On Thu, Nov 30, 2000 at 02:34:58AM +1000, Anthony Towns wrote:
> The other, independent, question is what to do when the Condorcet winner
> doesn't meet it's supermajority requirement. That is, a simple majority
> of people prefer some particular option to all others, but there isn't a
> supermajority that's willing to accept it. There are two ways of handling
> it I can think of: either try the next preferred option, or go back to
> further discussion.
>
> My initial impression was that further discussion was the safer choice,
> but I'm not convinced of that, at the moment.
One problem if you don't have further discussion win more often than it
perhaps should is as follows:
Suppose you have three options on your ballot, A, B and F. A requires a
3:1 supermajority. Sincere preferences are:
60 people order the options A, B, F
40 people order the options B, A, F
in which case A would win by dominating B 60:40 and F 100:0 (33.3:0). But
if the 40 people voting BAF instead insincerely change their vote to:
40 people order the options B, F, A
then the order becomes:
A dominates B, 60 to 40
B dominates F, 100 to 0
F dominates A, 40 to 33.3
if you then go ahead and simply ignore A, the B votes win.
Being able to change your lower order preferences and force your first
preference to win (in spite of only minority support) is considered to
break some fairness criterion or another.
OTOH, letting A win, even though it doesn't meet its supermajority
requirement would seem stupid (although it may not be, I dunno).
Which at least seems to mean we ought to bias towards F if F appears in
the Smith set. There's probably no need to bias towards F more than that
though, I guess.
Cheers,
aj
--
Anthony Towns <aj@humbug.org.au> <http://azure.humbug.org.au/~aj/>
I don't speak for anyone save myself. GPG signed mail preferred.
``Thanks to all avid pokers out there''
-- linux.conf.au, 17-20 January 2001
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