[EM] Yee/B.Olson Diagram Remarks

[Abd ul-Rahman Lomax]

At 06:46 PM 12/8/2008, fsimmons at pcc.edu wrote:
>If Yee/B.Olson says you're bad, then you're bad.  The converse is 
>not true.  If the electoscope does not say you are bad, that doesn't 
>mean you are good.

There are sometimes other considerations.

>Borda doesn't look bad under this electoscope, because Borda 
>complies with Consistency and Monotonicity, but Borda is worse than 
>IRV.  Borda is like the little boy that is always nice in front of 
>the teacher, but gets mean when the teacher is not around.  But at 
>least careful attention to the electoscope shows Borda's Clone Loser 
>problem as clones are added to a loser.
>
>It is interesting that the electoscope is not sensitive enough to 
>reveal  Copeland's Clone Loser problem.

I've been harping lately on the fact that Borda is actually a method 
of approximating Range. Assume a sincere preference distribution that 
is even across the candidate spectrum. (I.e., each voter's candidate 
utilities, unmodified by lottery probabilities, are evenly stepped, 
the preference strength between each pair of candidates  is a 
constant, 1/(N-1) of the total preference spectrum present, where N 
is the number of candidates. The method is Range N. Borda's problem 
-- I think Saari thinks it a strength -- is that it does not allow 
equal ranking. This distorts the assumed utilities, making Borda fail 
ICC. Borda, allow equal ranking -- which is actually easier for 
voters, and it's Range.

Saari, and Borda himself, think that Borda is ideal with sincere 
voters, but the clone problem has nothing to do with sincerity, it 
exists with fully sincere voters. Saari objects to the alleged 
indeterminacy of Approval and, I'm sure, of Range, but those methods 
are not actually indeterminate, they only appear so when the only 
input is (1) a preference list, which is clearly inadequate 
information to allow overall optimization of voter satisfaction. The 
other inputs are (2) Voter estimation of election probabilities. (3) 
Voter overall preference strength, which affects how much effort the 
voter will put into voting. Bullet voting is a simple strategy which 
requires little effort. While the second input is confused and 
assumed to be specific knowledge regarding other voters, those 
probabilities could be based on a simple assumption by the voter that 
the voter is reasonably typical. Most of us are, by definition!

Saari's negative example, regarding the "evil" Approval, shows what 
he thought was a preposterous result: 9,999 to 1 majority with strong 
preference (50% preference strength) for one candidate, and 1 voter 
with reversed preferences, who determines the outcome as the mediocre 
candidate. He simply assumed a totally preposterous voting strategy, 
and what he showed was that the strategy was preposterous, not that 
the method was preposterous. The method itself, given what the voters 
fed it, made the right choice. But had one or two voters used an 
actually sensible strategy -- such as the voter's presumption that 
most voters would agree with the voter, which is a zero-knowledge 
strategy -- which then allows a more correct estimation of "mean 
utility," which Saari thinks he's using -- We'd have seen Approval 
results that reasonably represent the social order, including 
preference strengths. And allow the "maverick" voter to know that his 
opinion is probably idiosyncratic, -- most would --- and thus vote as 
he actually votes in Saari's scenario, we'd get even more accuracy. 
And that is with 9,999 out of 10,000 voters with the exact same preferences.

In fact, voters are spread across a spectrum, which allows more 
accurate estimation of preference strengths even with a primitive 
expression like (0,1).

In any case, fixing Borda is practically trivial: Have a fixed number 
of ranks, equal to the number of candidates, (or greater than it, 
could be N times the number of candidates, to allow voters to use 
exact Borda expression if they want -- it's not a bad first pass 
approximation. But it's probably close enough for folk music to 
simply have a lot of ranks, like 100. And even 10 might be quite 
decent. It's amazing how good just 2 are.) Then allow equal ranking 
(or more refined ranking in higher-resolution Range), which implies 
empty ranks.

So the voter, to vote sincere Range, could start with a Borda 
distribution. How to get it? I'd start with the best at the top and 
the worst at the bottom. Then I'd look to see if there are any 
candidates where I have a difficulty deciding which is better, the 
candidate or one of the extremes. Even if it's a minor difficulty, 
I'd rank them the same. This is, so far, *more sincere* -- i.e., more 
accurate -- than forced ranking. Then I'd look at the remaining 
candidates, which are the favorites, which are the worst? I'd rank 
them at the next Borda ranks down or up, respectively, and iterate 
until all candidates are ranked. This gives me, if I've equal ranked 
any, a larger preference strength in the middle, which is likely to 
be strategically optimal. Now, are any of the above-the middle 
candidates not acceptable? If so, move them down to fill up the ranks 
from the bottom. Preserve preference order wherever there is a 
significant preference: if there are not enough full Borda ranks, use 
intermediate ranks, from the bottom, to allow compression below the 
approval cutoff.

(I am starting to assume, and we need to consider, that majority 
approval is needed for any election. That is standard deliberative 
process, and it is clearly an option in public process for a primary 
election. I would argue that *no* election should be valid without 
approval of a majority, and I'd use Asset techniques to make runoff 
elections far easier. Without this restriction, the shift of votes to 
below the approval cutoff isn't necessary, perhaps, though it may 
still optimize the outcome.)

Because voters will use strategy, period, it's how human beings make 
choices, and it's a good thing, causing us to generally make better 
choices, we need to incorporate strategy into methods for comparing 
voting methods. The simulations should include the possibility of 
strategic nomination; ICC covers that, so if simulations don't 
consider the nomination process, ICC failure, of the kind that harms 
results in Borda, should be noted, at least.

Generally, Range, normalized to the "real election," i.e., to any 
reasonable candidate set, and with voters voting sincerely or with 
reasonable strategy, is independent of clones. It only appears not 
when we assume that voters will shift their rankings simply because 
an irrelevant candidate is added. In real life, they won't, unless 
they use a very poor strategy, not the way people really vote in 
significant numbers. Borda forces this bad strategy. Whether you 
think a candidate is irrelevant or not, you must still assign that 
candidate full preference strength over the next lower ranked 
candidate and assign full preference strength to the next higher 
ranked candidate, thus shifting all the ratings (and real rankings; 
clones, as perceived by a voter, should be easily votable as equal 
rank, the method treating them as the voter sees them: as equally 
satisfactory or equally unsatisfactory.

Thanks for your work on Yee diagrams and the like, Mr. Simmons.

What we need now is popular explanation of this work, making it 
accessible, and we need for this to be published in a peer-reviewed 
publication. Voting Matters might be interested. If not, the Election 
Methods Interest Group was designed to function as a kind of ad-hoc 
peer review committee, and a publisher could use EMIG process as its 
peer review process, discovering consensus on an article. "Publisher" 
does not have to be a print publisher, it could be a web publisher 
with a clear editorial process and responsibility.

I've got a number of topics to write on now, if I ever get around to 
it.... I'd like to encourage others to use EMIG for a focused review 
of papers and draft papers, where there can be a voting process to 
measure consensus regarding the merit of the paper. This list (EM) is 
great for discussion and debate, but lousy for measuring consensus, 
we don't know if silence means everyone's been satisfied, or that 
everyone has concluded that the writer is a nut case and not worth 
the time of discussion. And maybe sometimes it's a bit of both: those 
who disagree just shut up unless they are bored with nothing to do....