Best algorithm for a photo/art contest?

February 14, 2022 2:23 PM

We have about 70 entries and between 3 and 5 judges. We want to have a 1st through 5th place winners. What form of ranked choice voting would be best? I'm looking for an algorithm to implement.

One scenario with 4 judges:
Pictures A, B, C and D gets 1 first place vote and no others, Picture E gets 2 second place votes and no others, Picture F gets 4 third place votes

If 1st place is 5 points, 2nd is 4 points, 3rd is 3 points, 4th is 2 points and 5th is 1 point then:

Picture F is in 1st place with 12 points, Picture E is second with 8 points, and ABCD are tied with 5 points each.
What could be done to break ties without a second vote?
I'd be happy with a totally different way to count votes, and links to sites with descriptions.

posted by Sophont to Law & Government (7 answers total)

This might be too arduous, but could you start with getting each judge to score the entries (say out of 100), then convert each score to a rank and apply a standard ranked choice voting method. In the case of ties, you could resolve these by going back to the original scores. (I must confess I haven't thought this through in detail).
posted by piyushnz at 3:04 PM on February 14, 2022

Response by poster: I'm looking for a method that will give me the top 5 places, in order, and not just a single winner.
posted by Sophont at 4:13 PM on February 14, 2022

Best answer: I think you could get all 5 places by repeating the ranking 5 times and throwing out the winner after each iteration.
posted by piyushnz at 4:29 PM on February 14, 2022 [1 favorite]

Multi-winner ranked choice voting is complicated. It comes in two varieties. The first variety is essentially single-winner rank choice voting repeated over and over. This is simpler to understand, but it allows a majority bloc to win all the seats in a multi-seat election. If the Purple Party has 52% of the vote, they will win all the seats. The Yellow Party, with 48% of the vote would get no seats. Proportional multi-winner rank choice voting attempts to address this by de-weighting the value of a ballot after one of its candidates has secured a seat. In the previous scenario, if there were two seats available, one would go to Purple and one to Yellow.

I apologize for not explaining the algorithms more fully. I don't have them recorded to memory and don't have time to re-research them.

The problem is that, unfortunately, neither of these approaches works for your scenario. No form of ranked choice voting I'm aware of ends up with ranked winners. Ranked choice voting gives you winners and losers. It doesn't give you "first place", "second place", "third place", etc. I'm not familiar with a system that does that using a ranked choice algorithm.

Sorry if this is not helpful. Perhaps someone who is deeper into the algorithms of rank choice voting will be able to offer a simple suggestion.
posted by Winnie the Proust at 5:10 PM on February 14, 2022 [1 favorite]

Judges get a certain number of tokens. Each judge gets a different color of token. Judges are free to "spend" their tokens on whatever artwork they think is best... they may allocate multiple tokens or none to a given artwork. The artwork with the most tokens gets first place, the artwork with the second most amount of tokens gets second and so on. Ties are broken by number of judges who voted for that artwork.
posted by oceano at 5:59 PM on February 14, 2022 [2 favorites]

Seconding oceano. I think you don't have enough judges but like sports judging you would get seven judges and throw out the highest and lowest scores. That's a lot of pictures and I'd make them put something on each one, full ranking, maybe just one (which would be the same as none) and sorta "you're art sucks so much that nobody would even" sort of way...

Colored sharpies and a few rolls of pennies? Colored paper and paper cutter to make fake money? Go buy a set (or few) from the local dollar store of fake play money, have the judges try to buy everything they can get for their monies? The rest would be sorting.
posted by zengargoyle at 10:46 AM on February 15, 2022

I think an initial round of culling would help you. Do a first pass where every judge just votes to move it to the next stage or not. Any photo that doesn't get a single yes is out.
posted by Threeve at 5:48 PM on February 15, 2022