Re: Condorcet Voting and Supermajorities (Re: [CONSTITUTIONAL AMENDMENT] Disambiguation of 4.1.5)

[Raul Miller <moth@debian.org>]

This is a drastically chopped down version of my response to the
Buddha/Eudora message trilogy.  I want to focus on one issue.

On Wed, Nov 29, 2000 at 06:17:13PM -0500, Buddha Buck wrote:
> Option:  Smith/Condorcet
> 
> Of the n options in the Smith set, order the n*(n-1) pairwise results by 
> number of votes for the winning choice, strongest to weakest. (e.g., if A 
> beat B by 100:50, and B beat C by 76:74, order them as AB first, BC second, 
> because 100 is bigger than 76).
>
> Drop the weakest defeat iteratively until one option is unbeaten.  That 
> unbeaten option is the winner.
>
> Advantages: Variants have been studied for 200+ years.
> Disadvantages

[I picked this mechanism because it's the first one for which you claimed
"no disavantages".  I believe that your "disadvantages" for these various
methods are incorrect in a large number of cases, but I don't feel like
tackling that issue point by point.]

I'm trying to figure out how to implement the concept of "supermajority"
in this voting system.  I don't think it can be done in a reasonable
fashion, because in this system (and many of the others), you're voting
against yourself.

Here's an example set of votes (for a ballot which offers "ABCDE"
as options):

ACBDE
AD
AEBD
BACED
BEC
C
CABED
CADB
CDA
E

Here's the condorcet strengths:

  7:2 C:D 
  7:2 A:E 
  6:1 A:D 
  6:2 A:B 
  6:3 C:E 
  5:2 B:E 
  5:3 C:B 
  5:3 B:D 
  5:4 E:D 
  5:4 C:A 

C wins (it's unbeaten).

Now, if we introduce a 3:1 supermajority which only affects C, C loses:

  7    : 2      A:E 
  6    : 1      A:D 
  6    : 2      A:B 
  5    : 2      B:E 
  5    : 3      B:D 
  5    : 4      E:D 
  4    : 1 2/3  A:C
  3    : 1 2/3  B:C
  2 1/3: 2      C:D 
  2    : 3      C:E 

And, that makes sense, because I constructed that set of votes with
a linear random number generator.

But, let's try a simpler multi-option ballot, with everyone in favor.
Ballot: ABC, 3:1 supermajority required for A, 10 votes, all cast as:
ABC.

If there was no supermajority, the ballots would look like:

10:0 A:B
10:0 B:C
10:0 A:C

And you can figure out by inspection that A wins.

However, with the 3:1 supermajority which affects A, you get:

10    : 0  B:C
 3 1/3: 0  A:B
 3 1/3: 0  A:C

B wins.

There is a similar flaw even without supermajority (by indicating a
second or even third preference, I can tip the balance in favor of another
option, causing it to win), but that's a bit more subtle to talk about.

What's interesting is that most of the voting mechanisms you posted
about share this characteristic about supermajority votes.  [Of course,
the characteristic goes away if you offer a simple 2 choice ballot,
because in that circumstance they're all equivalent.]

-- 
Raul

P.S. pseudocode *is* poorly written english.