On Mon, May 26, 2003 at 12:14:55AM -0400, Andrew Pimlott wrote:
> 1. Approval voting has obvious incentives to strategic voting.
Yes, that's true. There are two responses to this: one is that the
benefits are worth the risks; the other is that (hopefully) the incentives
to vote honestly outweigh the incentives to vote strategically. The
addition of approval voting (which is to say, the default option) only
comes into play in the following ways:
* failing to meet quorum
* failing to make a majority
* failing to make a supermajority
Meeting quorum should be easy for the supporters of an option to ensure
-- it's a fairly low requirement, and with a reasonable turn out, if
any option meets its quorum requirement, the Condorcet winner will.
If an option doesn't make its supermajority by strategic voting,
well, that's something we just have to accept. Making changes to the
constitution is meant to be hard, and if people aren't positively for it,
then that's somewhat too bad. If the strategic voters win, then they can
continue acting strategically in future votes, and have a stable result.
The only time voting against an option that only requires a simple
majority is useful is if you can arrange for "A beats B, D beats A,
B beats D" to be the outcome, thus getting A dropped, and B winning.
However, to manage this, at least some proportion of the majority that
thinks "A beats B" voters has to prefer making no decision to *either*,
which seems a difficult thing to rely on; and if it's the case, well,
at least we're acting on the votes we actually receive.
Note also that this isn't exactly a combination of approval and condorcet
voting. If it were, you could mark, say:
[1] [N] A
[2] [Y] B
which would say something like "I hope A will win, then get shot down;
but if B wins, well, okay, I can accept that". That sort of strategy
isn't possible -- the closest you can come is an honest vote for "let's
not decide yet".
> For example, consider the biases
> introduced if there is a contingent of "moral" Debian developers
> who vote sincerely, and another of "pragmatic" developers who
> vote strategically.
I'd be interested in seeing a scenario of a practical strategy that can
get an option B to win against a 2:1 supermajority option A, that involves
less than, say, 1/4 of voters acting strategically. I think you'll have
to end up relying on fairly specific behaviours of the remaining 3/4,
and without perfect knowledge, end up with roughly equal odds that B will
win or that there'll be no decision (in the latter case, your sincere
preferences end up thwarted). Basically, I don't think voting strategically
will actually buy you significantly more assurance of a win.
> You could (and I think you have) also argue that these
> discontinuities don't happen in realistic scenarios. But in
> making this claim, you have implicitly ignored problem 1.
For quorum, the fix is to have more people vote, which realistically
has never been an issue, and is one that can't be defeated by opposing
strategists.
> I
> think that if many voters use strategy, such outcomes are
> plausible (perhaps not for the quorum case, but for the defeat
> by the default option case).
The question is whether, in particular (realistic) circumstances, some
given strategy is more likely to produce a favourable outcome than
voting sincerely.
I can't produce any that convince me, but I'm not up to a disproof
atm either.
How do you measure the favourability of an outcome? If my sincere
preference is A > B > C > D, and the probality of A is p_a, B is p_b,
C is p_c, and D is p_d, what's the total favourability? 3*p_a + 2*p_b
+ p_c? (Which is very Borda-esque) Or 3 - p_b - 2*p_c - 3*p_d? Or
something else?
Cheers,
aj
--
Anthony Towns <aj@humbug.org.au> <http://azure.humbug.org.au/~aj/>
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