…and I have no idea what its properties are and whether it’s a good idea.
I was wondering how you might extend random ballot to multi-winner elections. Specifically the case where you have C candidates and you want to elect N of them. The following is the system I hit upon:
Voters provide a list of candidates they would like elected, in order of preference for how strongly they would like them to be elected. They do not have to rank all the candidates, though strategically I think it’s advantageous to rank the full candidate list.
We now run the following algorithm:
While we have elected fewer than N candidates, iterate the following procedure:
- Remove all votes including only candidates that have already been elected.
- If we have no votes left, something has gone terribly wrong and we can’t actually elect enough candidates.
- Now pick a random voter.
- Add the voter’s highest ranked preference who has not yet been elected to the list of elected candidates.
Note that the sampling is with replacement: We do not remove a voter when we pick their vote.
I currently have no idea what the properties of this procedure are, but I think it might be interesting. My intuition is that it’s probably strategy proof in the sense that you have no incentive to vote other than your true preference (if so, the sampling with replacement is crucial for this – otherwise you might rank a less preferred but also less widely popular candidate first), but I haven’t worked through the details so there’s a high likelihood of this being wrong.