Re: Another proposal.

[Andrew Pimlott <andrew@pimlott.net>]

On Tue, Nov 19, 2002 at 02:54:50AM +1000, Anthony Towns wrote:
> On Tue, Nov 19, 2002 at 12:06:20AM +1100, Clinton Mead wrote:
> > Andrew Pimlott wrote:
> > > So for example, the clause, in most drafts, that first eliminated
> > > options that were defeated by the default option, was a direct
> > > invitation to insincere strategic voting. It would encourage voters
> > > to put the default option second, in an attempt to knock out the
> > > other candidates early. Exactly what we're trying to avoid with the
> > > Condorcet method.
> 
> But it's exactly what we're trying to achieve with the supermajority
> requirement, isn't it? Allowing voters to vote strategically so as to
> knock out candidates they don't like?

I confess I'm not sure what we're trying to achieve with the
supermajority requirement.  Based on the discussion, I don't think
I'm alone.

However, I don't see why you'd want to encourage insincere (ie,
strategic) voting, ever.

Note that the issue of strategic voting arises with most of the
proposals, even even absent supermajority or quorum requirements.
So I think it's worthwhile to ignore supermajority and quorum issues
for a moment, and consider only the affect of the default option on
"even" votes.

Consider the election between candidates A and B, with default Z.
Say the sincere preferences are

    40  A B Z
    25  B
    35  Z B A

N(i,j) is the number of voters who prefer i to j.

                    A   B   Z
                A      40  40
    N(i,j) =    B  60      65
                Z  35  35

B is the condorcet winner.

Suppose the A B Z voters either truncate their vote to A, or switch
to A Z B.  In straight Condorcet/CSSD, this causes either B or Z to
win (respectively); so strategic voting by A partisans fails.

However, if you add the rule that anyone losing pairwise to Z is
eliminated early, B would be eliminated early, and A would win.  So
this is an example where the special rule involving the default
option encourages strategic voting.  And I don't think you could
argue that this is a good thing.

Now that was just one example; I'm not saying I proved anything.
However, straight Condorcet/CSSD is known to be strategy-resistent,
and variants with special rules are not.  So I think we should
resist the temptation to introduce special rules, even if our
intuition tells us the default option should be special.

To state my view directly, I strongly feel that in an election with
no supermajority or quorum requirement, the default option should be
treated as any other.

Does anyone have a good argument against that?

Andrew