[EM] Condorcet as a way of getting around path dependence
km_elmet at t-online.de
Sun Jan 26 05:18:20 PST 2014
I've been thinking a bit more about the increasingly complex CPO-SL
method I posted, and I think I see a more general pattern.
That is, one can get around path dependence issues by considering every
possible path and then solve by a Condorcet method. More abstractly, one
could consider the matrix as a two-player game where one player proposes
a particular way of doing (whatever it is that suffers from path
dependence). Then the other player proposes a second way, and the winner
is decided according to some criterion. If there is a CW, it will be the
dominant strategy: i.e. anyone who picks that particular strategy will
win against every other strategy.
That might be a bit too abstract, though. So let's consider ordinary
single-winner Condorcet as an IRV version of the above.
The reasoning is simple: ordinary IRV (and generally, all elimination
methods based on weighted positional systems) exhibit the problem that
who is eliminated at stage n depends on who were eliminated at stage
(n-1). (This leads to IRV's sensitivity on initial conditions, its
"chaos" that is easily seen in Voronoi diagrams.)
So one could imagine someone thinking: "Okay, who is left at the end
depends on who we eliminate before we reduce to the one-candidate case.
So let's consider every possible way of eliminating candidates so that
only one is left. Obviously if we're free to specify the ordering, it
doesn't matter whether we eliminate X and then Y later or vice versa.
But we can only tell whether this order is more justified in relation to
another order that leaves someone else as the last candidate standing".
Then that leads right to a game interpretation: "I'm going to eliminate
everybody but X, he's going to eliminate everybody but Y. If we're going
to compare our outcomes, we both need to eliminate everybody but X and
Y, and then we'll check who gets the most points on the most ballots".
Because the reduction is to a two-candidate election, fortunately, the
weighted positional system no longer matters and we get plain old Condorcet.
Now, I'm not going to assume that this is how Condorcet came about in
the first place, but if that is a valid interpretation, then we can
extend it. Multiwinner methods based on elimination are easily "fixed"
this way: STV becomes CPO-STV and Sainte-Laguë/Webster becomes CPO-SL.
Unfortunately, I suspect that setwise generalizations of multiwinner
methods would be too complex for ordinary voters to understand. That
might in itself not be a problem (just consider New Zealand's use of
Meek), but again, I suspect that the Condorcet generalizations are too
complex even for that to work - i.e. they are hard to explain even in
practice, so reformers can't simply say "it works to maximize this, but
the details are kinda hairy".
It might still be a good pattern to use when encountering path
dependence in a method, though! Try every possible option and then pick
the Condorcet winner, because then every path gets its fair hearing.
It's a brute force solution, but it should work!
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