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

```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.

[I picked this mechanism because it's the first one for which you claimed
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
AEBD
BACED
BEC
C
CABED
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