[EM] Better runoffs

[Jameson Quinn]

This could make for boring runoffs in many cases. To solve that problem, it
might be possible to reduce the pressure for people to vote in the runoff,
by making it so the first-round winner is not supplanted unless the turnout
in the runoff is high enough. For instance, if the first round were
approval (I know this doesn't meet LIIA, but to make my point), the winner
could be the highest vote total in the first or second round. A low-turnout
runoff would leave the first-round winner in place.

Jameson

2012/7/10 Dave Ketchum <davek at clarityconnect.com>

> On Jul 10, 2012, at 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, and A and B remain in the second round, they'll vote A
>> over B in the second round.
>>
>
> This seems reasonable to me - however much they thought, they decided on A
> vs B for the previous round and have no real need for more thinking now.
>
> However, those preferring C or D have only A and B available in the
> top-two runoff round and therefore must change.
>
> Should C and D have lost in the previous round?  Experience with IRV
> demonstrates that those deserving to win can lose due to bad methods before
> runoffs.
>
> Assuming C and D deserved to lose,  their backers need to accept their
> weakness and move on.
>
> Further, C and D could be clones who lost out because the method was
> Plurality, in which clones often lose due to the method.  Plurality has
> primaries to help with this but clones can get nominated via multiple
> parties.
>
>>
>>  DWK
>
>
>> 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. But let's consider top-two runoffs and, to
>> begin with, that the voters will stay consistent.
>>
>> The kind of criterion analysis performed on top-two then says that
>> top-two Plurality runoff is not monotone. Furthermore, it is worse than IRV
>> (i.e. fails participation, consistency, and so on, but also things IRV
>> passes like MDT and mutual majority).
>>
>> If we want to have a method that does better, what would we need?
>>
>> Some methods (like Ranked Pairs or Kemeny) pass what is called local IIA.
>> Local IIA says that if you eliminate all candidates but a contiguous subset
>> (according to the output ranking), then the order of those candidates
>> shouldn't change. If you eliminate all candidates but the ones that
>> finished third and fourth and rerun the election, then the candidate that
>> finished third should win. More specifically, for runoff purposes: if you
>> pick the two first candidates to the runoff, and voters are perfectly
>> consistent, then the order doesn't change.
>>
>> Thus, all that you really need to make a runoff that isn't worse than its
>> base method is that the method passes LIIA. Use Ranked Pairs for both
>> stages and there you go -- if the voters change their minds between rounds,
>> conventional criterion analysis doesn't apply, and if they don't change
>> their minds, you don't lose compliance of any criteria.
>>
>> However, such runoffs could become quite boring in practice. Say that
>> there are a number of moderates in the first round and people prefer
>> moderates to the rest. After the first round is done, two moderates are
>> retained and run in the second round. What does it matter which moderate
>> wins? The closer they are to being clones, the less interesting the runoff
>> becomes.
>>
>> More formally, it seems that the whole voting population is not being
>> properly represented. Two candidates represent the middle but nobody
>> represents either side. That might be okay if voters are normally
>> distributed around the candidate, but if they are, you wouldn't need the
>> runoff to begin with.
>>
>> If that's correct, then it'd be better to have a proportional ordering.
>> That proportional ordering should still put one of the moderates first
>> (assuming he'd be the winner had there been only one round), but also admit
>> one of the side candidates. But here's the tricky part. That proportional
>> ordering method should also pass LIIA, so that all the criterion
>> compliances held by the base method are retained. It's thus necessary that
>> the winner of the base method comes first. Beyond that, however, I have
>> little idea how the method might be constructed, or if it's even possible
>> to have both a proportionality criterion and LIIA.
>>
>> Finally, if such a method were to be found, one could possibly have more
>> than two candidates in the runoff. The runoff would serve as a way of the
>> method to say "hey, look at these candidates more closely", where their
>> positions could then be compared and voters possibly change their minds. If
>> the method passes LIIA, it doesn't matter how many (or few) candidates you
>> put in the second round - the method acts like the one-round method if all
>> the voters remain perfectly consistent. Practically, also, if there are
>> only two candidates and one is a moderate, the "other" wing not represented
>> might feel cheated out of a chance if only one of the wings are
>> represented. If the centrist and the leftist goes to the second round, the
>> right-wingers may complain that their candidate is not represented, whereas
>> ordinary top-two runoff would have no such problem because both the
>> right-wing and left-wing candidate would be represented at the cost of the
>> centrist.
>>
>
>
>
>
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