Re: Dec 15 voting amendment draft

[Raul Miller <moth@magenta.com>]

[First off, I should apologize: I've let this whole issue slide for the
last month.  I'm having a terrible time getting decent connectivity,
but it's my fault for letting that get in the way.]

On Fri, Feb 14, 2003 at 05:33:37PM +1100, Clinton Mead wrote:
> Monotonicity Criteria.
> 
> If
> (i) There is an election X in which option A wins,
> (ii) There is a vote V that ranks option B above option A.
> (iii) There is an election Y which is identical to election X except 
> that vote V has option A and option B swaped on their preference list.
> then
> Option A must win election Y.

I have a few quibbles about quantifiers (for this to be correct,
(ii) should begin "For any vote V" and (iii) should begin "For
all elections Y"), but essentially this is correct.

> Smith Criteria.

That definition was also too relaxed -- mind you, in this relaxed form
the proposal complies with this criteria where if it was expressed in
exact form the proposal wouldn't.  But I guess it doesn't really matter,
since that's not what Clinton is writing about.

> Also, another criteria.
> 
> Participation Monotonicity.
> 
> If
> (i) There is an election X in which option A wins.
> (ii) There is a vote V ranks option A over option B.
> (iii) There is an election Y identical to election X except that it has 
> an additional vote V.
> then
> Option B must not win election Y.

I did a web search on "participation monotonicity", the only hit I found
was http://www.wiwi.uni-bielefeld.de/~imw/papers/332/convexfuzzygames.pdf

Where did you find this criteria?  [Did you make it up?]

One way of modifying the current proposal to satisfy this criteria
would be to make quorum and supermajority failures be transitive.  But,
if you recall, my last attempt at that violated monotonicity (a much
worse failing, in my opinion).  Also, Anthony Towns has made a fairly
convincing case that supermajority failures should not be transitive.

In my opinion, "participation monotonicity" is something we should
minimize, but I'm not convinced we should entirely eliminate it -- I
don't think it's more valuable than monotonicity, quorum, supermajority,
nor than preference ranking of options (nor than condorcent voting
for elections where all votes satisfy quorum and supermajority), and I
think we'd have to effectively give up some or all of these to guarantee
"participation monotonicity".

That said, if you can show that the Feb 7 proposal does not minimize
failure along this dimension within the above constraints, or if you
can show that there's a better set of constraints, I think we'd all be
interested in hearing about that.

Thanks,

-- 
Raul