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
"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
Here's an example set of votes (for a ballot which offers "ABCDE"
Here's the condorcet strengths:
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:
If there was no supermajority, the ballots would look like:
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
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.]
P.S. pseudocode *is* poorly written english.