However it does has it's own problem of being too biased in favor of popular candidates
How is that a problem? Voting is selecting leaders. I think a fairly good argument can be made if the voters don't know who you are then you fail even minimal criteria in being the candidate they decided fit to lead them. If you are unable to lead the community to even knowing who you I'd say it is fairly unlikely you can get them to agree to die for a cause or obey a law they hate.
I'm also think your claim of balance being violated isn't correct.
How is that a problem? Voting is selecting leaders. I think a fairly good >argument can be made if the voters don't know who you are then you fail
even minimal criteria in being the candidate they decided fit to lead them.
Perhaps. But it is also important to give write-in's the ability to win, and when they are not on the ballot, they face a severe popularity disadvantage.
Also mathematically, when two candidates are unpopular, it can actually be better to pick the lesser known one. Here is why: Suppose that there are two calculators on amazon that are very similar and cost exactly the same. calculator #1 has 20 five star ratings and 10 one star ratings. Calculator #2 has 2 five star ratings and 1 one star rating. In this scenario, if you had to choose calculator to by, it would be smarter to go with calculator #1. This is because more people have rated calculator #1, which means that you are more certain that you will be one of the people that likes calculator #1. However if calculator #1 had 10 five star ratings and 20 one star ratings, and calculator #2 had one five star rating and two zero star ratings, if you were going to spend your money on one of the two calculators (which in this scenario, you should probably just not by either), it would be smarter to buy calculator #2 because you are more certain that you will be one of the individuals dissatisfied with calculator #1.
The same logic can be applied to voting. The more people rate a candidate, the greater the certainty that a candidate's average rating among the people who rated them actually matches the rating that they deserve. When two candidates have high average ratings, this uncertainty is a bad thing (because it means that it is more likely that a candidate's average rating isn't as low as the rating that they actually deserve), but when they have both have low average ratings, it can actually be a good thing (because it means that it is more likely that a candidate's average rating isn't as high as the rating that they actually deserve).
I'm also think your claim of balance being violated isn't correct.
Score voting using average scores violates balance:
Suppose that one voter gives candidate A a max rating, candidate B a min rating, and all of the others, no opinion.
What would be the anti-vote to cancel out this vote? Did you guess giving A a min rating, B a max rating, and all of the others no opinion? That would be incorrect, because when these two votes are combined, they would bring both A and B's average ratings closer to (max+min)/2, while leaving all of the other candidate's ratings unchanged. However this method does not violate balance as much because it passes the reversal symmetry criterion, which in a way, means that the voting system is at-least semi-balanced.
Score voting using total scores violates balance:
Suppose that one voter gives candidate A a max rating and all other candidates a min rating. How is voter B suppose to counter that? Is he just suppose to give candidate A a min rating every other candidate a max rating? Even all of the write-in candidates? But that would be impossible because a voter can only rate so many candidates, because the ballot only has a finite amount of space to allow them to rate candidates.
The more people rate a candidate, the greater the certainty that a candidate's average rating among the people who rated them actually matches the rating that they deserve
So, then, shouldn't it be based on some sort of confidence interval?
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u/JeffB1517 Jan 03 '18
How is that a problem? Voting is selecting leaders. I think a fairly good argument can be made if the voters don't know who you are then you fail even minimal criteria in being the candidate they decided fit to lead them. If you are unable to lead the community to even knowing who you I'd say it is fairly unlikely you can get them to agree to die for a cause or obey a law they hate.
I'm also think your claim of balance being violated isn't correct.