[EM] serious strategy problem in Condorcet, but not in IRV?

[Forest Simmons]

On Wed, 20 Aug 2003, Alex Small wrote:

> Forest Simmons said:
> > Is it possible that increasing resistance to manipulation requires a
> > sacrifice in the performance of the method in the zero information case?
> >
> > In other words, manipulation resistance requires a thick skin that puts
> > a limit on the possible sensitivity and responsiveness of the method to
> > sincere ballots.
>
> Well, if it isn't responsive to changes in the electorate, then it isn't
> very responsive to the ballots received, be their sincere or insincere.

Here I was thinking in terms of signal filters.  High pass filters are
more responsive to the signal than low pass filters, but also let more
noise through.

Election methods are like filters.  The inputs are ballots that reflect
the "noise" that the voters are exposed to as well as the signal, the
truth that they are able to partially discern (mixed in with all of the
noise).

A simpler example is measuring the length of a board.  Each voter casts a
vote which is his measurement of the length.  An average, median, mode,
midrange, or some other compromise value is taken as the best estimate of
the true length.

Suppose that the length of the board is slowly changing.  As new
measurements come in, they can be averaged with recent estimates by a
digital filter y[n+1]=alpha*y[n]+beta*x[n+1] , where alpha+beta=1.

If alpha is large compared to beta, the filter is low pass. It responds
slowly to changes in the length of the board, but it filters out the
measurement errors well.

If alpha is small compared to beta, the filter has greater responsiveness,
but allows measurement errors to have greater influence, as well.

In the context of elections, the electorate changes gradually with the
times.  Approval voters, at least, use previous election experience to
help them judge where to put their cutoffs, especially if there are no
reliable comprehensive polls.

It seems to me that there is a trade off in responsiveness and noise
filtering capability in election methods analogous to the same kind of
tradeoff in signal filters.

Forest