Juho wrote:
On Jul 31, 2008, at 0:50 , Kristofer Munsterhjelm wrote:
In any case, the left-right problem would still be a limitation to
RRV, where ballots are set so that RV (and any sensible method) would
elect Center first, but where electing an assembly of two should elect
Left and Right. For some reason, that problem doesn't appear in party
list, but I don't know why.
I'm not sure if I understood you correctly, but isn't that the same
difference as between highest average based methods
(http://en.wikipedia.org/wiki/Highest_averages_method) and largest
reminder based methods
(http://en.wikipedia.org/wiki/Largest_remainder_method) that both can be
used with party lists?
To be more clear, this is an example I devised for Range:
52: Left: 1.0 Center: 0.5 Right: 0.0 (leftists)
50: Left: 0.0 Center: 0.5 Right: 1.0 (right-wingers)
13: Left: 0.0 Center: 1.0 Right: 0.0 (moderates)
In pure Range, Left has a score of 52, Center has a score of 64, and
Right has a score of 50. Obviously, in the single-winner case with Range
rules, Center should win.
However, in the assembly of size two, the Left and Right voters have a
Droop quota each, and thus, if the method is to fulfill the Droop
proportionality criterion, it must elect Left and Right.
I guess any method that picks the winners one by one until sufficient
number of representatives has been elected fails to elect both the
centrist (1 representative) and left+right (2 representatives) in the
example above. On the other hand if we follow the example that means
that Alabama paradox is what we want.
It would appear as such, since a candidate can lose by having the
assembly size increase (if that candidate is a centrist). If we use the
example above and say that Left and Right contribute to the left and
right side of the spectrum equally, but the centrist contribute to both,
then electing Center and (either Left or Right) is undesirable, because
it tips the balance of power to either left or right, respectively.
But party list PR doesn't have a problem with the Alabama paradox, yet
it doesn't fall to this problem, either. Why is that? I think the reason
is that in party list PR, you only have one vote. Therefore, the Left
and Right voters must vote Left only and Right only. Because of party
proportionality, there's no vote splitting problem*, so one can vote for
the favorite party.
With a divisor/average method like Sainte-Laguë, since it's protected
against the Alabama paradox, that means that it'll fail when the
assembly is small enough. In the case above, it would elect Left with an
assembly size of one.
Thus it seems that in order for the method to be able to compromise
effectively, it must technically break the Alabama paradox. I think that
hybrids are possible, though. Although I haven't checked it in detail,
QPQ (which I mentioned earlier) seems to be such a hybrid, because it
reduces, or is claimed to reduce, to D'Hondt (or Sainte-Laguë) when
voters vote strictly on party lines. More research would be needed...
* Well, significantly less of a vote splitting problem; it depends on
the size of the districts and the nation. Here in Norway, we have
additional measures to compensate district disproportionality with
nation level seats, kind of like MMP but with parties only.
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