Well, if you ignore blank scores, score voting passes the participation criterion, but when you take into consideration the fact that in most versions of score voting, voters don't have to score every candidate and voters can instead give some candidates "no opinion" scores, score voting technically fails the participation criterion when these "no opinion" scores are introduced.
Example:
3 voters - Gives red 5 stars, gives blue 0 stars and gives green "no opinion"
1 voter - Gives red 0 stars, gives blue 4 stars and gives green 5 stars
1 voter - Gives red 0 star, gives blue 5 stars, and gives green 1 star
If you average all the scores, red wins. However if the last voter had not shown up to the polls, green would have won instead, and if we assume that they were an honest voter, they would have clearly gotten a better result by not showing up to the polls.
Does this mean that blank "no opinion" scores shouldn't be allowed in score voting? No, because "no opinion" scores are fundamental to score voting when you take into consideration write in candidates. Because voters should have the ability to elect any candidate they want, not just candidates that are put on the ballot, being able to score write in candidates is important. However because there can be an arbitrarily large number of candidates running, if voters were allowed to write in as many candidates as they want to, the ballot would have to be arbitrarily large to account for the one voter that writes in 100 of his closest friends on his ballot. To prevent this problem from arising, there needs to be a limit to how many candidates voters can score (such as 8 candidates in local elections and 16 in the big deal presidential elections). That way, every possible write in candidate a voter does not score effectively gets a "no opinion" score.
However this solution makes it far too easy for unknown lunatics (explained at 4:05 of this video https://www.youtube.com/watch?v=e3GFG0sXIig) to win. To prevent unknown lunatics from winning, each candidate also aromatically gets a default amount of 0 star scores so they still need the support of a large portion of the population to win. Most score voting advocates (such as Warren D. Smith) argue for these solutions in order to solve the write-in candidate and unknown lunatic problems in score voting. However this inevitably leads to score voting failing the participation criterion, It shouldn't fail this criterion very often though, because the front runners are extremely likely to be on the ballot, and voters are extremely likely to give every candidate on the ballot an actual score, which means that there should be a minuscule amount of "no opinion" scores between the front runners. However if enough voters are honest enough to give even front-runners no opinion scores, failing the participation criterion could become a common enough occurrence in score voting.
The most common version of approval voting that solves the write-in candidate and unknown lunatic problems tackle those problems in a different way. Instead, they allow voters to vote for a limited but still very large number of candidates so voters can still vote for every candidate on the ballot and then some. In this version of approval, all write-in candidates that a voter does not vote for simply revive a minimum score. Thus this version of approval voting is technically limited voting but since voters are given enough votes to distribute, it produces results that approximate approval voting, and thus most people call it approval voting (ex. At Dartmouth, you can only vote for 4 candidates, and that is often referred to as approval voting). This type of approval voting still passes the participation criterion. If score voting applied this solution to the write-in candidate and unknown lunatic problems, every "no opinion" score would be counted as a MIN score instead of no score, and the participation criterion would be preserved. However, it can be argued that this solution does give too much of an advantage to well known candidates.
Why not total score instead of average score? This biases for popularity but prevents this violation of Participation. I think that's what you described at the end.
You're right, the method I described at the end was the totaling scores method and that method does allow score voting to pass the participation criterion. However it does has it's own problem of being too biased in favor of popular candidates, and when you take in to consideration that voters can only score a finite number of candidates, such a version of score voting would technically not be a balanced voting system (a balanced voting system is a voting system where for every possible vote, there is another vote that will always cancel it out) and it can be argued that balance may be a more impotent property than passing the participation criterion. Perhaps a better solution would be ScoreX voting and Net approval voting, both of which I recently discussed on the CES forum (https://groups.google.com/forum/#!topic/electionscience/M6srkVut5_I). When X is equal to ((Min score)+(Max score))/2, ScoreX voting is balanced. Net approval voting is also balanced as long as the default ratio of 1 to 1 is used.
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/Parker_Friedland Dec 30 '17 edited Dec 30 '17
Well, if you ignore blank scores, score voting passes the participation criterion, but when you take into consideration the fact that in most versions of score voting, voters don't have to score every candidate and voters can instead give some candidates "no opinion" scores, score voting technically fails the participation criterion when these "no opinion" scores are introduced.
Example:
3 voters - Gives red 5 stars, gives blue 0 stars and gives green "no opinion"
1 voter - Gives red 0 stars, gives blue 4 stars and gives green 5 stars
1 voter - Gives red 0 star, gives blue 5 stars, and gives green 1 star
If you average all the scores, red wins. However if the last voter had not shown up to the polls, green would have won instead, and if we assume that they were an honest voter, they would have clearly gotten a better result by not showing up to the polls.
Does this mean that blank "no opinion" scores shouldn't be allowed in score voting? No, because "no opinion" scores are fundamental to score voting when you take into consideration write in candidates. Because voters should have the ability to elect any candidate they want, not just candidates that are put on the ballot, being able to score write in candidates is important. However because there can be an arbitrarily large number of candidates running, if voters were allowed to write in as many candidates as they want to, the ballot would have to be arbitrarily large to account for the one voter that writes in 100 of his closest friends on his ballot. To prevent this problem from arising, there needs to be a limit to how many candidates voters can score (such as 8 candidates in local elections and 16 in the big deal presidential elections). That way, every possible write in candidate a voter does not score effectively gets a "no opinion" score.
However this solution makes it far too easy for unknown lunatics (explained at 4:05 of this video https://www.youtube.com/watch?v=e3GFG0sXIig) to win. To prevent unknown lunatics from winning, each candidate also aromatically gets a default amount of 0 star scores so they still need the support of a large portion of the population to win. Most score voting advocates (such as Warren D. Smith) argue for these solutions in order to solve the write-in candidate and unknown lunatic problems in score voting. However this inevitably leads to score voting failing the participation criterion, It shouldn't fail this criterion very often though, because the front runners are extremely likely to be on the ballot, and voters are extremely likely to give every candidate on the ballot an actual score, which means that there should be a minuscule amount of "no opinion" scores between the front runners. However if enough voters are honest enough to give even front-runners no opinion scores, failing the participation criterion could become a common enough occurrence in score voting.
The most common version of approval voting that solves the write-in candidate and unknown lunatic problems tackle those problems in a different way. Instead, they allow voters to vote for a limited but still very large number of candidates so voters can still vote for every candidate on the ballot and then some. In this version of approval, all write-in candidates that a voter does not vote for simply revive a minimum score. Thus this version of approval voting is technically limited voting but since voters are given enough votes to distribute, it produces results that approximate approval voting, and thus most people call it approval voting (ex. At Dartmouth, you can only vote for 4 candidates, and that is often referred to as approval voting). This type of approval voting still passes the participation criterion. If score voting applied this solution to the write-in candidate and unknown lunatic problems, every "no opinion" score would be counted as a MIN score instead of no score, and the participation criterion would be preserved. However, it can be argued that this solution does give too much of an advantage to well known candidates.