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Re: Hybrid Theory

On Mon, Dec 09, 2002 at 03:20:20AM +1000, Anthony Towns wrote:
[what are the underlying things we're trying to achieve]:

> Here's a start:
> 	(0) The default option should be to leave the vote unresolved;
> 	    if people wish to actively preserve the status quo, they should
> 	    ensure that is listed as a separate option on the ballot.
> 	(1) We want a voting system that handles quorums.
> 	(1a) Quorums are handled on a per-option basis.
> 	(1b) Electors are counted toward the quorum if they vote, and if they
> 	     rank the option above the default option.
> 	(2) We want a voting system that handles supermajorities.
> 	(2a) An option requiring an N:1 supermajority means that 1/(N+1) of
> 	     the voters may block that option from passing.
> 	(2b) An option that does not meet its supermajority requirement does
> 	     not affect the outcome of the vote.
> 	(2c) Options with a supermajority requirement should be treated as
> 	     similarly to other options as possible.
> 	(2c.i) The supermajority requirement should be satisfied by more
> 	       than N/(N+1) voters ranking that option above the default
> 	       option.
> 	(2c.ii) All other comparisons, including transitive comparisons,
> 		should not be scaled.

Here's my view:

[A] The default option represents voter approval of the ballot -- options
ranked below the default option are options that voter would rather have
been left off the ballot, options ranked above the default option are
options the voter considers acceptable.

[B] We want to use quorum and supermajority.

Looking back at your items,

(0) follows from [A] as options which are not on the ballot
can not be resolutions from that ballot.

(1) follows from [B].
(1a) and (1b) Follow from [A] and [B}.

(2) follows from [B].
(2a) stands alone, and seems fine to me.
(2b) and (2c) stand alone and conflict with each other.
(2d) follows from (2a).
(2e) follows from [A] and (2a).

Interestingly enough, the problem which has lead to all these voting
mechanics proposals very much has to do with the conflict expressed here
between (2b) and (2c).

As an aside: I have been to trying find a theory for using condorcet
to choose between options with sufficiant approval with respect to the
default option.  My requirement has been: don't give bad results for
any of the cases people have brought up where earlier systems could not
be justified.  I've been expressing my understanding of this theory as
voting mechanics drafts.

> In particular, dropping the options that don't meet their supermajority
> requirement before applying CpSSD meets the above criteria better than
> strengthening the default versus supermajority-option defeat: it avoids
> scaling transitive comparisons and ensures that options that don't meet
> the supermajority requirement don't prejudice other options. There may
> be other reasons to go the other way, but if we're going to stop going
> round and round in circles on this, we need to be *explicit* about them.

I've rejected this idea because it introduces
problems which Buddha illustrated in

I think it's better to strengthen the defeat of the default vs
supermajority option and to wait to drop related supermajority options
until the point where the presence or absence of this scaled defeat
would cause a problem.

> Raul, can you give a good a priori reason for declaring the vote:
> 	30 ABD  (A requires a 2:1 supermajority, B a simple majority)
> 	10 BDA
> 	10 DAB
> to be a draw between B and D [0], when the vote:
> 	40 BD   (ie, how the vote would've gone if A had not been an option)
> 	10 DB
> would have been a clear win to option B?

No, I can't give a good a priori reason for declaring this to be a tie
between D and A.

As an aside, the message you're responding to has an explicit example
with a clear win for option B where A requires 2:1, B 1:1, D is default,
with 1 BDA and 1 DAB and 3 ABD votes.

> [0] There's a tie amongst B,D,A, and A defeats B 40:10 and B defeats D
>     40:10 are equally weakest defeats, so both are dropped, if A is
>     kept around.

As an aside, the system I proposed earlier today drops A for exactly
that reason.


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