[EM] IRV vs Plurality (back to the pile count controversy)

[Abd ul-Rahman Lomax]

At 09:52 PM 1/22/2010, robert bristow-johnson wrote:
>now remember in the case we're discussing here, there is only two
>candidates.  again, what consequence to the outcome of the election
>(that is, who of A or B wins) occurs whether a ballot is marked
>"A" (and B is last by default) or is marked "A>B"?
>
>there is none.

If there are only two possible choices, that's the case. However, in 
fully democratic elections, the only case where there are only two 
choices is election by motion. The question is of the form of 
"Resolved: that A be elected to the office." Yes/No.

I will be putting together a document that compiles relevant rules 
and discussion from Robert's Rules of Order as it relates to voting, 
elections, ballots, and particularly preferential voting, because I 
consider an understanding of deliberative election process as 
essential to understanding voting system optimization. It is far more 
sophisticated than any "voting system" on the table, and the only 
problem is one of efficiency. While it is a method of election, in 
the general sense, it has been neglected because it is very difficult 
to study. It is not deterministic from a single set of preference 
profiles, even if they include preference strength information.

In public elections where write-in votes are allowed (which is so 
much the norm in the U.S. that it is preposterous to neglect it, and 
sometimes write-in candidates win), there are actually a practically 
unlimited number of optional votes. That *normally* write-in votes 
are largely irrelevant does not change this. The methods must allow 
for the possibility. So, as a compromise, canvassing methods may 
neglect the possible variety of write-in votes, and canvass them as 
if for a single candidate. But, then, if the number of votes for the 
single write-in candidate, were they all one candidate, possibly 
affect the result, it becomes necessary to count and report those 
individual write-in votes. I have not detailed how this would be 
done, and it is possible that, depending on conditions, it could be 
made more efficient than simply reporting every vote. But in some 
cases, reporting every vote might be necessary!

>i'm not going to discuss this any more with Abd, because he's not a
>straight shooter, but James, if you want to get into this, it's
>pretty much "cut and dried" from the POV of Information Theory (a.la.
>Claude Shannon).

This conclusion depends on understanding the situation to which the 
theory is being applied. That's what Robert misses. He makes 
simplifying assumptions without being aware that these assumptions 
are not applicable in the general case, but he does not specify the 
assumptions, nor does he take note of them when they are specified by 
others, including me, he merely concludes that I'm not a "straight 
shooter," which would imply some deceptive intent, but he has adduced 
no evidence of that, merely his idea that I am "wrong," which he has 
repeated over and over as if that would establish it as a fact, 
rather than a detailed examination of the evidence and arguments. His 
privilege, here.

>1.  there are three eligible candidates, A, B, and C.
>2.  a particular voter has A as his/her first preference.
>3.  the same voter has B as the second preference.
>4.  the same voter has C as the last preference.

The question is whether or not the vote A>B>C is different from A>B, 
whether or not the difference is worth reporting, or, stronger, 
necessary to report. And that depends on details of the rules, which 
Robert has neither stated nor accepted, and he has denied, without 
evidence, comments that did specify exceptions to the rules he 
proposes, -- not "made-up," but real-world exceptions.

I'll give the most notable: if a majority is required for election, 
and according to accepted parliamentary procedure, "majority" means 
more than half of all non-black ballots cast. Whether or not a 
candidate is eligible or not is irrelevant! Robert has adduced a 
preference profile, but has not specified one critical piece of 
information, in determining the relevance of an A>B>C vote compared 
to A>B. Is the voter willing to accept the result of the election of 
C, or would the voter prefer that the election fail? In short, does 
the voter approve of the election of C? We cannot tell that from the 
raw preference profile without approval information.

I gave examples -- and analyzed Robert's examples -- where the two 
votes are different in consequence.

Now, let's narrow the question, being aware that we are now more 
narrowly specifying it. If the election is election by plurality, 
does the third preference vote make a practical difference? Not in 
determining the result, but it is still important in assessing 
election quality, and examples could be shown where this is important 
as public information. There are rarely IRV elections which are by 
plurality, where, if the counting is continued one more step, the 
election would be by a majority. Even though this is legally 
irrelevant for election purposes, it is very important for assessing 
election quality and thus to the public for making decisions in the 
future about election methods.

Neglecting this purpose, then, and specifying the scope, Robert's 
assertions become true, and the third preference votes become 
irrelevant. But, then, I asked why the third preference option was 
even on the ballot? And in many jurisdictions, it would not be. Often 
IRV is mandated as a voting system only when there are more than two 
ballot candidates, and if write-ins are involved, with "three 
eligible candidates," that would mean only two were on the ballot. 
And IRV would not be used. Robert's Rules, by the way, covers the 
issue, that will be in my report. They strongly discourage *ever* 
disallowing write-in votes, and the protection against the spoiler 
effect is clear: they always require a majority and strongly 
discourage allowing election by plurality.

>again, the number of piles *necessary* (for recording and
>transmitting the information) when there are precisely N distinct
>candidates is
>
>            N-1
>     P(N) = SUM{ N!/n! }
>            n=1
>
>not
>
>            N-1
>     P(N) = SUM{ N!/n! }
>            n=0
>
>the latter redundantly (and unnecessarily) divides N! piles into
>twice that number with no difference of information between the two
>piles of each pair.

This was covered in detail, and Robert is repeated what was accepted 
and specified accurately. The difference between the two different 
approaches depends on exact election rules, which boil down to 
whether or not the last elimination is done. With some rules, it is 
never done, with others, as James Gilmour has noted, it is done.

>this is not social science.  it's not politics.  it's not opinion.
>it's just math.

I often see this kind of argument from people who don't understand 
the situation they are applying the math to. The math was not denied. 
What was denied was the general applicability. And, remember, Robert 
was claiming that what others had written (myself and several others) 
was a stupid mistake....

>i think i am now going to bow out of this.

Way cool. If you do.

>it's similar to the alien abduction controversy.  no matter how many
>people claim to be abducted by extra-terrestials and can provide
>vivid and detailed information of they're alleged abduction (and even
>scars, where they stuck the needles in), even if it is hundreds of
>witnesses and i am only one, i know that what they're saying is
>untrue.

Way cool, again. Omniscience. A probability of being correct is not a 
certainty of knowledge, and, in fact, when I've seen this kind of 
intransigence, it's often demonstrably in error. Robert has misstated 
the situation re alien abduction. The case against alien abduction is 
not must "only one," and there is a difference between witnessing and 
an opinion. What would be Robert's testimony *as a witness* in this 
case? Unlikely that his opinion is based on witnessing at all, it is 
based on inference and opinion and assessment of probabilities.

"Alien" abduction, for example, is a conclusion. What if some group 
of people, real people, were abducting people, masquerading as 
aliens, and doing all the stuff that the witnesses claim? There is a 
presumption at law that testimony is presumed true unless 
controverted, and simply rejecting the testimony because conclusions 
we might draw from it are deemed impossible is an error. The 
testimony stands, and what is rejected (provisionally and for 
efficiency) is the conclusion we might draw: that there are really 
aliens abducting people. But that is only one possible explanation 
from a universe of explanations. There are others: the hundreds of 
witnesses are all lying; they are suffering from some collective 
delusion or hallucination; they are telling the truth but it isn't aliens; etc.

>   you can bring up the fact that all other planets in our
>solar system are able to support such life naturally, they'll say ET
>came from another star system.  you can bring up the known value for
>c and what we know about special relativity and they'll deny its
>validity (or invoke wormholes or something).  eventually you just
>have to walk away.

In other words, Robert has a defective approach to logic, he hasn't 
understood the difference between testimony and opinion about it, 
and, in particular, the difference between a logically necessary 
conclusion from testimony and mere speculation or opinion regarding 
the implications.

In this case, because he doesn't understand testimony (such as my 
reports from Robert's Rules of Order, which describes a 
single-transferable-vote method of canvassing preferential votes), he 
rejects the testimony and considers it to be deceptive. Did he check? 
I rather doubt it. But he's welcome to contradict me, if my guess is wrong.