[EM] PR-STV with approval based elimination

[Raph Frank]

A nice feature of PR-STV is that it still meets the Droop Criterion no
matter who you pick to eliminate in rounds where no candidate meets
the quota (assuming you don't eliminate an elected candidate).
However, there doesn't seem to be much discussion on using a better
elimination method.

The eliminate worst candidate rule, means that PR-STV collapses to IRV
in the single seat case.

A simple modification would that voters cast 2 ballots, an approval
ballot and also a ranked ballot.

The method would proceed as normal except that in elimination rounds,
the least approved non-elected candidate would be eliminated.

The means that assuming that voters only approve candidates from
within their own faction, then the intra faction election method would
be approval voting, even though PR-STV is used to allocate ensure that
the result is proportional.

Another option would be to have the voter submit a ranked ballot and
also have an "approval threshold" candidate.  All candidates ranked
higher than that psuedo-candidate would be considered approved.
However, that gives voters less freedom to approve across party
boundaries (or less freedom to interfere with who is elected for other
parties, depending on your viewpoint).

It may have the effect of electing the most centerist of each party's candidate.

In the single seat case, this would yield a hybrid approval/IRV
method.  If no candidate gets a majority, the least approved candidate
is elected.  An approval winner who is also the condorcet winner is
guaranteed to win.