[EM] Better runoffs

Kristofer Munsterhjelm km_elmet at lavabit.com
Wed Jul 11 14:55:01 PDT 2012

On 07/10/2012 08:19 PM, robert bristow-johnson wrote:
> On 7/10/12 6:51 AM, Kristofer Munsterhjelm wrote:
>> When runoffs are subjected to criterion analysis, one usually
>> considers voters to vote in the same order in each round. If they
>> prefer A to B in the first round,
> now how is this known, without a ranked ballot?

It isn't. In the analysis, one imagines the voters having hidden 
preferences (be they cardinal or ordinal), and the voters then vote 
according to that preference as best as they're able.

For instance, if voter X has a hidden preference A>B>C>D, is honest, and 
the system is top-two runoff, he'd vote A in the first round. If, say, B 
and D go to the second round, he'd then vote for B.

>> and A and B remain in the second round, they'll vote A over B in the
>> second round.
> that is, if nothing changes their mind. during our big IRV slugfest we
> had in 2010 (as a consequence of the 2009 IRV election), one of the
> points of the opponents of IRV was that they felt they deserved the
> right to make up or even change their minds about A and B. even if they
> voted for A or B in the first round.
> i, of course, felt it is a reasonable requirement that voters make up
> their minds about candidates by Election Day and that the downside of
> delayed-runoffs exceed this nebulous "freedom to change my vote" that
> the opponents touted. (one argument these folks made was that if their
> favorite candidate was eliminated in the first round, these voters would
> like to know who, of the remaining candidates in the runoff, their
> candidate might favor. i still don't see that as a compelling argument
> for delayed runoff.)

There are game-theory advantages to having multiple rounds. In an 
exhaustive runoff, one can show there's an equilibrium where the honest 
CW wins, for instance. This holds in the three-candidate case for 
top-two runoff. The strategy involves the majority that prefers the CW 
coordinating so that the CW is never eliminated in an earlier round, and 
so is probably unrealistic, but it shows runoffs can do things 
single-round rules can't.

>> This may not necessarily fit reality. Voters may leave or join
>> depending on whether the second round is "important" or not, and the
>> same for later rounds in exhaustive runoff.
> and this can be adequately dealt with using a ranked ballot. as long as
> all of the candidates are in the race up to Election Day, if it's
> important enough to vote during *any* round, it's important enough to
> rank it on a single ballot.
> i know there is more to your post, Kristofer, but i have to decode more
> of it before i can say anything about it. at least in my experience, all
> non-IRV elections were either straight plurality, or had a top-two
> runoff. and, besides the problem of greatly reduced turnout for the
> runoff, it is not clear that the top-two vote getters should be the
> candidates in the runoff. indeed, my argument to Democrats who voted
> against IRV (to return us to plurality/runoff) is that the candidate who
> should have won the 2009 race (who was the Dem candidate, so we Dems
> felt screwed) would *not* have ended up in the delayed runoff, had that
> been the law at the time. so voting against IRV and returning to delayed
> runoff did nothing to solve that problem.
> so i dunno how we do "better" delayed runoffs without using a ranked
> ballot in the first round to begin with. and if you do that, then what's
> the point (other than allowing voters to change their mind after
> Election Day)?

The kind of systems I'm talking about would accept ranked ballots. The 
runoffs would, apart from allowing voters to change their mind, also 
protect against simple strategies. Say that the method is Condorcet and 
enough people go on a burial spree to push the "honest" winner to second 
place in the outcome. Then the runoff is still honest (majority rule is 
strategy-proof), so the right candidate would win.

I suppose that furthermore, I'm thinking it could be useful to know 
about better runoff rules in case Plurality's Duvergerian tendencies are 
inherent to single-winner single-round methods in general. I don't think 
it is actually so, but in case, being prepared about methods that do 
work can't do harm :-)

We know that runoffs counter two-party rule to at least some extent, 
because nations that use them tend to have multiparty rule whereas 
nations with ordinary Plurality don't -- and while IRV has superior 
criterion compliance according to the type of analysis I mentioned, IRV 
nations aren't multiparty either (unless 2.5-party rule counts as 
"multiparty"). So something is going on that makes top-two better than IRV.

Now, if advanced ranked methods like Condorcet are good enough, then no 
problem. All we need is Condorcet and we're done. But if they're not (or 
preparing for that possibility), then we should try to figure out why 
top-two succeeds where IRV fails - and how we might construct a method 
that's both good according to criterion compliance analysis (which is 
where the whole LIIA reasoning comes into play) and according to the 
counter-Duverger properties seen in top-two.

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