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

[Dave Ketchum]

If you object to "plurality" as I used it below, then WHAT label would  
you use for this major (often used) election method?

I did go to Robert's 10th which is not into our level of detail on  
this topic (I see neither approval nor Condorcet mentioned).

I went to Wikipedia, which I see as agreeing with what I wrote as to  
all three categories.

On Feb 13, 2010, at 4:33 PM, Abd ul-Rahman Lomax wrote:
> At 11:55 PM 2/11/2010, Dave Ketchum wrote:
>> We all get careless and stumble, sooner or later!
>>
>> But I choke on two details here:
>>
>> You misuse the label "plurality" - having only the ability to vote  
>> for
>> 1 even though, for many races most intelligent voters will find there
>> is only one candidate deserving approval.
>>     Even Approval has more power, letting voters vote for more than
>> one, though unable to differentiate.
>>     Condorcet is another important step up, letting voters vote for
>> more than one while indicating which they like best.
>>
>> Forcing voters to act as if they wanted to vote for more than they
>> wish to is a step backward, and should not pretend to be an asset for
>> a method.
>
> I'm not following Mr. Ketchum's arguments here. But "plurality" was  
> used in a very ordinary sense. Any method which elects without a  
> vote of a majority of those who cast non-blank ballots in an  
> election is an election by plurality, using the definitions of  
> Robert's Rules (and of most parliamentary procedure manuals, I  
> believe, if not all). There is room for interpretation on whether or  
> not a non-blank ballot that does not contain a legal vote should be  
> included in the basis for majority, but no room for excluding from  
> the basis those who do cast a valid vote, but for a candidate that  
> is, say, later eliminated due to low vote count.
>
> Hence almost all voting systems that have been considered, absent  
> vote coercion (as with mandatory full ranking or penalization of  
> partial ranking, as happens with some versions of Borda Count), are  
> "plurality methods," including Approval and Range and, the point  
> here, Condorcet methods.
>
> I did incorrectly state the case at first, by showing lower rankings  
> that did add additional votes for other candidates by A. The example  
> was clearer with all bullet votes. What this points out is that a  
> ranking of, say, A>B>C>D>D>F>G>H is, from this point of view, a vote  
> for G over H. Should this be considered an "approval" of G? The  
> voter has expressed that, in an election between G and H, the voter  
> would prefer H, though, in fact, in a deep ranking like that, this  
> is probably noise for the most part. (Robson Rotation is, in fact,  
> used to eliminate some of this noise by averaging it out so that, at  
> least, it is not produced by ballot position.)
>
>> "Majority" is a word whose merits need more serious thought - see an
>> earlier post from today.
>>
>> Ditto "runoffs".

Your words below seem intended as response - but I see little if  
anything as to merits.

Dave Ketchum
>
>
> Indeed. Voting systems theory, early on, focused on attempts to find  
> the ideal single-ballot system, from various perspectives. While  
> this is a theoretically interesting question, it essentially misled  
> the entire field when applied to real election reform, ignoring the  
> most widely used voting reform, top two runoff, as if it were merely  
> a more expensive and cumbersome version of Sri Lankan Contingent  
> vote. Or batch-elimination IRV, same thing. It isn't. It produces  
> different results than IRV, in about one-third of runoffs in  
> nonpartisan elections. (Probably in partisan elections, it produces  
> roughly the same results.)
>
> In addition, this approach ignored the *universally used* direct  
> democratic method, repeated balloting, with no decision being made  
> without a majority of those voting supporting it. None. No exceptions.
>
> Ignoring explicit voter approval, then, is one of the widespread  
> systemic errors. Another one, arising early on, was the assumption  
> that pure preference profiles were adequate to understand how voting  
> systems would amalgamate votes and produce a useful social ordering,  
> when, in fact, any sane method of studying how voting systems work  
> would realize that a strong preference is different from a weak or  
> barely detectable one, not to mention an indistiguishable one that  
> is forced by a voting system to be crammed into one of A>B or B>A,  
> with no allowance for A=B. And real, human, social decision-making  
> systems, outside of voting, do consider preference strength, very  
> much.
>
> And any system that attempts to maximize benefit to a society based  
> on preference profiles would have to take preference strength into  
> account. That it may be difficult to do this, that it may be  
> difficult to determine commensurability, does not change this. What  
> we can see through the device of assuming absolute utilities for  
> voters in simulated elections is that the Condorcet Criterion and  
> the Majority Criterion, for similar reasons, can require  
> preposterous results, in situations where, with a single ballot and  
> no other amalgamation method operating, will produce a result that  
> will later, if it's tested, be *universally rejected.* I'd call that  
> a Bad Decision. And any system which considers preference strength,  
> that allows the expression of it and then uses that information for  
> other than simply resolving a Condorcet cycle, *must* fail the  
> Condorcet Criterion.
>
> Originally, my assumption, as with many students of this field, was  
> that the Condorcet Criterion was the King of Criteria. Well, the  
> King has been dethroned. It's a good and useful criterion, it has a  
> place. But applied rigidly, it is quite possibly harmful.
>
> I've argued that if ballots show a Condorcet winner, an election  
> should not resolve in favor of another candidate, except possibly in  
> situations where a legitimate cause of Condorcet failure can clearly  
> be identified and it can be known that voters would then reject the  
> Condorcet winner, knowing the results of the first election. Other  
> than that possibility, I would always want to see Condorcet failure  
> submitted again to the voters for review and possible confirmation  
> or rejection of the failure. Rejection of the failure would probably  
> mean election of the Condorcet winner, and, as long as the voters  
> can do this, it must be said that the *overall method* satisfies the  
> Criterion. It only looks like it didn't by not immediately jumping  
> for the Condorcet winner in a primary. The later ballot completely  
> supercedes the former, which is totally standard democratic process.