This is just a brief preliminary reply to Alex's message about
Approval with 2 ballotings.
I agree that for replacing municipal elections that now use Runoff,
people likely will be reluctant to give up the top-2 runoff.
I once suggested letting all the candidates into the 2nd balloting,
so that
Dear Forest,
you wrote (31 Dec 2002):
> Determining the Kemeny order from ranked preference ballots suffers the
> "combinatorial explosion" because there is no way of getting around one by
> one testing of most of the N! permutations of candidates in order to see
> which of these permutations mini
Linear algebra, graph theory, probability, statistics, measure theory,
metric spaces, combinatorics, piecewise linear topology, linear
programming, multivariate calculus, mathematical logic and set theory,
theory of algorithms, etc. are all good for the tool box.
Most of the minimization can be do
Forest Simmons said:
> Note that with a 50% Approval cutoff (and no other limitation on the
> number of candidates surviving to the runoff) Approval wouldn't be such
> a bad filter after all. If Larry, Curly, and Moe can muster 50%
> Approval, that means that more voters want them to be in the run
This sounds like a good idea to me for situations in which it is not too
inconvenient to do an actual two stage process.
As Alex said in his "filter" posting, if we're going to go to all the
trouble of having primaries, why not do them right?
Using two stage cumulative approval we could say that
Somewhere up this thread Blake Cretney brought up the idea that some
Condorcet methods may satisfy a certain modified consistency criterion.
If the method gives a complete ranking as output, and if two subsets of
ballots produce the same ranking, then the output based on the union of
the two subse
On Fri, 27 Dec 2002, Alex Small wrote:
>
> Another point is that Approval is a very BAD idea for the primary. Say
> that we're narrowing it down to 4 candidates. The largest faction could
> all approve their favorite and the 3 Stooges. The second stage would
> likely include those 4 candidat
Your example is correctly done.
Despite the intractability of the method for large numbers of candidates,
it seems like an ideal method for some situations.
One application could be in choosing between several orders that have been
found by other means.
[The main computational difficulty of find
Adam's response is precisely correct and well written.
I would add only this:
Determining the Kemeny order from ranked preference ballots suffers the
"combinatorial explosion" because there is no way of getting around one by
one testing of most of the N! permutations of candidates in order to see
Adam Tarr said:
> It seems from previous posts that Donald and other IRV backers do not
> really see a distinction between the left, center, right example and
> the one I just gave. In their minds, the center candidate is weak,
> just like the Green and Libertarian candidates I show above. The
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