[EM] IRV ballot pile count (proof of closed form)

[Kristofer Munsterhjelm]

Abd ul-Rahman Lomax wrote:
> At 12:20 PM 2/8/2010, Kristofer Munsterhjelm wrote:
>> Abd ul-Rahman Lomax wrote:
>>
>>> Given that much better methods exist, have been tried and worked, and 
>>> are much easier to canvass, WTF?
>>
>> If I were to guess: in part a desire to produce a stepping stone to 
>> STV, and in part organizational inertia. FairVote bet on IRV and now 
>> will "stay the course".
> 
> That's right. One of my first observations on this, when I became aware 
> of the election methods list and the Approval voting list, and 
> discovered the Center for Voting and Democracy, which had started as the 
> Center for Proportional Representation, and which became FairVote, was 
> that people trying to reform democracy didn't trust democracy, they 
> would always gravitate toward nondemocratic institutions which are 
> easily co-opted to become self-preserving and inflexible. Typical co-opt 
> is by staff!

"Who says organization, says oligarchy". One has to be careful not to 
have the organization become undemocratic, because the default tendency 
is for it to turn so, since it is (initially) more effective that way.

> Yes, it's quite likely that they will stay this course right into the 
> ground. Hitching proportional representation (a very good idea) on to 
> single-winner STV (a quite bad idea) may have seemed like a good idea at 
> the time, perhaps because of the "brilliant" invention of the name, 
> "instant runoff voting," which itself suggested a strategy to spread the 
> idea by attacking a vulnerable institution, but it was, in fact, not 
> sustainable.
> 
> Some of the reasons why it is not sustainable were not necessarily known 
> then. Who would have expected that IRV would closely imitate Plurality 
> in nonpartisan elections? Lots of people seem to be surprised that IRV 
> doesn't produce real majorities, but that one was known.

I think there's somewhat of an "improvement no matter how small" aspect 
to it, as well. "IRV handles the spoiler problem with minor third 
parties, woo hoo!" and then they stop there. But how much of that is 
after-the-fact justification (means for the ends that is STV) and how 
much of that is truly believed is hard to tell.

> And the prior history of IRV in the U.S. should have been a clue. What 
> was it replaced with? Often -- not always -- with top two runoff. 
> Because of the desire for majorities....

For multiwinner STV, you could argue that the reason it was replaced was 
not because it did so badly, but because it did too well. Consider New 
York. After STV, there were many parties, not just the Democratic 
stranglehold. What did the Democrats do, seeing their power being 
diluted? Since they didn't want to share, they started employing 
red-scare tactics, with such rational appeals as calling the method 
"Stalin Frankenstein".

As for IRV, the single-winner method, you're probably right. In some 
situations, the reason is that it seems to provide no different results 
than Plurality. In others, there's complexity (which is made no better 
by that IRV isn't summable).

>> To address the former: the grail here would be a polytime monotone 
>> summable multiwinner method that reduces to a good Condorcet variant 
>> (or Bucklin/Range/etc) in the single-winner case. A multiwinner method 
>> can be summable in two ways: summable with the number of seats held 
>> fixed, or summable no matter what.
> 
> Well, Asset bypasses the whole shebang, by making what we think of as 
> "elections" irrelevant. At least in theory. Everyone wins in an Asset 
> election, or, if not, then there is someone very specific for the voter 
> to blame: the candidate the voter voted for in first preference. (Asset 
> may be STV with the Asset tweak for exhausted ballots, or it could just 
> be vote-for-one. I, personally, would see no need or desirability to 
> rank more candidates, provided my choice has a backup (a proxy should be 
> allowed in case of incapacity), but some people seem to think otherwise. 
> I'd rather not yank my vote away from my most-trusted candidate to put 
> it in the hands of this less-trusted candidate, but then to return it to 
> the most trusted if the less-trusted drops out somehow. .... rules in 
> STV/Asset have not much been delineated.)

Dissolving the problem - making it irrelevant - is the best solution, 
when it can be done, yes. However, I feel unsure about Asset because it 
hands power to someone who may hand power to someone who may ... and so 
on. The closest thing to it around in governmental elections is where 
parties (or candidates) specify an inheritance order, and your vote 
follows that order; what results is that the candidates might transfer 
your vote in the wrong direction. For instance, if you vote for X 
because of Y, and X also likes some property Z that you don't, then if 
he transfers to Z, that is not what you want. Asset's logic is that you 
don't have to do that (because you can vote for a minor player and your 
vote will still not be wasted), but why doesn't that logic hold for vote 
inheritance orders? It seems like it would, yet we see the effect 
mentioned above...

The iterated variant (some times called "liquid democracy") has another 
problem: the graph (who is a delegate of whom) is transparent - 
therefore, vote buying and selling becomes very simple. Now you may say 
that the voters won't accept a candidate who sells his power and so will 
desert the candidate, but as long as there's inertia (and reality seems 
to support that), the problem remains.

If I were to dissolve the problem of elections, I'd rather look towards 
Gohlke's triad idea, or a larger PR variant. If the base layers have 
some measure of randomization, it becomes hard to influence the 
candidates ahead of time, because everyone (who's interested) is a 
potential candidate.

>> What's important is that we don't know of such a method; but also that 
>> the stepping stone strategy itself might be dangerous - if the base 
>> method is bad, then it may fail to dislodge those whose interest is in 
>> less democracy, and so the objective of moving to multiwinner never 
>> gains any additional strength by the so-called stepping stone.
> 
> My own decision about all this is that it's best to begin with NGOs, 
> voluntary organizations that demonstrate how advanced methods work. The 
> Election Science Foundation held an Asset election for its steering 
> committee. It was quite interesting....

Would the various (smaller, usually technical) organizations and groups 
using Schulze count in this direction?