Correct, I meant rate. My strategy isn't about strategic voting, it's how to represent the actual preferences of voters when all you have is approve/not approve.
You assume most people will vote at random? That is a completely uninteresting case that does not happen in reality.
People tend to approve of candidates they know of. Likewise they tend to not approve candidates they do not know of or they dislike for any number of reasons.
So these marks are not drawn from random distribution at all.
Absolutely not. I'm saying that if in an election using approval voting people carried out my strategy that overall happiness with the results would be higher than if people voted according to the 'normal' instructions. Purely hypothetical, but to me illustrates the point that approval voting destroys valuable information about voter preferences because voters will turn out happier if they encode those preferences in their vote.
That doesn't make sense. Your ballot can NEVER express your actual preferences except in a statistical sense—we can have some probability distribution for the actual preferences that created that Approval ballot.
Thus using the standard strategy I mentioned is the most accurate way to convey your preferences. If you want them to appear as honest as possible, you just treat all candidates as equally likely to win, such that the formula simplifies down to your approval threshold being "average utility of all candidates".
If you're truly on the line about approving of a candidate then it's exactly the same quandary as being on the line between two candidates in a plurality decided election.
There's literally no difference. It's up to you to make your choice.
In my hypothetical, I'm not on the line about approving of the middle candidate. I disapprove of them strongly... but I also vastly prefer them to Satan. If Satan and the middle candidate are the only ones with a shot at winning then I absolutely want to vote for the middle one. If the third candidate can win then I don't want to vote for the middle one. If I'm not sure who's viable then I need to figure it out and hope I get it right.
It's much simpler in a plurality system. First, I decide if I want to make a statement or a difference. If I want to make a statement, I vote for the candidate I like best and that's it. If I want to make a difference, I choose the candidate I prefer from the two major parties. In the unlikely event that I like them both equally, I can either keep looking until I find a reason to prefer one, or I can abstain knowing that either one is equally good (or bad). Note, I'm not saying this is good, just that it's simple.
I'm saying that asking that question "should I approve of this candidate" is just as intractable as "who should I vote for" when you're on the line between two candidates.
The problem with instant runoff voting is that you can actually be harming your preferred candidate by ranking them ahead of the middle candidate.
I meant “close” in terms of preference. If you rate both of them 5/7, for example, then it’s hard to choose which one to vote for, but it’s also unimportant.
By that logic first past the post is ranked choice across the population.
The whole point of alternative vote systems is to be able to both designate your preferred candidate while also being able to specify your tertiary preferences so you can both vote for who you want to win while also not sabotaging your ability to vote against those you don't want to win.
But expressing your preferences doesn't actually accomplish anything useful.
You can do it, but what does it get you?
Instant runoff is not monotonic: there are times when the best strategy is to vote your favored candidate second and your second choice first so that the second choice can push out your least favored candidate.
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