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

[Dave Ketchum]

Perhaps we have spent enough time plotting how to best count ballots  
in IRV, while some note that the best planning is actually how to get  
away from IRV:
      Plurality - a reminder that we need to move ahead.
      Condorcet - my preference, partly for moving ahead and partly  
for accepting votes ala IRV.
      Bucklin and other variants of Condorcet.   Rules for these make  
them more complex than Condorcet - I see their rules making them less  
desirable.
      Range - I see this as competitive with Condorcet, with valid  
arguments for claiming either is better.
      Asset - Abd ul likes.  I doubt that the rest of us have looked  
close enough to judge its merits.
      Approval - true step up from Plurality; questionable whether it  
is competitive with any others above.
      Any other that let voters indicate which is/are best liked, best  
liked of remainder; etc.

Condorcet does an N*N matrix showing for EACH pair of candidates which  
is better liked - used in counting and usable by others to help plan  
their future.  Often there is a CW which wins for winning in all of  
its pairs; else a cycle in which each would be CW if other cycle  
members were not candidates.
      How best to resolve a cycle is debatable, but a simple method  
could be used unless others are demonstrated to be much better:   
Delete weakest pair used to define the cycle; repeat until remainder  
defines a CW.
      Note that N*Ns show progress, or lack of such, among non-winners.

On Feb 10, 2010, at 5:33 AM, Kristofer Munsterhjelm wrote:
> 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?
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