[EM] Arrow's axioms

[Forest Simmons]

On Fri, 5 Mar 2004, Ken Johnson wrote:

<snip>

>
> Kevin,
>
> It isn't evident. It is reasonable to stipulate non-dictatorship
> axiomatically because this principle is non-controversial and nobody is
> championing dictatorship as a viable election method. On the other hand,
> if the objective of elections is to maximize "social utility", then CR
> probably represents the simplest and most natural way to measure (or at
> least define) social utility, and it should not be excluded from
> consideration axiomatically.

We can use a less fuzzy concept than "social utility" to be measured by CR
ballots.  If we take the CR values to be probabilities of adequate
representation, then the sum over all ballots of the CR for a candidate is
the expected number of voters that will be adequately represented by the
candidate.  We might better call this expectation "social representation"
rather than "social utility."

Since elected candidates are supposed to represent the voters (not only
the big campaign contributors) this expectation would seem to be an
appropriate quantity to maximize.

When my students show their work on a problem, I assign them partial
credit according to the probability that they could work another similar
problem without error.

Then when I add their partial credit to the number of problems that they
did correctly, the resulting sum is the number of problems that I would
expect them to get right on a similar test (based on their current
ability).

If I divide by the number of problems on the test to get a number between
zero and one, this average is an estimate of the probability that this
student could adequately solve a randomly chosen problem on a similar
test.

Similarly, the average CR (on a scale of zero to 100%) for a candidate
could be interpreted as an estimate of the expected probability of
adequately representing a randomly chosen voter.

Forest