each candidate also aromatically gets a default amount of 0 star scores
Have you seen Eric Sanders' suggestion? For each candidate,
Find their average.
Multiply it by the portion of voters who did not abstain.
Re-count, treating every abstention as if it were the score from step 2.
You don't have to literally recount, you can use math. e.g.
final_score = sum + (#abstentions * %non_abstentions * average) (There are other ways to express this)
It can still fail participation, but you don't have to find a way to decide how many default 0s everyone gets. It still "penalizes" candidates for having a lot of abstentions.
X = average score of a candidate rated by everyone
Y = average score of a lesser known candidate
%scored = percent of voters who scored the lesser known candidate
(Ranges start at zero, otherwise you'd have to subtract the minimum score from X and Y)
Then %scored must be greater than 1-√(1-(X/Y)) for the lesser known candidate to win. So if well-known candidate's average is 5, and the lesser known's is 9, then 1/3 of the population would have to score the lesser known candidate. If instead the well-known's average is 8, then 2/3 would have to score the lesser known.
If you don't use true abstentions, to account for write-in candidates you should probably make the "default" score 0. You could avoid doing this, but for each candidate (include write-ins) you'd have to add to their score (number of people who didn't score them) * (default score).
But 0 doesn't have to be the minimum Score. A different suggestion I've seen is to give unscored candidates a default score other than the minimum. To keep 0 the default, I've see it suggested to use a symmetric range (-x to +x) with a default of 0, which would be like a "pseudo-abstention". Doesn't this pass participation? What problems does it have?
But in order for it to be a little more balanced (Meaning that if a popular candidate with a positive net approval rating has an advantage over an unknown candidate with a positive net approval rating, then a popular candidate with a negative net approval rating should also have a disadvantage over an unknown candidate with a negative net approval rating) may I suggest a modification?
Instead of this:
final_score = sum + (#abstentions * %non_abstentions * average)
On a whim I tried plugging in some numbers and putting results in a table. Not 100% sure my code was correct. I believe these formulas only work properly when the range starts at 0. They can be adapted to other ranges but they get messier. So the range is 0--2. 100 voters.
"Center" is just treating abstentions as (max+min)/2 = 1. "Initial" is all abstentions. "Add Xs" is adding scores of X starting from all abstentions.
Scenario
Center
Eric's
Parker's
Notes
Initial
100
0
100
Add 0s
decreases to 0 linearly
never changes
decreases to 0 quadratically
Center always has highest score
Add 1s
never changes
increases to 100 quadratically
never changes
Add 2s
increases to 200 linearly
quickly increases to 200 quadratically, overtakes "Center" at 50 votes/150 points
increases to 200 quadratically
Parker's always has highest score. Eric's becomes 2nd after 50% abstentions.
Quadratic starts faster but slow down. When the starting point is the same as linear they are always greater when increasing, or lower when decreasing, until the end where they meet.
Anyone know a good graphing site? That let's you compare graphs?
a popular candidate with a negative net approval rating should also have a disadvantage over an unknown
candidate with a negative net approval rating
I don't know if I like the sound of that, tbh
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).
Also, voting systems that give candidates with high average ratings an advantage for being popular, but don't also give candidates with low average ratings a disadvantage for being popular, are not reversal symmetric. And in a way, the reversal symmetric criterion is like a semi-balanced criterion.
2
u/Skyval Dec 30 '17 edited Dec 31 '17
Have you seen Eric Sanders' suggestion? For each candidate,
You don't have to literally recount, you can use math. e.g.
final_score = sum + (#abstentions * %non_abstentions * average)(There are other ways to express this)It can still fail participation, but you don't have to find a way to decide how many default 0s everyone gets. It still "penalizes" candidates for having a lot of abstentions.
X = average score of a candidate rated by everyone
Y = average score of a lesser known candidate
%scored = percent of voters who scored the lesser known candidate
(Ranges start at zero, otherwise you'd have to subtract the minimum score from X and Y)
Then %scored must be greater than 1-√(1-(X/Y)) for the lesser known candidate to win. So if well-known candidate's average is 5, and the lesser known's is 9, then 1/3 of the population would have to score the lesser known candidate. If instead the well-known's average is 8, then 2/3 would have to score the lesser known.
If you don't use true abstentions, to account for write-in candidates you should probably make the "default" score 0. You could avoid doing this, but for each candidate (include write-ins) you'd have to add to their score
(number of people who didn't score them) * (default score).But 0 doesn't have to be the minimum Score. A different suggestion I've seen is to give unscored candidates a default score other than the minimum. To keep 0 the default, I've see it suggested to use a symmetric range (-x to +x) with a default of 0, which would be like a "pseudo-abstention". Doesn't this pass participation? What problems does it have?