Re: Condorcet Voting and Supermajorities (Re: [CONSTITUTIONAL AMENDMENT] Disambiguation of 4.1.5)
Dear Buddha,
you wrote (14 Nov 2000):
> Could someone explain to me, in simple terms, how
> Condorcet-based voting schemes work in the face of
> a supermajority requirement?
>
> My understanding of Condorcet is that a ballot like
> Anthony Towns used as an example ("Remove non-free
> // We Love non-free! // Status-quo // Further
> discussion") would be, during the first analysis,
> treated as if it were 6 separate 1-on-1 votes, with
> each of the four choices paired against each of the
> remaining 3. If any of the four wins all three of
> the 1-on-1 votes it's part of, it wins the full
> balloting. Otherwise, we use a fall-back resolution
> method (of which there are several varieties in the
> literature to choose in advance from).
>
> This works fine if all the options required a plurality
> to win (note: I'm not even sure if "majority" or
> "plurality" are appropriate descriptions of the victory
> condition in Condorcet-based schemes). The system is
> balanced.
>
> But if one of the choices explicitly requires a 3:1
> supermajority to work, I don't see how it works quite
> so well.
To my opinion, one should at first check which proposals
are "available" (i.e. which proposals can be passed without
violating the supermajority requirement) and then one
should use a Condorcet method amongst these "available"
proposals.
Definition ("available"):
"X >> Y" means that a supermajority of the voters
strictly prefers proposal X to proposal Y.
"There is a qualified beat path from proposal A to
proposal B" means that
(1) A >> B or
(2) there is a set of candidates C[1],...,C[n] with
A >> C[1] >> ... >> C[n] >> B.
"Proposal D is available" means that there is a
qualified beat path from proposal D to the status quo.
Explanation:
If and only if there is a qualified beat path
D >> C[1] >> ... >> C[n] >> StatusQuo from proposal D
to the Status Quo, then proposal D can be passed
without violating the supermajority requirement.
Those voters who prefer proposal D to the Status Quo
will at first propose proposal C[n] to the Status Quo
so that proposal C[n] becomes the new Status Quo.
Then these voters will propose the proposals
C[n-1],...,C[1] successively so that C[n-1],...,C[1]
successively become the new Status Quo wihout
violating the supermajority requirement. Then
they will propose proposal D so that proposal D
becomes the new Status Quo wihout violating the
supermajority requirement. Therefore the above
mentioned definition of "available" proposals
makes sense.
The above mentioned definition of an "available" proposal
is very weak. Even proposals that are Pareto-inferior to
the Status Quo (**) can be "available" due to the above
mentioned definition. But this is not a problem at least
as long as the used Condorcet method guarantees that such
a proposal cannot be chosen.
Markus Schulze
(**) "Proposal Z is Pareto-inferior to the Status Quo"
means that every voter strictly prefers the Status Quo
to proposal Z.
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