So I accidentally designed a voting system

…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:

1. Remove all votes including only candidates that have already been elected.
2. If we have no votes left, something has gone terribly wrong and we can’t actually elect enough candidates.
3. Now pick a random voter.
4. 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.

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4 thoughts on “So I accidentally designed a voting system”

1. John

Sorry in advance if I have missed something in your earlier writings on random voting that answers the following…

Is this system intended to elect candidates for “electorates/seats” (the Australian term)? If so, it seems to me that there is a fundamental flaw with the whole random voting concept in that there is a chance that someone with very few votes will win an electorate. I understand that this will in all likelihood be balanced out over all the electorates, but it’s very unfair on those people who live in the electorate where very few of them actually voted for their representative.

I understand that in Britain you don’t have preferential voting as we do in Australia. If I lived there I too would be looking for a better solution than the highly unfair first past the post system. But is there any reason why a random voting system is more likely to produce a “fairer” result than a preferential voting system?

1. david Post author

So, first off, it’s not a distinction between preferential and random voting systems. This is a preferential voting system, just one which introduces a randomized element as part of the procedure

This isn’t necessarily intended for electing candidates for single constituencies (I think this is what you call an electorate?), but you could use it that way if you wanted multiple seats per constituency (which I think may be a good idea, but is not something I’ve formed a strong opinion on), but if you were voting for just single seats there’d be no point. I have however talked about using just random ballot for constituencies before, and I still think it’s a good idea.

If so, it seems to me that there is a fundamental flaw with the whole random voting concept in that there is a chance that someone with very few votes will win an electorate.

This is something of a feature rather than a bug. The problem is that if you only people with a large local mandate, you’re still being unfair to a lot of people – those who have happened to live in an area which disagrees with their political beliefs. This is especially problematic for small groups which are geographically distributed.

Basically you’re trading one type of unfairness, which is pretty much guaranteed to happen, for another type of unfairness, which is less likely to happen the more unfair it is. Someone with only a few hundred votes in a constituency of 50,000 people. In any given election (over 650) constituencies, you’ll expect to get a small handful of these, and it’ll almost never happen to the same constituency twice in a row – it balances out over time as well as geography.

I’d also note that the consequences of not having your particular local MP be good at representing your views are much lower than your views having no representation in parliament at all.

I understand that in Britain you don’t have preferential voting as we do in Australia. If I lived there I too would be looking for a better solution than the highly unfair first past the post system. But is there any reason why a random voting system is more likely to produce a “fairer” result than a preferential voting system?

So it’s worth noting that in practice I don’t expect anyone to adopt any of the voting systems I’m proposing at the national level and that I would entirely get behind some sort of preferential voting or proportional representation movement (but after the disaster that was our AV referendum I’m less than hopeful about this). I don’t see much political chance of being able to persuade people at a national level that randomized methods of voting are a good idea.

However, I think randomized methods of voting are much better for geographic constituencies for any deterministic system – preferential or otherwise – because they produce a much better balanced house than any deterministic system can. I’m undecided on whether they’re really superior to doing away with geographic constituencies entirely and/or moving to something much closer to pure PR (they definitely have advantages over it, and I think they’re important ones, but I’m not sure if the greater predictability of deterministic PR is enough to offset them)

For a list of things this does better, I’ll link to my previous post on the advantages of using random ballot for your constituencies and note that it’s pretty much impossible to satisfy these with any system that applies a deterministic voting procedure to each constituency.