Abd ul-Rahman Lomax wrote:
At 03:36 AM 12/25/2008, Kristofer Munsterhjelm wrote:
Do you think my runoff idea could work, or is it too complex?
For years, attempts were made to find a majority using advanced voting
methods: in the U.S., Bucklin was claimed to do that, as it is currently
being claimed for IRV. (Bucklin, in fact, may do it a little better than
IRV, if voters vote similarly; my sense is that, in the U.S. at least,
voters will respond to a three-rank Bucklin ballot much the same as an
IRV one, so I consider it reasonable to look at analyzing IRV results by
using the Bucklin method to count the ballots. If the assumption holds
-- and prior experience with Bucklin seems to confirm it, Bucklin
detects the majority support that is hidden under votes for the
last-round candidates.
The methods generally failed; holding an actual runoff came to be seen
as a more advanced reform, worth the cost. All this seems to have been
forgotten in the current debate. Bucklin, IRV, at least one Condorcet
method (Nansen's, apparently) have been used.
The error was in imagining that a single ballot could accomplish what
takes two or more ballots. Even two ballots is a compromise, though,
under the right conditions -- better primary methods -- not much of one.
I think I understand your position now. Tell me if this is wrong: you
consider the iterative process of an assembly the gold standard, as it
were, so you say that all methods must involve some sort of feedback
within the method, because that is required to converge towards a good
choice. That feedback may be from one round to another, as with TTR, or
through external channels like polls, as with the "mutual optimization"
of Range.
Is that right?
When considering replacing Bucklin or IRV with top two runoff, what
should have been done would have been keeping the majority requirement.
This is actually what voters in San Jose (1998) and San Francisco (2002)
were promised, but, in fact, the San Francisco proposition actually
struck the majority requirement from the code. Promise them majority but
given them a plurality.
If the methods hadn't been sold in the first place as being runoff
replacements, we might have them still! The big argument against
Bucklin, we've been told by FairVote (I don't necessarily trust it) was
that it did not usually find a majority. There is little data for
comparison, but I do know that quite a few Bucklin elections that didn't
find a first preference majority *did* find a second or third round one,
but in the long Alabama party primary series, apparently there was
eventually little usage of the additional ranks. But even the 11% usage
that existed could have been enough to allow the primary to find a
compromise winner. What they should have done, in fact, was to require a
runoff, just like they actually did, but continue to use a Bucklin
ballot to try to find a majority. This would avoid, in my estimation, up
to half of the runoffs. Since Bucklin is cheap to count and quite easy
to vote, this would have been better than tossing preferential voting
entirely.
If you're going to use Bucklin, you've already gone preferential.
Bucklin isn't all that impressive, though, neither by criteria nor by
Yee. So why not find a better method, like most Condorcet methods? If
you want it to reduce appropriately to Approval, you could have an
"Approval criterion", like this:
If each voter has some set X he prefers to all the others, but are
indifferent to the members among X, there should be a way for him to
express this so that if this is true for all voters, the result of the
expressed votes is the same as if one had run an approval election where
each voter approved of his X-set.
All methods that satisfy this will be limited to the criterion
compliance of Approval itself, because criteria either pass or fail, and
if it's possible to force the method into Approval-mode, then it's also
possible to make the method fail any criteria that Approval does fail.
Sure. Setting conditions for runoffs with a Condorcet method seems like
a good idea to me. One basic possibility would be simple: A majority of
voters should *approve* the winner. This is done by any of various
devices; there could be a dummy candidate who is called "Approved." To
indicate approval, this candidate would be ranked appropriately, all
higher ranked candidates would be consider to get a vote for the
purposes of determining a majority.
So, an approval cutoff. For a sincere vote, what does "approved" mean
here? Is it subject to the same sort of ill definition (or in your
opinion, "non-unique nature") that a sincere vote for straightforwards
Approval has?
In Range, it could be pretty simple and could create a bit more accuracy
in voting: consider a rating of midrange or higher to be approval. This
doesn't directly affect the winner, except that it can trigger a runoff.
Not ranking or rating sufficient candidates as approved can cause a need
for a runoff. If voters prefer than to taking steps to find a decent
compromise in the first ballot, *this should be their sovereign right.*
A Range ballot can be used for Condorcet analysis. Given the Range
ballot, though, and that Range would tie very rarely, it seems
reasonable to use highest Range rating in the Smith set, if there is a
cycle, to resolve the cycle.
Hm, this may work, or at least be better than Range. Since the cardinal
ballot is interpreted as an ordinal ballot - by rank as well as by value
- there's not as great an incentive to compress-compromise. That still
doesn't explain what the ratings of a cardinal ballot actually mean,
though, but inasfar as people have an intuitive sense of what they do,
it might work.
Thus we'd have these conditions for a runoff:
(1) Majority failure, the Range winner is a Condorcet winner. (probably
the most common). Top two runoff, the top two range sums.
(2) Majority failure, the Range winner is not a Condorcet winner. TTR,
Range and Condorcet winner (cycles resolved using range sum).
(3) Majority, both Condorcet and Range, but Range winner differs from
Condorcet winner. same result as (2).
(4) Majority for Range winner, not for Condorcet. or the reverse. I'm
not sure what to do about this, it might be the same, or the majority
winner might be chosen. A little study would, I think, come up with the
best solution.
I think the easiest way would be to drop the probing of the majority.
Just have a two-candidate runoff between the CW candidate and the Range
candidate. If the two are the same, the second place would be the second
candidate of the social ordering of either the Condorcet method or Range
(unsure which). If there's no CW, discover it by the tiebreaking system,
or if that's too complex, by Range.
There's also the somewhat strategy resistant variant that has been
proposed earlier: voters input ballots that rank some or all candidates.
All ranked candidates are considered "approved". Break Condorcet cycles
by most "approved" candidate (or devise something with approval
opposition to preserve clone independence, etc). The point, at least as
far as I understood it, is that you can't bury without giving the
candidates you're burying "approval", thus burial is weakened.
Range is theoretically optimal, as optimal as is possible given an
assumption that most voters will vote a full strength vote in some pair.
However, normalization or poor strategy can result in distortion of the
Range votes compared to actual voter utilities. One of the symptoms of
this might be Condorcet failure for the Range winner. If it is true that
the Range winner truly is best, then we have a situation where the first
preference of a majority might not be the Range winner, or, supposedly,
the Range winner vs the Condorcet winner might award the election to the
Condorcet winner. But, in fact, it is normal for small electorates to
set aside the first preference of a majority in favor of some greater
good. I see no reason not to extend that as a possibility to large
electorates. My own opinion is that, *if the Range votes are accurate*,
the Range winner will normally beat the Condorcet winner, because of
differential turnout and weak preferences that reverse during the runoff
campaign. On the other hand, having this runoff possibility answers the
common objection to Range: majority criterion failure.
With a runoff system like this, MC failure doesn't occur, because the
majority in the final and effective election has voted for the winner.
(That's not 100% absolute, if write-in votes are allowed in the runoff,
as I believe they should. But if the runoff is, say, Bucklin, maybe
two-rank, I think that spoiled majorities will be relatively rare, and
that the elections that end up with a plurality would almost always be
resolved the same way if an additional runoff were held. Thus, short of
Asset Voting, this could be almost perfect.
You could also use the same method as in the first round, which saves
you the trouble of having to define it twice. Just show that it reduces
to "elect whoever has the most votes" in the number of candidates = 2
situation - that's the only strategyproof method when there are only two
candidates.
Want perfect? Asset Voting, which bypasses the whole election method
mess! Single-vote ballot works fine! And that's what many or even most
voters know how to do best.
Or have a parliament and bypass the whole thing.
So I've shifted to proposing Bucklin, though Approval remains a simple,
do-no-harm, cost-free reform. Introduce it to a TTR system, some runoffs
may be avoided. Introduce Bucklin, more.
Do you propose Bucklin because it gradually transforms to Approval (as
more ranks are counted), or because of its own properties? If the
former, the criterion I gave above might be useful if we can find a
method that is better on its own terms yet has that property. If the
latter, I think other methods are better. I'll note, though, that it's
quite easy to make a PR version of Bucklin (and I've done so in an
earlier post), so that claimed advantage of IRV would also hold for Bucklin.
But Range Voting, a ranked form, was written into law in the U.S., I
think it was about 1915. Dove v. Oglesby was the case, it's findable on
the net. Lower ranked votes were assigned fractional values; I think it
was 1/2 and 1/3. Relatively speaking, this would encourage additional
ranking, I'd expect.
By that reasoning, any and all weighted positional systems are Range.
Borda is Range with (n-1, n-2, n-3 ... 0). Plurality is Range with (1,
0, 0, ... 0). Antiplurality is Range with (1, 1, 1, ..., 0), and so on.
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