logoalt Hacker News

AnthonyMousetoday at 2:49 AM1 replyview on HN

No, to begin with the people who want to play stupid games would give the highest score to every candidate they approve of and the lowest score to everyone else, and then it devolves to approval voting, which is significantly better than FPTP -- and IRV.

And even doing that is people being too clever by half.

Imagine there are three candidates. The one you prefer is polling at a score of 6/10, another that you like almost as much is also polling at 6/10 and a third that you very much don't like is polling at 4/10. If you were voting honestly you'd give the first candidate 10/10, the second 8/10 and the third 1/10. So what should you do if you're voting strategically?

If you do the one that devolves to approval voting you give the first two candidates 10/10. But that's pretty dumb, the third candidate was just barely in the race and all you're doing then is screwing yourself by giving your second choice a better chance against your first choice.

If you do the one that devolves to FPTP you're really screwing yourself, because then you're putting the third candidate, which you hate, back in the running by tanking the chances of the second candidate that you were pretty okay with. You're making it so if your first choice doesn't win you get your third choice, which is bad for you, because the amount you wanted the first to win over the second is much smaller than the amount you wanted the second to win over the third but then you foolishly failed to express that even though the voting system allowed you to.

You can find some "proofs" that giving every candidate either a 1/10 or 10/10 is the optimal strategy, but the thing those proofs take as an assumption is that you know exactly how everyone else is going to vote, i.e. you have perfectly 100% accurate infallible polls. Which, of course, you don't.

And then think about what you have to do with that second candidate you'd like to give 8/10: Under that logic you're "required" to either give them 10/10 or 1/10. But you can't be sure if giving the second candidate a 1/10 will cause the first candidate to win or the third. Without knowing that, you can't know which one is actually better for you.

At which point the optimal strategy is to hedge by picking a number in the middle, and choose which one in proportion to how strongly you feel about each risk. But that's the same as voting according to your actual preferences! You end up giving the second candidate 8/10 because that's the measure of how much more you prefer that they defeat the third candidate than that they don't defeat the first.

The only real strategic choice here is to put some consideration of the polling into the weighting. If Hitler is on the ballot then you're definitely giving him the lowest score, but if he's only polling at 2/10 and you're pretty sure he's not going to win, you might want to give someone else you only moderately disfavor a 3/10 rather than 5/10 because you're not that worried about the probability of Hitler defeating them even if you're very worried about the consequences if it happened. But you still don't want to give them the same score as you give Hitler because you still want to hedge at least a little bit against even a small chance of something that bad.


Replies

galangalalgoltoday at 2:56 AM

Interesting, and what are your thoughts on the star variant? Also what is so bad about irv?

show 1 reply