Re: supermajority options

[Andrew Pimlott <andrew@pimlott.net>]

On Tue, Nov 19, 2002 at 05:54:30PM -0500, Raul Miller wrote:
> [2] Discard the election if the winner doesn't meet supermajority.

This doesn't seem too bad, but ...

> Perhaps, if the ballot has nondefault options with differing supermajority
> ratios, immediately hold another election using only the options with
> a lesser supermajority ratio.  I'm leaning towards this at the moment.

with this addition, it has similar implications to [5].

> [3] (current draft) Only consider supermajority in terms of defeating
> the default option.  This gets a bit confusing to think about in the
> context of transitive defeats.
> 
> [5] (Nov 16 and earlier drafts) Discard options which don't satisfy
> supermajority before considering transitive defeat.  This gets a bit
> confusing to think about in the context of transitive defeats.

This is aj's proposal, but to clarify, it also includes discarding
options that don't require supermajority, but are beaten by the
default.

Here is an example--which happens to be much less contrived than
most of those we've been throwing around.  A requires 2:1
supermajority, and sincere preferences are:

    60 A B D
    40 B A D

This is a win for A under all of the above methods.

Under aj's proposal, if partisans of A and B both reverse their
second choice, the election is a stalemate.  If everyone agrees
something must be done, it comes down to who will flinch first.
That is why I feel that approach gives too much power to the default
option.

You could improve things a bit by only discarding options requiring
supermajority.  At least then, only B's partisans can knock out A
early, causing B to win.  This seems to be what aj wants.  You might
support this if you feel we should generally try "normal" measures
before "extreme" measures, even if the extreme measures are more
popular than the normal.

If, however, you feel that the more popular measure should win even
if it is "extreme", then the default option is still too powerful.
In fact, after thinking about the above example (consider what
happens when one or both groups reverse their second and third
choices), I think the current draft still gives too much power to
the default.  I would adjust it so that if an option fails to get
its required supermajority, the count preferring the supermajority
options should be divided by the supermajority ratio, rather than
the count preferring the default be multiplied.  (If an option does
get its supermajority, I think the could preferring the default
should still be multiplied.  I think.)

Consider, under the current draft, what happens if B's supporters
reverse A and D, and A's supporters defend by truncating:

    60 A
    40 B D A

Then

    A > B (60, 40)
    B > D (40, 0)
    D > A (80, 60)
    
Because the D > A victory has been inflated, D wins.  Under straight
Condorcet/CSSD, this can't happen[1].  If instead we make my change,

    A > B (60, 40)
    B > D (40, 0)
    D > A (40, 30)

And A wins.  In fact, A would win even without truncating.  So I
believe this is the most strategy-resistant approach.

Andrew

[1]  http://www.electionmethods.org/evaluation.htm :

    Compliance with SDSC means that a majority never needs any more
    than truncation strategy to defeat a particular candidate, even
    when countering offensive order reversal by that candidate's
    voters.