and the average would find the optimal candidate. The granularity of score causes a rounding effect. With an infinite number of scores to choose from you could perfectly express your preference (in theory). As the number of options is reduced to 10 there is a bias introduced due to the rounding/quantization. With 10 options it is generally assumed that there is not significant loss in ability to express preference. When you go to score with only two options (ie Approval) it should be clear that the effect is significant. So maybe it is technically better to say score is insignificantly biased to moderates but approval is significantly biased to moderates.


Your last sentence doesn’t make sense? Maybe you meant score is less biased to moderates than Approval? Under any amount of strategic voting and candidates leaving the race, I think both Score and Approval start electing almost the exact same kind of candidates over time. They would tend towards one moderate, rather than two extremists.


Edited. Yea that was a typo.