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Median Rating voting system

I just read this Humanity+ article about Democracy+: Beyond Majoritarianism. It presented alternatives to simple majoritarian voting systems, most prominently the Borda count:

Basically when there are N candidates, voters must assign them N, N-1, N-2, … , 1 points in descending preference. The candidate with the most points wins.

It seems like the Borda count is not a bad preferential voting system, but I think the following one, which I call the Median Rating voting system:

There are N candidates. Every voter can, but doesn’t have to, rate each candidate with a score between 0 (worst) and 100 (best). They can also give the same score to different candidates in order to express their indifference between them. Ratings are normalized so that the highest rating is adjusted to count as 100 for the result. Alternatively, voters are required to rate at least one candidate with a score of 100. The candidate(s) with the highest median score(s) win.

How is the median score of a candidate calculated? List all the scores that the candidate has got like this:

100, 100, 100, 95, 90, 78 ,69 ,64, 57, 50, 46, 45, 43, 38, 35, 33, 31, 27, 27, 23, 14

Count the number of votes for that candidate. In the example it’s 21. The median is the value in the middle, the “10.5th” value. Because there is no actual “10.5th” value the average of the 10th and 11th values is taken, which is 48 in this example.

The Median Borda Method makes voting easier for the voters (they can abstain from voting on candidates they don’t feel confident judging and they can quantify their preference to some degree), while it makes it a bit more difficult to compute the results. The scores are higher in order to reduce the probability of draws occurring and to make the expression of preferences more fine grained, especially when the number of candidates is low.

For example there are three candidates A, B, C and 5 voters which vote like this for A, B, C respectively:
100, 100, 0
80, 100, 25
10, 60, 100
100, 5, 70
10, 50, 100

Median: 80, 60, 70
Sum: 300, 315, 295

Candidate A has won due to his high score from voter 2, even though candidate B has a higher sum of points. In order words: He has won, because he’s the best second best option. Note than all three candidates get the maximum of 100 points from 2 voters, because voter 1 is indifferent between A and B, so there is no clearly best first choice candidate. Every voter has clear favourites and a candidate that he really doesn’t like. But all those extreme votes play no role for the median which only really depends on the moderate ratings, which represent more or less the quality of the “best second best option”.

I think this is a pretty good voting system in general, because it nudges people to really think about the quality of each option and how good or bad it would really be. Neither fanatic love nor hate can sway the outcome too much, unless it’s a true majority is fanatically in love with its favourite.

It would be cool to have plug-in for this forum for this kind of voting mechanism. There would be some interesting advantages to it:

  • Removing and adding options during the vote wouldn’t be catastrophic. It would still be a valid vote.
  • People could give more detailed feedback than within a simple poll.

Anyway, I propose that we use this voting system for serious stuff even if it isn’t properly implemented in software. After all, people still can vote openly manually. And this system would provoke more interesting discussions, I suppose.

I am not too knowledgeable in statistics, but thinking about this, I am worried that it is too dependent on moderate ratings. As in, imagine two candidate A and B with scores 100, 100, 100, 100, 70, 70, 60, 40, 40; while another one has 90, 80, 80, 80, 80, 60, 20, 5, 0. These scores can come from a population where everyone except one person preferred candidate A, but B has still won due to a single vote that happens to be the median.

As I said, I haven’t analyzed this properly, and it may be that this situation is not very likely, but still, I would prefer it to not be possible at all.

Yes, this looks like a rather contrived example, but I think the objection is valid nevertheless. This may be resolved by using the sum of middle “quartiles”: Instead of only taking the value in the absolute middle, also take those in the middle of upper and lower halves. With 9 votes that would be the 3rd, 5th and 7th values.

For candidate A: 100 + 70 + 60 = 230
For candidate B: 80 + 80 + 20 = 180

This method is more complicated, but has the advantage that no single voter will effectively determine the outcome of the election.