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
