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Re: Constitutional amendment: Condorcet/Clone Proof SSD vote tallying

On Fri, May 23, 2003 at 12:54:50AM +0200, Jochen Voss wrote:
> I fully agree.  But then the per-option quorum has this problem, too.
> And here it is harder to understand (see my example) and more relevant
> (can occur for votes with many voters) than in the case of global
> quorum.

> This problem is explained at
>     http://www.mathematik.uni-kl.de/~wwwstoch/voss/comp/quorum.html
> there you will find an example, where voting in favor of
> some option B causes B to loose!  The effect is caused by
> the quorum.

Ugh, that's an overcomplicated example. Here's a simpler one:

Three options, A, B and D (the default option). Quorum is 10. Votes are:

	9 ABD
	4 BDA

A defeauts B, 9:4; B defeats D, 13:0, A defeats D, 9:4. A is dropped because
of quorum, B wins. One more person votes:

	9 ABD
	4 BDA
	1 BAD

A defeats B, 9:5; B defeats D, 14:0, A defeats D, 10:4. A isn't dropped,
and wins. Voting "for" B, thus causes A to win.

However, it's not really that simple. There were two ways that last person
could've voted: "I prefer B to A, and I find both acceptable", or "I prefer
B to A, and I find A unacceptable". The first was the way he actually voted,
the latter was the way the other four folks in favour of B voted. 

If only nine developers find A acceptable, well, it deserves to lose.

This conclusion,

] The example shows that the introduction of the per-option quorum
] requirement breaks monotonicity in a hard-to-predict way.

just seems wrong. It's easy to predict the way the per-option quorum
affects things: it does it in the _exact_ same way as if the option had
failed to acquire the requisitie number of seconds in the first place.

And, as I've already posted elsewhere, you'll note there's no problem
at all here if number of votes received is twice the quorum, which,
historically, it almost always is.


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

  ``Dear Anthony Towns: [...] Congratulations -- 
        you are now certified as a Red Hat Certified Engineer!''

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