[EM] Condorcet How?

[Abd ul-Rahman Lomax]

At 12:20 PM 4/10/2010, Kevin Venzke wrote:
>To me the only thing that matters is whether there is even one scenario
>that could realistically arise and which is bad.

Two problems: what does "realistically" mean? and

What's "bad."

Let me propose an answer. If a good model is built of voter behavior, 
given simulated absolute utilities, a model which could be tested by 
feeding it reasonable assumptions from polls, political contribution 
patterns, voter turnout, and actual election results, with more 
detailed ballot data being a great help, it then becomes possible to 
simulate large numbers of elections, with variables constrained 
within, or not insanely far from, what is found in actual voting 
situations. From this, the frequency of some pathological scenario 
can be estimated.

But even more importantly, the damage from that scenario can be 
estimated. A "pathological scenario" that seems *awful* based on 
assumptions about what is necessary in elections, if it actually 
improves utility, isn't harmful at all! It simply shows that the 
criterion that wasn't satisfied was defective.

So, to start, in considering possible harmful scenarios, don't assume 
that the scenario is *realistically* harmful unless it can be 
connected with some utility profile that would actually function as 
assumed, *and* that would result in significant loss of overall utility.

Sure, you can show technical failure of a criterion by making up any 
scenario you like. And that fact is used by FairVote to avoid the 
implications of center squeeze, by arguing that no voting system is 
perfect, and, besides, the scenario is "not known to have occurred in 
any election," which, with center squeeze, was always known to be 
false, by analogy with top-two runoff, which IRV supposedly 
simulates, and which is now known to be a realistic possibility 
because of the recent Burlington election, where it happened.

Still, the FairVote objection, if it had been about some other 
criterion failed, does have a level of validity, provided that 
failing scenarios are made up without any attention being paid to 
realistic voting patterns. That's not true for Center Squeeze, which 
is well-enough known to be covered by Robert's Rules of Order in its 
criticism of "instant runoff voting" (they call it preferential 
voting, but they use a true-majority-required single transferable 
vote method, and then criticize it because of center squeeze as well 
as on the loss of additional information, valuable to the voters, of 
the results of earlier polls in a repeated ballot election, and they 
require the election to be repeated if no candidate (because of 
truncation) gains a majority of the votes, i.e., a majority of all 
ballots cast that aren't "blank" contain a vote for the winner. 
FairVote has lied about this for years.)

>  It seems like there
>is a hold up with the fact that B voters won't vote for C. So feel free
>to change the scenario to:
>
>49 A
>5 B
>19 B>C
>27 C>B
>
>It remains bad.

There is absolutely no way to tell that an outcome is bad unless 
underlying utilities are studied.

This is a classic vote-splitting outcome. What if there were a 
face-off between A and B? Voting systems students, unless they are 
wise to this point, will say, of course, B will win. Though only by 
51:49. They don't generally consider that turnout will depend on 
preference strength. For the A voters, from the bullet votes, it's 
easy to infer high preference strength, relatively. We don't know 
about the B and C voters and how strongly they prefer B to A, except 
we can infer strong preference for 5 of them.

Suppose that some section of the C voters -- this is most likely with 
them -- have some utility profile like:

C: 10
B: 1
A: 0

Will they bother to vote? If they do vote, sure, they will vote for B 
in an A/B faceoff. But in a real election, many won't actually vote.

Now, was this election for A a "bad outcome?"

I'm just going to make up some utilities that would fit the votes. 
I'm not going to use weak votes, though an accurate analysis would. 
(i.e., I will normalize absolute utillities to one full vote for each voter).

                 A       B       C
49 A            10      0       0
5 B             0       10      0
19 B>C          0       10      5
27 C>B          0       5       10

totals          490     375     365

Now, please explain to me why A is a "bad" outcome? I assumed 
utilities that were effectively sincere normalized Range votes in a 
Range 2 election.

>  I can't see what criticism would remain of this, other
>than saying that in a real election we might be lucky enough to have
>some A voters vote A>B and accidentally give the election away.

Well, a criticism remains! And we wouldn't be "lucky."

Sure, I can imagine scenarios where something else would happen. The 
values I used above were extrapolations from an assumption that 50% 
was considered the minimum rating for "approval," and that voting for 
a candidate was that approval. It's the "expected value" of the election.

What if I consider the worst case, still with the 50% approval level? 
A scenario maximally strong for B (C minimized):

                 A       B       C
49 A            10      4       0
5 B             0       10      0
19 B>C          0       10      1
27 C>B          0       9       10

totals          490     679     289

And minimally strong for B (C maximized)

                 A       B       C
49 A            10      0       4
5 B             0       10      4
19 B>C          0       10      9
27 C>B          0       1       10

totals          490     267     657

My point is that from a mere preference profile, one cannot determine 
who the "best" winner of an election is. Preference strength 
information is necessary. Doing this in a real election can be 
difficult without additional constraints, and the most common one is 
the requirement for majority approval.

> > > By the way, I do want to maximize the sum of
> > utilities. I just don't
> > > think you can be so direct as to ask for them.

Perhaps, butI now disagree, there is a way to ask for them, and get 
sincere utilities in response. It takes the possibility of more than 
one ballot. Something that has been overlooked is that a series of 
repeated ballots tests absolute preference strength.

> >
> > Sum of utilities would be a good approach for many uses if
> > we could get the personal utilities. In some non-competitive
> > elections and polls we can get them but political elections
> > may be a more difficult environment.
>
>Well, I have assumptions about what tends to maximize utility. The ideal
>scenario for me is that the median voter has 3+ viable options to pick
>from (and not find the choice obvious).

An assumption about what tends to maximize utility can be way, way 
off. That's what I believe I showed above. With a simple, normalized 
utility Range 2 election, that made the votes rational without making 
additional assumptions, A was, by quite a margin, the best winner 
from utility analysis. it took more extreme analysis, using a Range 
10 election, to produce results favoring (by high margin) B or C.


> > (There may also be some extreme situations where the sum of
> > utilities is not what we want. For example it might make
> > sense to improve the utility of all voters worth 10 points
> > rather than improve the utility of all but one voter with 12
> > points and then kill or otherwise cause a major decrease in
> > utility to that remaining one voter.

Eh? It might make sense to appoint our favorite the dictator, as 
well. Why bother with these stinkin' elections?

>  In this case one could
> > btw also consider allowing the voters to give ratings like
> > "minus infinity" to avoid this kind of situations, i.e.
> > ratings would not be based on a fixed range but some wider
> > scale, maybe indicating that 0 means "neutral", 100 means "I
> > like a lot" etc.)
>
>Yes. If we could perceive utility more clearly I might have to clarify
>my opinion.

We can. I assumed normalized utilities above, which is a decent 
starting place, because there is no basis for assuming anything else. 
We know that the voters -- assuming they were free -- had enough 
preference strength to be bothered to vote in the election. Whether 
that's high or low depends on many factors. Was the election on the 
same ballot as a high-value election to the voters, but they have low 
value or even no value for this one, but voted out of habit? Or was 
this very important, and to which voters?

In any case, the sound approach, in the end, is to study *absolute* 
utility profiles. I'm not saying that the sound approach is easy! We 
can, for the time being, make the "equal voter" assumption, and thus 
normalize utilities, but we must keep in mind that this is actually 
an unrealistic assumption, and there is ample proof in real election 
turnout figures that the assumption doesn't hold. Besides being preposterous!

Simulations would properly start with the entire electorate, with 
utilities assigned via relatively realistic probability distributions 
on the "heaven-hell" scale. Then there are two kinds of elections: 
"happen to be there" elections, where the voter is voting regardless 
of absolute preference strength (over the entire set of reasonable 
candidates), and true "voluntary elections," where the voter will 
turn out to vote because of relatively high preference strength, on 
average, and not if the preference strength is low.

This really does affect runoff elections, I'm sure. It is a likely 
reason for "comeback" elections, I suspect, which seem to occur in 
about 1/3 of non-partisan runoffs.

>While the scenarios I bring up show some strategy, I consider the strategy
>natural and not something consciously plotted in advance. In fact if you
>called the truncating voters strategic, I think they would be offended
>and not see it that way at all.

I projected utilities from the votes that assumed that the votes were 
sincere. That's why the first scenario was Range 2. We don't have 
more data than that. Then I went to the best and the worse, for B and C.

I didn't show the additional possibilities, that if we were to look 
at absolute utilities, we might see something like this (I'll 
maximize for A, that is, I will normalize absolute utilities on the 
scale determined by the A voters, and then assume maximally favorable 
utilities for A that still explain the B and C voter patterns):

                 A       B       C
49 A            10      0       0 (A voters have strong feelings, B/C 
are the same for them)
5 B             7       10      8 (This gives motive to truncate for B alone)
19 B>C          7       10      9 (This gives motive to add C)
27 C>B          7       9       10

totals          847     483     481

Now, make it worst for A. I'll set this up to maximize B, C low:

                 A       B       C
49 A            10      9       0
5 B             0       10      0
19 B>C          0       10      5?
27 C>B          0       9       10

totals          490     924     365

>Again I don't think voters will view truncation as a strategy, and will
>always do it (especially with more candidates).

Real voters tend to vote for one, in most elections, unless they have 
party labels to guide them. It's about the limited information they 
have. This is the problem that Carroll addressed more than 120 years 
ago with Asset Voting. Truncation isn't so much a strategy as a necessity.