[EM] Re: Problems with finding the probable best governor

[Blake Cretney]

> Blake said:
> [regarding the best candidate estimate issue]
> 
> 
> My reasoning is this.  If we have majority (of those expressing a
> preference) decisions that form a cycle, we know that they cannot
> all
> be correct.  So, which one should we discard?  Presumably, the
> decision that has the least probability of being true.  The one
> where
> the balance evidence is least compelling.  This, I argue, is the
> proposition with the smallest margin of victory.
> 
> I reply:
> 
> I understand that part. What I don't understand is how that
> makes Tideman(m)'s winner the candidate most likely to be the
> best.
> 
> You correctly said that I was guessing you reasoning. I guessed
> that you were assuming that if the fact that A beats B says that
> A is more likely to be the best than B is, and the fact that
> B beats C means that B is more likely to be the best than C is,
> means that A is more likely to be the best than C is.
> 
> It's not like A beats C. Maybe C beats A. Doesn't that mean that
> the people said that C is more likely to be the best than A is?
> Sure, A>C was a weaker defeat, and has been dropped (or skipped).
> But the people nonetheless said, with that defeat, that C is
> more likely to be the best than A is, since you take a defeat as
> a statement of that type.

The problem is that you are imagining that there is some kind of
popular will and that this can be determined by finding the will of
the majority.  But there is no popular will and various majority
wills can easily come into conflict with each other.  That's one
reason I view an election in terms of evidence and probability
instead of "what the people said".  You're giving human
characteristics (will and opinion) to what is only a group of humans,
and does not have these characteristics.  Sometimes this can be
useful for brevity, but we should never think that it is accurate.

> So I said that the assumptions needed to say that A is the most
> likely to be the best because it's the Tideman(m) winner are
> arguably less convincing than the assumption that we can judge
> a candidate's probability of being the best by counting how many
> favorable individual pairwise preference votes he has.
>
> So I was saying that a claim that Borda picks the candidate most
> likely to be the best seems to require less questionable
> assumptions than a claim that Tideman(m) picks the candidate most
> likely to be the best.
> 
> Blake wrote:
> 
> Of course, there are some other possibilities.  You could decide to
> overturn more than one majority, or you could argue that a number
> of
> smaller majorities should be more powerful than one larger one. 
> I'll
> address these points if asked.
> 
> I reply:
> 
> Yes, that 2nd argument seems a good one.
> 

The problem is that you can only introduce multiple smaller
majorities to defeat a larger one if you assume some level of
independence of the smaller majorities.  But assuming independence
(which is Borda's main failing) leads to disaster.  First, these
different majorities are likely to be highly dependent.  Second, by
assuming independence we make failure of GITC inevitable (at least as
far as I can see).  It is much safer to assume no level of
independence.

This is what Tideman does.  The first and second highest majorities
should be locked because the only way to contradict them using
majority decisions would be to give lesser majorities some level of
independence.  And this is how the method progresses, if a majority
decision contradicts no higher majority decisions, the only reason
for overturning it would be lower decisions.  But the only way a
number of lower decisions could overturn a higher one, would be if we
would ascribe to them some level of independence.  Tideman's method
is the inevitable result of trying to find the most probable winner
without assuming any level of independence of the majorities.  Borda,
I understand, finds the most probable winner when assuming full
independence.

---
Blake Cretney