bramcohen: flow based voting

Bram Cohen (

bramcohen) wrote,
@ 2005-05-15 22:54:00

flow based voting
Here's an idea for a ranked ballots voting algorithm. We imagine each voter has a little water spigot which puts out water at a unit rate, and each candidate has a bucket the size of the droop quota. Each candidate turns their spigot to the bucket of the candidate highest on their list. When a bucket gets filled, everyone who was pouring water into it redirects their spigot to the bucket of their next-higher candidate. This continues until all buckets are filled. The candidate whose bucket finished filling last is then scratched off everyone's ballots, and the process is repeated, scratching off candidates until there are only as many candidates left as there are positions available.

This technique is conceptually very simple and easy to analyze (albeit computationally a bit intensive, but that's hardly a concern with modern hardware). It also does very well at some basic gameability criteria. For example, the extent to which a voter can increase the power of their vote by putting a heavily disfavored candidate first is minimized. Also, if there's a block of voters who have picked out a slate they can't get any advantage as a group by playing games with how they arrange the candidates on their ballots. The water output for the group is fixed, and if they have just barely enough votes to get their candidates in and noone else votes for their candidates and they put all members of their slate before all non-members of their slate then they will manage to exactly get their slate in, regardless of ordering of their votes within the slate and after the slate.

My thanks to Paul Crowley, who first suggested the water flow analogy, although he did so in the context of trust metrics, not voting systems.

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	voldemort234 2005-05-16 06:30 am UTC (link)
	Ah, instant run-off voting. It's highly unlikely to happen, as it seems like a person is voting twice, which isn't really allowed. (Reply to this) (Thread)

bramcohen
2005-05-16 06:40 am UTC (link)

'Instant runoff' is just about the silliest algorithm for deciding the winner of a ranked ballot election available. The real question is whether one uses ranked ballots.

Ranked ballots are in fact used in major elections in lots of large countries, including Great Britain and Australia. So your 'unlikely to happen' comment is wrong - they most definitely do happen.

Not using ranked ballots is an archaic, technologically backwards, and thoroughly undemocratic process. If one were to write a new constsitution for a 'democratic' country today it would only be common sense for it to mandate that there be no first past the post (i.e. US-style) elections.

In any case, the algorithm I'm proposing here is for elections where there are multiple winners, so it's a subsitute for Single Transferable Vote, not Instant Runoff.

(Reply to this) (Parent)(Thread)

	mlinksva 2005-05-17 07:11 pm UTC (link)
	Ranked ballots and first-past-the-post/single winner districts are orthogonal FWIW. I'm a fan of approval voting -- big improvement, very simple. (Reply to this) (Parent)(Thread)

	bramcohen 2005-05-17 08:37 pm UTC (link)
	The problem with approval voting is that it's extremely susceptible to strategic voting. Non-gameability is a big deal, you want voters to simply vote honestly. (Reply to this) (Parent)(Thread)

	zestyping 2005-06-22 06:45 am UTC (link)
	What makes approval more susceptible to strategy than other schemes? (Reply to this) (Parent)(Thread)

	bramcohen 2005-06-26 07:26 pm UTC (link)
	If you have a 'legit' winner (that is, the one who would win if everyone votes honestly) then everyone who favors someone other than the legit winner is incentivized to put a very dishonest 'no' vote for the legit winner. In practice this can easily result in someone who should win in a landslide having a crushing defeat. (Reply to this) (Parent)

	IRV = STV only if there's one seat to fill. (n/t) (Anonymous) 2005-05-16 06:26 pm UTC (link)
	n/t (Reply to this) (Parent)

	Single Transferrable Vote misterajc 2005-05-16 06:45 am UTC (link)
	Won't this give the same result as STV, which is widely used in Europe? See http://www.seo.sa.gov.au/canada/flash500.htm for an explanation of STV. (Reply to this) (Thread)

	Re: Single Transferrable Vote ciphergoth 2005-05-16 07:05 am UTC (link)
	No - note that second preference votes take part in deciding the first elimination. The only election in the UK that uses ranked ballots that I know of is the London mayoral election, which is decided using a truly mad system known as the Kellner system despite being a perfect fit for a Condorcet method. (Reply to this) (Parent)(Thread)

	Re: Single Transferrable Vote bramcohen 2005-05-16 07:30 am UTC (link)
	That's a shame, I was under the impression that STV was used in the UK. Perhaps it's that I've heard that STV is a popular idea in the UK, and got confused. (Reply to this) (Parent)(Thread)

	Re: Single Transferrable Vote ciphergoth 2005-05-16 08:05 am UTC (link)
	I was mistaken - STV is used to elect the Northern Ireland Assembly. Northern Ireland is not in Great Britain but it is part of the United Kingdom. (Reply to this) (Parent)

Re: Single Transferrable Vote
(Anonymous)
2005-05-16 05:36 pm UTC (link)

STV has been used here in the Republic of Ireland for most elections since the foundation of the state (by-elections and presidential elections aside, where STV degenerates into IRV), despite many attempts by one of the bigger parties to replace it with First Past The Post. You wouldn't believe the number of people that think we're still part of the UK. :-)

On to other matter. Now this might be down to my ignorance of the mathematics behind voting systems, and I present this with the caveat that I haven't really though this through, but why even use quotas? Why not just go:

Assign votes;

Eliminate the lowest ranking candidate;

Distribute their votes, striking off their first preference and bumping up the preferences of the other candidates on their ballot;

Repeat until any surplus candidates are removed.

Even if used when voting for a single candidate, it's not going to degenerate into FPTP. I really can't see what big advantage distributing surplus votes is aside from giving the appearence of greater proportionality. My evidence is only anecdotal: candidate surpluses here tend to be quite small in most cases, usually about 3% IIRC. I can't see this having a great effect on the outcome of an election, and eliminating redistribution of surplus votes simplifies counting drastically.

(Reply to this) (Parent)(Thread)

	Re: Single Transferrable Vote bramcohen 2005-05-16 05:46 pm UTC (link)
	In STV the quota is necessary for greater proportionality. The small excesses you see are due to people gaming the system a little bit - A party can increase their political influence in STV by distributing their first place votes evenly over the number of candidates they can get elected, so they generally do that. (Reply to this) (Parent)

	Re: Single Transferrable Vote bramcohen 2005-05-16 05:49 pm UTC (link)
	Oh, I forgot to mention in my last reply - an explicit Droop quota isn't necessary in the algorithm I gave, but it's still there, just implicitly. (Reply to this) (Parent)

	Re: Single Transferrable Vote (Anonymous) 2005-05-16 06:41 pm UTC (link)
	Kellner? Never heard of that method. Wasn't it the Supplementary Vote (http://en.wikipedia.org/wiki/Supplementary_Vote) that was used? (Reply to this) (Parent)