On Tue, Nov 21, 2000 at 12:30:28AM -0800, Rob Lanphier wrote:
> You guys caught me sleeping. This is the type of discussion I joined the
> list to chime in on.... :)
Heh :)
> On Tue, 14 Nov 2000, Buddha Buck wrote:
> Here's how it would work. Voters rank all candidates or options, but also
> put in a "cut line" above which all candidates/options are approved, and
> below which, no candidates/options are approved. One could create a dummy
> candidate to achieve this if the ballot isn't conducive to the "cut line"
> idea.
Presumably the "further discussion" option that's on all ballots would
work for this?
> In really rare cases this might lead to paradoxical situations where the
> winning option doesn't have the required approval rating, but a lesser
> option does.
Some possibilities:
a) A clear condorcet winner, that doesn't have enough of a
supermajority to succeed.
b) A tie for first place (ie, the schwartz set has two or more
options in it), where "further discussion" is one of the
equal winners, and it pairwise beats whatever is chosen as
the real winner.
c) A tie for first place where all the winners beat further
discussion, but the winner selected by whichever tie breaker's
used requires a supermajority that it doesn't have, and one
of the other winners has all the majority it needs (because
it only requires a smaller one, say)
For (a), I think it's reasonable for further discussion to win: a majority
of people like the idea, but a minority aren't willing to accept it. They
should discuss the matter, or address whatever problems are identified,
and bring it up again later. I think treating this as a win for "further
discussion" is a much better idea than treating it as a win for "no".
For (b), you could end up with a situation where the "winning" choice was
specifically disapproved of by the majority. It would have to be a *very*
close vote, with a very big split in what people prefer for this to happen
though.
There are a couple of ways (c) could come about, I think: either two
options that are supported by largely different groups of people (like
the non-free vote), or two fairly similar alternatives, one of which
is a compromise that's hopefully got more chance of winning because it
has a lower (or no) supermajority requirement. In particular because of
the latter case, I'm inclined to think that the option that came second
should win, since the one that came first couldn't.
> However, my brain hurts trying to come up with the example,
> so you're going to half to ask someone smarter with more time on their
> hands. :) If one really wanted to handle this corner case, one could
> call for a second vote among all options that had the required approval
> score, or one could reverse the order of application of Approval and
> Condorcet, and use Condorcet as the tiebreaker among all options that have
> supermajority approval.
One possibility might be to do something like:
* eliminate all options not in the schwartz set
* eliminate all options without the required (super)majority over
further discussion
* if there are no options left, further discussion wins
* if there are options left, use Tideman/Schulze or something
to choose between them (finding a new Schwartz set as necessary)
noting that any of the remaining options are legitimate winners [0]
I'm inclined to think a second vote would probably be something to avoid
where possible... It'd be interesting to see what happens to all the
fairness proofs for condorcet voting schemes when a "further discussion"
option that wins whenever it possibly can is thrown into the pot.
Cheers,
aj
[0] Further discussion won't ever win here with a condorcet scheme since
the only remaining options are those that beat further discussion in
pairwise contests (since otherwise they wouldn't have the required
majority, let alone supermajority).
--
Anthony Towns <aj@humbug.org.au> <http://azure.humbug.org.au/~aj/>
I don't speak for anyone save myself. GPG signed mail preferred.
``We reject: kings, presidents, and voting.
We believe in: rough consensus and working code.''
-- Dave Clark
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