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Re: Another proposal.

On Mon, Nov 18, 2002 at 05:28:37PM -0500, 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.  

Well, it's important to be clear on that before we start talking about how
to implement it, IMO.

First, I agree with Raul on this part:

> 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?

That's entirely irrelevant. If we ever have votes without those requirements,
we'll be doing straight CpSSD anyway.

But, anyway.

Supermajority considerations don't have any precedent in Condorcet theory
that I've seen (and I have looked, although I'm by no means an expert on it
or anything), so anything we do here is going to veer away from the main
track of that theory.

To work out what it's for, we need to look at normal votes, where you have
a single option that you can say "yay" or "nay" too. Normally, people just
compare the number of yays to the number of nays, and whichever there
are more of, that's the way we go. There are two alternatives though:
a supermajority can be required, in which case there need to be N yays,
for every nay for it to past; or unanimous votes, where there can't be
any nays at all.

The effect of both these alternatives is to allow a minority --
possibly a small minority, possibly a minority of one -- to block the
vote. In traditional circumstances this could easily require you to
vote insincerely: if you prefer some other option, but know that it
won't pass, you can't express that opinion by a "nay" vote, since the
effects of any nay vote are magnified.

What we'd like to do is something similar:

	* allow a pre-determined minority to block a vote.

	* allow them to express sincere preferences between options,
	  without being forced to invoke their minority block, _or_
	  being forced not to invoke their minority block.

We'd also like it to be fairly intuitive for people to do this.

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

I don't really think this is... meaningful. The default option isn't
something you can be particularly "sincere" about, and the entire point
of supermajorities is so you can voice a "strategic" opinion, to block
something that you don't like, but that the majority prefers.

The only real issue is the one where your sincere vote:

	A S D    (normal option, supermajority option, default option)

will cause S to win (thanks to you letting it pass its supermajority), but
your insincere vote:

	A D S

will cause A to win (thanks to S being eliminated early, by not passing its

The only case in which that can happen is if you have a circular tie:

	S > A, A > D, D > S (scaled)

But in that case, you're really just ending up with the same problems you get
in ordinary Condorcet voting, where the circular tie:

	20 A B C (X)
	25 B C A
	30 C A B

resulting in (B>C:45:30, A>B:50:25, C>A:55:20) C winning, where the folks
marked (X) can change their vote to "B A C" and improve the outcome from
their sincere POV.

Which is to say: I can't see any reason why "strategy" is a bad thing in
this case -- if a superminority of voters think an option is bad enough
that they want to vote strategically against it the whole *point* of a
supermajority requirement is to let them be successful at it.

And likewise, I don't think we're encouraging insincere voting with this,
but rather that we're just unable to minimise it further.

> 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.

We're not introducing special rules because the default option is
"special", we're making the default option special since it seems the
best way to handle the special rule we want.


Anthony Towns <aj@humbug.org.au> <http://azure.humbug.org.au/~aj/>
I don't speak for anyone save myself. GPG signed mail preferred.

 ``If you don't do it now, you'll be one year older when you do.''

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