Re: [spoon-discuss] Re: [Spoon-business] Let's play the Voting Game!

[Rob Speer <rspeer@xxxxxxx>]

On Sat, Jan 31, 2004 at 01:57:00AM -0500, Rob Speer wrote:
> Darn. It would have been fun. It makes me want to find the Nash
> equilibrium strategy.
> 
> Perhaps all five proposals could be made into non-proposals that you
> "vote" on using a different mechanism, and created with a real proposal.

Here goes. I can't be mathematically rigorous because there are
32^(number of voters) possible outcomes, but I think I'm looking at the
important ones.

There's no real advantage to voting no on spam, unless you have a really
good strategy involving voting no on more than one proposal. I don't see
one. So assume it passes, and you get 30 points for voting no on only
one proposal. Any winning strategy then has to do that.

With everyone only voting no on one proposal, at most one proposal can
fail. There's the odd chance that foo passes, but not with 2/3, and
something else fails too; I'm not considering that, because it would
require a crazy mix of strategies.

Here's a table with the expected value if the proposal on the column is
the only one that fails, and the proposal in the row is the one you
voted against ('f23' means foo fails to get 2/3 but passes):

    none f23 foo bar baz qux
foo   65  25  30  80  40  80
bar   65  65  60  80  30  30
baz   55  25  60  70  30  70
qux   55  15  60  70  30  70
	
Voting against qux is dominated by voting against baz, so nobody votes
against qux:

    none f23 foo bar baz
foo   65  25  30  80  40
bar   65  65  60  80  30
baz   55  25  60  70  30 

Now baz is dominated by bar.

    none f23 foo bar
foo   65  25  30  80
bar   65  65  60  80

And now bar dominates foo.

The result: everyone who votes rationally gets 80 points.
-- 
Rob Speer

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