At 05:48 AM 12/28/2008, Kristofer Munsterhjelm wrote:
Abd ul-Rahman Lomax wrote:
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.
It's not clear how close a method like Range can get to the idea in a
single round. If any method could do it, it would be Range. It may
depend on the sophistication of the electorate and its desire to have
an overall satisfactory result. In what I consider mature societies,
most people value consensus, they would rather see some result that
is broadly accepted than one that is simply their primary favorite.
What goes around comes around: they know that supporting this results
in better results, averaged over many elections, *for them* as well
as for others.
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?
Yes. Polls or just general voter impressions from conversations,
etc., "simulate* a first round, so voters may *tend* to vote with
compromise already in mind. And that's important! That's called
"strategic voting," and is treated as if it were a bad thing.
But, we know, systems that only consider preference are flat-out
whacked by Arrow's Theorem. And once preference strength is involved,
and we don't have a method in place of extracting "sincere
preferences with strengths" from voters, we must accept that voters
will vote normalized von Neumann-Morganstern utilities, not exactly
normalized "sincere utilities," generally. Real voters will vote
somewhere in between the VNM utilities -- incorrectly claimed to be
Approval style voting -- and "fully sincere utilities."
Such a system is claimed by Dhillon and Mertens to be a unique
solution to a set of Arrovian axioms that are very close to the
original, simply modified as necessary to *allow* preference strength
to be expressed.
But even a single stage runoff can introduce vast possibilities of
improvements of the result. The sign that this might be needed is
majority failure. ("Majority" must be defined in Range, there are a
number of alternatives.) Range could, in theory, improve results even
when a majority was found, but, again, we are making compromises for
practicality. A majority explicitly accepting a result is considered
sufficient.
(Asset can do better than this! But that's another argument for another day.)
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:
Simplicity and prior use. I'm not convinced, as well, that realistic
voter strategy was simulated. Bucklin is a phased Range method
(specifically phased Approval, but you could have Range Bucklin, you
lower the "approval cutoff," rating by rating, until a majority is found.
(I'll mention once again that Oklahoma passed a Range method, which
would have been used and was only ruled unconstitutional because of
the rather politically stupid move of requiring additional
preferences or the first preference wouldn't be counted.)
No, Bucklin isn't theoretically optimal, but my suspicion is that
actual preformance would be better than theory (i.e., what the
simulations show.) Bucklin is a *decent* method from the simulations, so far.
(Most voters will truncate, probably two-thirds or so. If a
simulation simply transfers preferences to the simulated ballots,
Bucklin will be less accurately simulated. Truncation results in a
kind of Range expression in the averages -- just as Approval does to
some degree. The decision to truncate depends on preference strength.)
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.
A Range ballot provides the opportunity for this kind of expression.
It's actually, potentially, a very accurate ballot. If it's Range
100, it is unclear to me that we should provide an opportunity for
the voter to claim that the voter prefers A to B, but wants to rate
them both at, say, 100 -- or, for that matter, at any other level.
What this means is that the voter must "spend* at least 1/100 of a
vote to indicate a preference. That's practically trivial. (It could
be argued that the "expense" should be higher. It's also possible
that the Range ballot isn't linear -- Oklahoma was not. But I won't
go there now.)
From the Range ballot, once can infer ranked preferences (equal
ranking allowed). There is no particular motivation to rank
insincerely. What motivation exists for is "exaggerating" --
allegedly -- preference strength. If there is Condorcet analysis,
then this is blunted just a little. Thus, if you have a significant
preference, there is motivation to express it, either accurately or
"just a little" or somewhere in between.
Borda essentially enforces this, the problem with Borda is that
assumption of equal preference strength. It's been pointed out that
with many candidates -- a "virtual candidate system" has been
proposed -- Borda becomes, in effect, Range, very much like the Range
I just proposed.
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.
Analysis of methods by criteria doesn't pass my criteria for
criteria. Unless it's one of the SWF (Social Welfare Function) Criteria.
Does Approval pass the Majority Criterion? It depends heavily on the
definition. And where it fails, it is quite arguable that it was the
criterion that was defective, not the method....
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?
It has a very specific meaning for me: it means that the voter would
rather see the approved candidate win than face the difficulties --
and risks -- of additional process.
It is a *decision*. Approval votes cannot be derived from a
preference profile alone. They *can* be derived from Dhillon-Mertens
normalized VNM utilities. That's why Dhillon and Mertens did propose
Approval as a possible implementation of Rational Utilitarianism.
Consider them rounded-off VNM utilities.
("VNM utilities" sounds complicated. It isn't, unless one insists on
*numbers*. It's how we normally make decisions! We weight outcomes
with probabilities. Instinctively.)
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.
Yup. I think so.
Consider a Range ballot as a ladder of rankings. The candidates can
be placed anywhere on the ladder, but voters will know that the full
vote is expressed if one, at least, is at the top, and one, at least,
is at the bottom. They will also know, quite instinctively, that if
one cares about influencing the outcome, a preferred frontrunner
should be placed close to the top -- or at the top -- and the worst
frontrunner at or near the bottom. They will not vote stupidly as
some Range critics have complained.
Very simple voter "strategy," call it "sincere compromise," will
result in normal votes that are *close* to maximally effective.
That's what I predict. But if they "distort," the result is Approval,
essentially, which is quite a good method! But there is a cost to
this for them: they lose expression of preferences that may be
significant. So they will be restrained in this, I expect.
The bugaboo of Bucklin, multiple majorities, didn't happen,
apparently, and won't happen except under very rare -- and very
fortunate! -- circumstances. Bucklin satisfies all conceptions of the
Majority Criterion if first rank votes must be single. (I don't like
it, but there may be reasons to do this.) That removes a possible
political objection. 3-rank Bucklin allows quite a bit more freedom
of expression, even as it was implemented almost a century ago, than
3-rank IRV.
And, as I mention, it's possible, then, with fairly minor tweaks, to
move toward Range. If there is a Bucklin Range ballot, the ballot
itself is a Range ballot, thus we are collecting that crucial data
and we can monitor election performance. The door opens again.
And, hint to students: we don't know how and why Bucklin disappeared.
What were the arguments? What was the politics? There were well over
fifty cities, including San Francisco!, which implemented Bucklin.
What happened?
One possibility: Bucklin, like IRV, was sold as a runoff replacement.
When it was realized that sometimes, still, a majority was not found,
that could have created a wedge against it. Watch what happens when
it starts to be realized that the current cities which have
implemented IRV have been snookered! They essentially replaced Top
Two Runoff, which comes up with a better result than Plurality in
maybe 10% of elections, with IRV, which almost always -- in these
nonpartisan elections -- matches Plurality. They claimed that a
majority would be found, when that claim was highly deceptive at best.
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.
No, you probe the majority *to avoid runoffs*! If a majority has
approved a winner, and there is no conflict, you are done. That's the
normal outcome! (Unless you get *many* candidates.)
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.
Sure. That, in fact, is Bucklin! Ranking a candidate is approval of
the candidate. (But Bucklin, itself, doesn't do Condorcet analysis.)
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.
No, you still have the question of how to get the parliament. Asset
Voting, actually, is the bypass. It can elect a parliament that is
rigorously "proportional" -- more accurately, it is fully
representative, with representation being created by free choices.
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?
I propose it because (1) it is cheap. (2) Yes, it phases into
Approval as needed; in the first round, it elects the same candidate
as Plurality *if* a majority is required and voters vote sincerely,
and it's beyond me why they would not. (Even if multiple votes are
allowed, it seems highly unlikely that voters with a significant
preference would use them in the first rank.) (3) It's been used. (4)
This is America, and it was known as American Preferential Voting.
(5) It worked, we have a fair number of detailed examples of elections.
It's Approval, in effect, in many ways, but with that first
preference expression that so many want. I don't like that one aspect
of Approval! (I still believe Approval would work pretty well,
because of who it is that would use the additional votes, but ...
they, too, will dislike equating Nader with Gore, it will grate. The
idea, though, that they wouldn't add a vote for Gore if they have a
significant preference for Gore over Bush, on the theory that this
might "harm* Nader, is preposterous. They would use those votes just
as much as with IRV.)
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.
Sure. FairVote screwed up royally, hitching their sleigh, not to a
star, but to a cinder, the *worst* kind of STV, single-winner, on the
theory that it would pave the way. It could block the road!
Bucklin was used multiwinner, but I'm not sure that the method was
optimal. Probably not. Could be done, though. Use Range ballots, though....
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.
Yes.
Borda is *clearly* Range. Simply with a weird restriction. Likewise
the others. Range with weird restrictions. But, here, I was following
my classic analysis:
Plurality: Vote one full vote for one only. Candidate with the most votes wins.
Approval: Vote one full vote for as many candidates as desired.
Candidate with the most votes wins.
Range: Approval with fractional votes allowed.
What fractional votes? That depends on the method. Nice one: 0, 1, 2,
but expressed as -1, 0, 1.
Has a nice majoritarian interpretation: Candidate must get a positive
vote to win.
Oklahoma was, I think, 0, 1/3, 1/2, 1.
(I'd have preferred, say, 0, 1/2, 2/3, 1, I think. Oklahoma gave too
much weight to the first preference over the second.)
But, hey, we will have enough trouble getting full-vote Bucklin in
place, enough trouble just to get jurisdictions to Count All the
Votes, i.e., to use Open Voting or Approval.
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