[EM] Richard's neat idea (was Tyranny of majority)

[Forest Simmons]

Richard, I see what you mean. I spoke without thinking it through
carefully enough.

Last night it hit me clearly that your new method is the ultimate method
for complying with the IIAC (Independence of Irrelevant Alternatives
Criterion) made famous by Kenneth Arrow in his Nobel Prize winning work.

The reason that methods based on ranked ballots have so much trouble
complying with the IIAC is that when you remove a candidate from the
ballots you remove a reference point in a sea of relativity (since all of
the candidates are ranked only relative to each other).

The introduction of virtual candidates such as MAC (Minimum Acceptable
Candidate) as reference points helps compensate for this problem.

What you describe is the ultimate in this direction, throwing in all
possible candidates for comparison purposes, including the ones that might
officially withdraw from the election.

Who can think of a more comprehensive way of satisfying the IIAC ?

Now having buttered you up a little bit, I want to point out that at least
one thing I said below is true.  Your great method is indeed strategically
equivalent to ordinary Approval.

Once the voters have in mind which of the real candidates they would like
to support (with eyes wide open having seen all of the alternatives) they
rank all the real candidates that they approve above all of the fake
candidates, whom in turn they rank above all of the real candidates that
they disapprove of. 

The virtual candidates then mark the boundary between the approved and the
unapproved.

Since there are infinitely many virtual candidates compared with real, the
number of victories of a real candidate is asymptotic to his number of
victories over virtual candidates, i.e. his approval count. Q.E.D.

This result doesn't subtract from the value of your suggestion. On the
contrary, your suggestion ...

(1) ... gives additional insight into the nature of Approval.

(2) ... would help approval voters decide where to draw the line,
especially in zero info cases. In fact, it might convince voters to vote
for none of the real candidates when they realize that the alternatives
are so much better. A cutoff quota could take advantage of this fact.

(3) In simulations (your contemplated application) it would be an
extremely attractive standard of comparison. 

(4) A variation in which the voters don't know which of the candidates are
really in the running (remember the old show "Guess My Line?") might work
in some situations like picking the most eligible bachelor. More thought
needed here.  There might be some serious applications. 

Your basic idea could also be used to make Universal/Dyadic Approval
comply with the IIAC.

This is related to something I was thinking of earlier.  Dyadic Approval
runoff doesn't improve on Dyadic Approval. In fact, it doesn't have
results nearly as good as plain Dyadic Approval or Universal Approval. The
reason is that Dyadic Approval ballots are so rich in information
(expressed in a rich relational style as opposed to absolute style) they
have more to lose when one of their reference points is removed. 

Great Work!

Forest



On Wed, 9 May 2001, Richard Moore wrote:

> Forest Simmons wrote:
> 
> > Suppose that f and g were the same. Then each voter could be asked to
> > compare each candidate to herself. This could be very appropriate in
> > a representative democracy where the representatives are supposed to serve
> > as proxies for the citizens that they represent.
> >
> > The ballot could be worded as follows: Check the YES box next to each
> > candidate that you believe would do a better job in the position to which
> > they aspire than you yourself would if you had the appropriate technical
> > competency and stomach for that kind of work.
> 
> Well, to the extent that we're asking voters how well the candidate
> represents our viewpoints, then nobody is more representative than
> ourselves. So your wording turns into a question (in part) about
> competence. You're really asking "Even though this candidate may
> not exactly match my position, is he close enough to that position
> to represent it AND competent enough to do so better than I
> could?"
> 
> But that doesn't match the question that is being asked in my thought
> experiment. The thought experiment asks, "Compared to the field of
> possible candidates, what percentile does this candidate fall in with
> regards to ability to win pairwise majorities?" (It's a question no single
> voter can provide an answer to.) If the field is restricted to the actual
> candidates, then there would be too high a probability of ties for the
> question to be useful, for if there is a 3-member Smith set, each of
> the members would achieve the same rating. Expanding the field to
> a much larger set makes ties very unlikely.
> 
> > >From this vantage point it is clear that your hypothetical standard of
> > comparison method is strategically equivalent to ordinary Approval in the
> > case where f = g , the most democratic case..
> 
> I see your point, but this is a thought experiment about evaluating a
> specific candidate; it's similar to asking the voter what his cardinal
> rating for the candidate is and requires the same degree of honesty.
> It differs from cardinal ratings (and therefore, from SU) on two key
> points:
> 
> 1. Instead of an arbitrary scale, the voter is asked to compare the
> candidate to candidates taken from a large background field. This
> background in effect provides an absolute scale that is grounded in
> something external to the voter. (Asking the voter to use an
> absolute scale that is purely internal would be like using a yardstick
> as the standard for measuring the length of the yardstick.) Also, if
> the background is non-uniform, the scale would become non-linear.
> If there is a rich pool of potential candidates in the policy space
> around voter V and candidate C is not part of that pool, then V will
> give C a lower rating than if that local pool were sparsely populated.
> 
> 2. The method of summing is different than a CR election (or an
> SU evaluation). In CR or SU, each voter returns a single number
> for each candidate, and these are summed over all voters for
> each candidate. What I am talking about is to hold a large
> number of hypothetical pairwise elections between a candidate and
> the background, and each of these elections returns a pass/fail grade
> for the candidate. The candidate with the most passes out of all
> the trials is the best candidate according to this standard.
> 
> > Also, don't just use normal and uniform distributions. Politics isn't very
> > interesting until you get into bimodal (and better) distributions. Any
> > simple minded method will do OK with a single peaked symmetrical
> > distribution, though some will do better than others.
> 
> I suggested uniform distribution because that's something I might
> try as a preliminary test if I ever get around to simulating this. Any
> other distribution could later be substituted for f and g. I think the
> first really interesting case would be single-mode distributions that
> are skewed away from each other. That's equivalent to asking, if
> the politicians (f) don't reflect the makeup of the general population
> (g), how close a result is a given method likely to produce? And of
> course, that represents a very real situation.
> 
> I hadn't given any thought to going beyond single-mode but
> as you point out, that can also make things interesting.
> 
> Richard
> 
> 
>