I don't think it was "wrong" of me to make the 2 frontrunners be
completely arbitrary. Although it might have been "an exaggeration of
the problem."
1. Consider the latest US presidential election. Trump became
a frontrunner with plurality voting in the GOP primary. The
reason that happened was not because
of some honest-voting polls plus added noise. The reason it happened
was because Trump was (a) famous and (b) different than all his
rivals who by comparison were all "nearly the same." Trump intentionally
loudly and eternally emphasized a & b.
The facts that Trump was the most unqualified,
oldest, and most-interest-conflicted, person
ever to become US president and ran with essentially no agenda
while telling more lies than any major candidate in the history of fact-checking
agencies, all were irrelevant. In fact most of that helped create more "b."
Therefore, AS A CONSEQUENCE of strategic voting behavior from then
onwards, he sailed to the nomination easily.
OK? Trump became a frontrunner for reasons which as far as any
simulation should be concerned, were
COMPLETELY ARBITRARY and had little or no relation whatever to
honest polling plus noise.
2. It often happens the anointed "frontrunner" is thus-anointed purely
because of press reports that he has accumulated an enormous amount
of money. E.g. Jeb Bush in 2016 whose campaign went nowhere
in spite of this anointment.
Is this due to "honest polling plus noise"? Well, it seems quite
arbitrary or maybe even worse-than-arbitrary in the sense that it
favors more-corrupt candidates.
I suppose you could consider the rich guys giving him the early money to be
thus "polled" but I would contend they are so far far off being
a representative sample that they have to be
viewed by a simulator as totally arbitrary.
3. If often happens that somebody wins Iowa and/or New Hampshire, then
is branded a "frontrunner" then as a consequence steams to the nomination
while meanwhile somebody who seems comparable or more qualified
etc is branded a "nonfrontrunner" due to poor Iowa
performance and thereafter dies the death.
Well, is that the result of "honest polling plus noise"? Well, certainly
arguably yes, if you regard the Iowa caucus as
some sort of honest polling plus noise. But there is a hell of
a lot of noise.
So rather than branding me as wrong purely based on your intuition, you
should actually consider the evidence from the real world.
But I think I like JQ's "honest polling plus noise" idea in principle for
determining "frontrunners," and note it becomes the same as my method
in the limit of high noise. I just want to say that
(a) my limit is not at all bogus.
(b) it is very simple to program and get right.
But the JQ approach is NOT simple to program and get right, in fact not
even easy to think about or define right. The more you think about it,
the deeper waters you find yourself swimming in.
To explain what I mean by that:
If you have an arbitrary (perhaps very complex)
voting method which has to be treated as a "black box"
inputting votes and outputting winners...
well, suppose we feed it some honest votes and it says "A wins."
Now what? Who should be the "frontrunner?"
Well, there may be no such thing -- for a general black box -- as a "2nd placer"
B so we have no general-purpose way to select "B" with greater chance than C.
And ok, what if we say "well, we'll feed in NOISE-DISTORTED
honest votes and then the winner will be somewhat random"
and we'll declare him frontrunner.
Well, then the problem is different voting methods
have different inputs, e.g. approval, ratings, or rankings,
also other things too are possible. In general the input is just a bitstring.
So if you try to "add random noise" to distort the honest votes,
you are doing something different for each
voting method, which might be unfair and comparing
apples to oranges.
Eh? So then you get into murky waters.
My way, it is at least transparently obvious it is totally apples-to-apples
and no definitional confusion and murkiness.
--
Warren D. Smith
http://RangeVoting.org <-- add your endorsement (by clicking
"endorse" as 1st step)