At 01:44 AM 1/15/2010, robert bristow-johnson wrote:
but the problem with considering *more* than pure ranking (Range) is
that it requires too much information from the voter. and the
problem with *less* (Approval or FPTP) is that it obtains too little
information from the voter.
There is a common error here, which is to assume that Range
"requires" too much information from the voter. First of all,
Approval is Range, simply the most basic Range method. So what you
have is a contradiction: "Range" requires both too much and too
little information. Surely it depends on the specific Range implementation.
But there is a more fundamental error: that of "requirement." Voters
may vote in Approval, and Range, as they would vote in Plurality, if
they want, and for most voters, this is a simple and powerful
strategy. If they favor a frontrunner, and if there are only two
frontrunners (the normal situation!), whatever else they would do
would be moot for election purposes. But they could cast votes to
show support, which has other salutary effects. That, in fact, is why
Warren Smith calls Range an incubator for minor parties. It allows
them to show their natural support, neither more nor less.
The only issue about "voting strategy" arises in a real three-way
race, which is not common. Most voters, however, would be reasonably
served by a very simple strategy. Vote first for your favorite
candidate, no strategy necessary or even useful. Then consider the
frontrunners, however many there are, it's the set of candidates that
you think have a prayer of winning, and vote for your favorite of
them. (in Approval, that's it, in Range, it means vote max or maybe
just short of max). Is your favorite one of the frontrunners?.
Vote minimum rating (i.e., in Approval, don't vote at all for) the
worst candidate, with no strategic considerations at all. Vote
similarly for the worst frontrunner: minimum rating or just a tad
higher if the system allows it.
And then where do you vote for the rest of the candidates, the ones
in the middle? Well, pay attention first to any remaining
frontrunners. (In most elections, there aren't any left, but we are
now talking about a situation where there are three or more, and we
should remember that this is rare.) My own conclusion from study of
the game theory involved is that possible expected improvement from
seriously optimizing Range votes is small at best over simply voting
sincere ratings, and as long as preference order isn't reversed, it's
all likely to average out. At worst, from clear exaggeration in order
to gain some strategic advantage, it's possible to cast a vote that
will leave behind serious regret once you know the outcome.
When you have ranked the frontrunners where it seems right, then fill
in any remaining candidates you want to rate. If it gets crowded,
equal rank a candidate being added with the one already ranked.
Rating equals ranking with the option of equal ranking.
Equal preference strength expression (i.e., if one spreads the
candidates through the rating space evenly) is Borda count. If you
don't like that, if it seems to be off, then fix it. Spread some
ratings apart, which necessarily compresses some. Don't hesitate to
equal rank if you have any difficulty deciding which of two
candidates are better. The fact that you have difficulty is a clear
indication that you don't have a strong preference!
I would not spend a lot of time actually doing the ranking/rating.
The hard part is learning enough about the candidates to have a
foundation for opinions. So if I don't have enough information to do
that, I don't have strong preferences! and so voting is easy, if I
simply express that. I can spread my vote over the full range if I
think that my intuition might be valuable (it can be! -- but it may
also be vulnerable to media manipulation). My choice. Range allows me
to express a weak vote, one that would indeed indicate all or part of
my preference order, but which really leaves the actual decision to
everyone else. If I do this in the "approved" range, it can avoid a
runoff. I won't detail how to do this.
I'm saying that if it seems hard to vote in Range, one doesn't
understand how the method works. It only gets hard if one tries to
figure out a power-maximization strategy. But if one simply votes a
reasonable approximation of one's actual value for each candidate, on
a scale of 0 (least valuable or more harmful) to 1 (one full vote,
preferred), this helps the method choose the overall satisfaction
optimizer. You can vote strategically if you want, and if you guess
correctly, you can amplify your vote's effect, but only by a
fractional vote increase, how much is it worth? If you really want to
do that, I'd suggest, you have a strong preference and you ought to
vote that anyway!
This is the paradox that I encountered. So-called strategic votes in
Range are sincere! This was the contradiction I encountered:
supposely a voter has, say, "sincere ratings" of 100, 50, 0 for three
candidates. But the voter wants to make sure that the midrange
candidate beats the lowest one. So the voter pushes the vote to 100.
Or the reverse, the voter really wants to avoid the midrange
candidate beating the favorite.
Which is more important? Let me give you a hint: if the voter has
difficulty deciding, the midrange vote is actually optimal! On the
other hand, say that the voter really likes the favorite, and is more
worried about the favorite losing to the middle one. I should say
that "worried" has to do with the perception of election
probabilities. That's why I suggested rating the frontrunners first,
rate all candidates who are perceived as constituting a set that will
contain the winner. Usually this is pretty obvious! If not, the voter
has very little information and the voter might just as well vote
sincerely since there is no way to apply any strategy other than
making sure that preference order is maintained.
There is no situation where voting out of preference order is
strategically optimal, and that is something that takes Range methods
and raises them above other methods.
... Again, as I mentioned, the Condorcet Criterion looks good, it's
"intuitively satisfying." Unfortunately, it depends on pure rank
order, neglecting preference strength.
i think Jonathan says it well:
>> Just for the record: for many of us that's an advantage.
Sure. But "us" does not include people who understand the importance
of preference strength. Remember, I'm talking about the Criterion
here, not a voting system. The Condorcet Criterion *requires*
outcomes, under some conditions not at all difficult to imagine, and
we have doubtless experienced them, that violate common sense and
what the majority would want once it realizes the situation. I'd call
that a true failure, a voting system that produces a result that the
majority actually dislike, once they know. (If they knew before, they
wouldn't have voted the way they voted, they would not have voted for
their "personal preference" but for what they now know is best
overall for the society. They would give up some small benefit for
the overall benefit. We do this all the time!
It's not a zero-sum game, and if I do this in one choice, ordinarily,
it comes back to me in another and the average result is benefit. For everyone.
Condorcet doesn't ask the voter for that information and, unlike say
Borda, doesn't assume anything about it.
That's not exactly correct. Generally, the Condorcet Criterion
assumes that every preference is equal to every other preference. I'm
not familiar, however, with the details of resolving cycles, and some
might involve assuming that a A>B>C preference is stronger than an
A>C preference. Or it looks at winning margins, which involve a kind
of estimate of preference strength, applied overall.
But for the raw determination of the Condorcet winner, an
A>B>C>D>E>F>G>H vote is exactly the same in the A>H pair, as
B>C>D>E>F>G>A>H. And that is the cause of the problem with Condorcet.
Let me put it this way. The voter is seriously dissatisfied if H is
elected in the first case, and happy if A is elected. In the second,
the voter is almost as unhappy if A is elected as the voter is with H
in the first example. And, in fact, if the method doesn't allow equal
ranking, there might be *no* preference of A over H.
in fact, all Condorcet does
is hypothetically break the multi-candidate election down into
multiple 2-candidate elections.
Yes. But so does Approval, in fact. So does Range, with more
expressive ability. But I'll take your point: Condorcet is sometimes
called Instant Round Robin. And you do, with Condorcet methods, get
to vote, generally, in every pairwise election by providing a
preference order. You do the same with Range of sufficient
resolution, with the exception that you only get, in Range one full
vote to express over all pairs, so you can concentrate the vote in
one pair, or spread it out among many, or divide the candidates up
into sets and express setwise preference (with, in the extreme, two
sets, Approved and Not-Approved, with maximum voting power applied
for the election of every candidate in the Approved Set and against
the election of every one in the Not-Approved Set.)
Condorcet appears to give you a full vote in every pairwise election,
and I suspect that some of the quirks arise from that.
The only voting system that satisfies a reasonable restatement of the
Arrovian conditions is Range Voting (which includes Approval). That's
been shown by Dhillon and Mertens, in a paper using notation that
even Warren Smith calls "notation from hell." However, I find their
conclusion intuitively correct. I'd be much happier if it was
independently confirmed as a mathematical proof. They say that the
voting system is a unique solution to the conditions. (They call the
method Rational Utilitarianism, but it's Range Voting with a rational
strategy suggested.)
that, for me, takes care of the
whole strategic voting problem.
I think you really ought to look again. But I'm not sure you are
being clear when you write about the "whole strategic voting
problem." What problem? Condorcet methods are vulnerable to strategic
voting, and the only way to vote "strategically" in a Condorcet
method is to vote insincere preference order.
Take a look at the participation criterion:
http://en.wikipedia.org/wiki/Participation_criterion. "The
participation criterion says that the addition of a ballot, where
candidate A is strictly preferred to candidate B, to an existing
tally of votes should not change the winner from candidate A to candidate B."
The article claims that all Condorcet methods fail, and also that
Bucklin fails. I've elsewhere written that voting systems criteria
can be unreliable; the Bucklin failure has to occur where a vote
causes the counting to advance to the next round instead of
terminating with a majority, and your vote for another candidate (not
the one that causes the Criterion failure, who would have won if not
for your vote) is in the earlier round, so it satisfies the condition
of the criterion (you have expressed a preference) but the majority
failure caused opens up votes from other voters in lower rounds which
overwhelm your vote. Approval passes, of course, as does Range.
i don't have to regret afterwards
(if only i had known the election would come down to one between
Candidate Better_than_nothing and Candidate Satan_incarnate, because
if i knew that, i wouldn't have voted for Candidate My_favorite).
the whole point (for me, anyway) is so i can vote for my favorite
(not knowing in advance what his chances are) and not risk electing
Satan.
Still, if all you have is a ranked ballot, and equal ranking is not
allowed,
i actually think it should be. and it would be perfectly meaningful
with Condorcet. with IRV, i dunno exactly how to properly divide the
votes that get promoted if they are equally ranked which might be one
reason it is not allowed in the present law in Burlington.
Let me put it this way: if you want to have your silly Condorcet
method (actually it's generally good, just not good enough compared
to what else is possible), I'm fine with it as long as I can
equal-rank to my heart's content, and as long as I'm allowed to
truncate (which is equivalent to equal-ranking last, but without all
the damn work).
What happens with eliminations with IRV with equal ranking are that
candidates are, as it were, struck from the ballots. So if a
candidate remains at a rank, that candidate is still active until
eliminated. I can't see any argument against this. No, that's not why
it's not allowed in Burlington. It's not allowed anywhere, and this
has been brought up. The only reason I've seen is spurious.
Supposedly it violates one-person, one-vote, by having two votes
active at once. But they are alternative votes, in fact, and it would
be possible to only count one at a time, it's just a more complicated
way of arriving at the same result. Mathematically equivalent, no
difference. The one-person, one-vote issue is bogus. At least if it's
single-winner. If it's multiple-winner, there are other problems that
would have to be addressed, I haven't studied it.
the Condorcet Criterion is probably the best that can be done.
that's pretty much all i've been saying.
And it is absolutely incorrect. It sounds good, because we think that
each one of these round robin elections is sound, and, done that way,
they might be. Except that it isn't actually a series of individual
contests, with the focused attention, it's a single ballot, a single
snapshot, and we know that most of the rankings, quite likely, are
more or less random (unless you allow equal ranking bottom, which
would be normal here), plus each election would have its own turnout
of voters more informed about that pair, etc.
I agree that if there is a Condorcet winner, there should be a quite
clear and good reason to pass this candidate over, and I'm
uncomfortable doing it without a runoff. Note that Condorcet
elections can be won with far short of a majority.
The best that can be done I will call voter satisfaction
optimization. There are various ways to approach it, so I won't
define this today, but it's equivalent to the thinking behind
Rational Utilitarianism, which is Range Voting, in essence, and it
can be proven that this is the only approach that satisfies
Arrovian-like criteria. (Arrow's Criteria actually can't be applied
to Range because they are strictly designed for rankings only.)
That's because a simple ranked ballot does conceal preference
strength information. Warren at one point discovered a paper where
an analyst noticed an anomaly with a deeply ranked Condorcet ballot
where the Condorcet winner was rather obviously the wrong choice.
But he made an assumption of equal preference strengths, averaged,
over the rankings, or a fair and reasonable distribution of the
candidates in issue space. I forget the exact argument.
i've had trouble with some of Warren's arguments. for aesthetic
reasons, i just don't like Range or Approval. but i recognize he's
been thinking about this deeply a lot longer than me.
Indeed. Approval voting works, by the way, I've seen it in action.
Far more efficient in direct democratic usage than plurality, and
forget about using IRV with a show of hands. Why would you bother,
anyway? But you can do Approval, not a problem at all, and what
happens? People just Count All the Votes, and that's it. It might not
even be noticed that people voted for more than one, except when you
have five alternatives, and the sum of votes is much higher than the
number of voters, it's obvious. And it's no big deal. What's not to like?
but, as with my critique of Terry's argument, i am not well impressed
with constructing very weird and pathological scenarios to use to
fault Condorcet (or some other method). weird things can happen with
any method, but what are the pathologies that are likely or even just
common to happen with some method? *that* is what is salient and
*that* is why i know that FPTP is bad in a context of credible 3rd
and 4th candidates in an election. IRV does a little better (it, at
least, doesn't elect the Condorcet loser, which FPTP would have in
Burlington in 2009, well, i guess the loser of the "big 3").
Sure, I understand the mistrust of weird constructed scenarios. But
it's easy to construct a perfectly ordinary scenario that is crystal
clear, and that shows that the Condorcet Criterion is seriously
defective as a rational method of making decision, *under ordinary
conditions.* Under some conditions it might be fine. But what happens
is that methods which don't suffer from this problem are then faulted
as violating the Condorct Criterion, as if that were more important
than making the best decisions. What the Eff is the Best Decision?
I can guarantee you that there is no general principle that it is the
first preference of a majority, taken without deliberation in a
context where the positions of the voters become known in the voting
process. If the majority, knowing the overall position, goes ahead
and goes for its preference, that's proper, it is the right of the
majority, and it is for the majority to decide if it's shooting
itself in the foot or not.
But we can get at it in this way. Consider a Borda ballot. Borda is
a ranked method which assumes equal preference strength in each
preference expressed.
yup. bad assumption.
Well, possibly inaccurate. Warren came up with a thought-method which
involved choosing virtual candidates from every position in issue
space. In such an election, Borda's assumption is accurate. However,
I do recommend a voter with zero strategic knowledge use Borda voting
as a starting position. It's actually a good start, on the average.
Then modify the votes where the preference strengths expressed seem
off (modification to sincere Range), or where inadequate voting power
is assigned to the significant races (modification to strategic Range).
if i vote A>B>C , i might think that A and B
are both okay (but i like A a little better and would want to support
him over B if it comes down to that) and i might think that C is a turd.
Yup. And that's exactly what you can express accurately on a Range
ballot. I like positive/negative range, for the very psychological
reasons that others dislike it. With positive votes, I'm expressing a
desire to support and elect, and with negative the opposite. And I
can shade it.
As normally used, equal ranking is not allowed, and all ranks must
be assigned (or the voter's ballot is discounted in some way). So a
Borda ballot with (N+1) candidates translates to Range N, with the
restriction that a range vote can be assigned to only one
candidate, and all possible Range votes are advisedly used for a
full strength vote.
For those not familiar with Borda, here is more detail: the voter
ranks the candidates, say it is favorite to least favorite. There
are various ways of stating the canvassing method, but one way
would be that each candidate is assigned a value from the rank,
with the highest rank being the number of candidates minus one. The
lowest rank is then zero in value. The value is the number of the
candidate, starting from zero, proceeding up to the highest ranked
candidate. The winner is the candidate with the highest total value
summed from all the ballots.
This is quite equal to Range N, with no overvoting allowed at any
rank and no empty ranks allowed. If you allow overvoting at any
rank and therefore empty ranks, it's Range. Borda assumes that if
you rank A>B and these are in sequence, a vote strength should be
assigned according to how many intermediate candidates are ranked
in between. This is obviously an approximation, even if the voters
are Borda's famous "honest men." He missed the point! If the
approximation is way off, as it can be when there are clones, or
large missing segments of the issue space not represented by a
candidate, the method can be wacky.
Donald Saari somehow seems to have overlooked that Range, which he
criticizes heavily, is the same as Borda, which he actively promotes,
boy, i just don't get that at all. both Borda and Range are icky,
even if the ballots are a little different.
Saari is very well-known and considered an expert. But Range isn't
icky, because it is actually the only relatively objective method for
determining the value of an election result turned into a voting
system. I.e., we use scoring all the time to evaluate alternatives,
to give each a value, to decide on investment options, to determine
the quality of contestants, etc. If we were just talking about
polling whereby voters would rate an election result on a scale of
0-10, where 0 would have been the worst possible result, and 1 the
best, wouldn't this be a measure of election quality? So, hey, why
not simply allow voters to do this in advance and then determine the
winner by the results?
Note that if we could somehow cause the votes to be absolute
utilities, we truly would have an absolutely ideal method for
optimizing the result. There are approaches that attempt to do that,
look at the Clarke tax. But short of that, we do have another
approach that is similar: assume that the satisfaction of every voter
is equal to that of every other voter. It's inaccurate, but it will
tend to average out.
And then let the voters decide how to express their
satisfaction/dissatisfaction, on a scale set up, could be 0-10,
0-100, (-1, 0, +1), or as simple as Yes or No or Yes as an explict
vote and No assumed otherwise. You get more information from some
voters with higher resolution.
It's argued that voters will exaggerate, but when they exaggerate,
all they are doing is removing some information from their votes.
They still will vote for their favorite (there being absolutely no
reason not to), with a maximum vote, and they will still vote against
the least favorite, with a minimum vote, and they will, at the
minimum, setting the proposal for average range aside, place all
candidates into at least two categories, which we can call Approved
and Not-Approved. But they also get, with higher resolution Range,
the ability to rate in intermediate categories, thus weakening some
votes, while leaving full-strength votes where they want to exercise them.
So what happens when voters withhold some of the "sincere preference"
information? Not much. It tends to average out, for one thing. For
another, sure, if the information disclosed is restricted, the method
becomes less efficient at choosing the true utility maximizer. But it
doesn't go far from that, and the ones who suffer are the ones who
didn't disclose accurate information when they could have. If they
didn't have accurate information to disclose (your worry, apparently,
Robert), not a problem. The system uses, and uses well, what they
disclose. We know from simulations that strategic voting doesn't
deeply damage Range results. With other methods, in fact, you must
vote strategically to maximize results, under some conditions, you
must vote with a preference order that is reversed.
The most obvious example is Plurality, of course, where to get good
*results* you may have to betray your favorite, ranking a frontrunner
over your favorite. The same is true for IRV, in fact, as the
Republicans in Burlington found out to their possible regret.
and the only difference is this imposed restriction that is
obviously artificial and which doesn't correspond to reality.
Basically, like many voting systems activists and experts, Saari
doesn't trust the voters. That's where I differ. They may make
mistakes, but if they express a strong preference or a weak
preference, when they have the unconstrained choice, I assume that
an expressed strong preference *is* a strong preference, because
there really is no *significant reward* for lying about it. Saari
and others miss this completely, imagining that voters will
necessarily cast strong votes because they "want to win," but
neglecting the fact that voters have other goals than simply
maximizing their favorite's chances and doing everything to hurt
the opponent of the favorite.
Sure, they will do that if they *actually have strong preference.*
But if their preference is, say, maximally weak, and they know
that, will they act in that way? Especially realizing that, by
hurting this clone, they might be shooting themselves in the foot,
if the clone is the only hope of defeating a much worse candidate!
I've done the study, and my conclusion has been that the optimal
voting strategy in Range is a kind of sincere vote.
man, if we had Range in Burlington last March, i just don't know how
i would have divided my point allocation between my top two
candidates.
Arggh. I suspect you don't understand Range. It is not cumulative
voting. You do not "divide up your point allocation." You may vote
the full Range for any or all candidates. Can I guess that your top
two were Kiss and Montrose? Which did you prefer? *How much* did you
prefer them?
There is another issue you might not think of, with what I suspect is
a history of partisan thinking. Which candidate do you think would
best be able to unify the town? To answer that question, which surely
is a question just as important as individual preference, you have to
have some idea of how others in the town feel. And not just those
voting, all who participate in and are affected by town life.
I don't have much doubt. Montrose, and that's no big surprise,
because Montrose is in the middle, basically.
Bucklin would make your decision pretty easy, because it's ranked
approval. Vote for your favorite first rank. If you have a
significant preference, vote for your next favorite second rank,
assuming this is a good outcome for you. Or if you really have a
strong preference for one of the top two over the other, why not only
vote for one? If it's Bucklin/Runoff, you could make your choice
later, or just accept the majority winner if it was one of the two.
it's because, going into the election, i would really
expect that either of those could win and i really want to defeat
this other candidate who is quite formidable. before the election
last March, it was a *real* tossup.
Okay, with Approval, your strategy is clear. And you can vote Range
as Approval, you know. But I think you'd prefer Bucklin or something
like Range/Bucklin. The latter would take your Range ballot, which
would ideally (for you!) be sincere relative ratings, and vote it for
you in a set of Approval elections with the approval cutoff sliding
down a click at a time, until a majority is found. You get your cake
and can eat it to. You can vote for your favorite first, and your
lower ranked vote is deferred until it's necessary to include all
candidates at your lower approval rating. Don't care about a majority
result? This voting would continue down into the negative part of the
scale (or the lower half), even all the way down to the next click
above the bottom. But I really don't like electing someone based on
bottom-of-the barrel preferences. Which is what Condorcet methods do,
by the way, unless voters understand not to rank candidates that
they'd rather not help elect.
i would have to strategize and
strategize my vote if it was Range.
it's just one bloody vote, Robert. And when you are worried about
ratings generally, it's more like worrying about a fraction of a
vote. Basic Range strategy is absolutely simple, but Bucklin makes it simpler.
but with a ranked ballot, it was
easy. i had my favorite, my fallback, a couple of candidates i
didn't worry about, and there was Satan that i didn't rank at all.
but, what i don't want is for IRV to take that information from me
and screw it up and use it to elect Satan. if i was a GOP Prog-hater
in Burlington, that is precisely what IRV did in 2009.
Well, not Satan, I'm sure. But, yeah, the worst candidate, possibly,
from their point of view. They'd have no trouble deciding the vote
for Kiss. They'd have no trouble deciding their vote for Wright,
either. So they only would have one candidate to think about.
Bucklin, trivial. Second rank the Democrat. Or third rank could be
better, hold out as long as possible for tossing in the vote for
Montrose. Give their own candidate a decent shot at winning, then let
the method place their vote for Montrose.
There is a common error about Approval Voting, which is to think that
it's about "approving" candidates in the sense that you even like the
person. Voting is about making choices, and responsible voting is
about making necessary compromises. In Burlington, to elect the
Democrat, for them, is a necessary compromise, otherwise they get
worse. Elsewhere, Green voters would similarly add a lower rank vote
for a Democrat, a Republican wouldn't. Voting is *not* simply about
personal preference, it is a method of negotiating compromises, at
least a good voting method is that. And Plurality actually works when
voters do this work in deciding how to vote, and if they understand
the situation. By "works" I certainly don't mean "works perfectly."
In a three-party situation, Plurality easily breaks down, unless the
parties and the voters really get it together and form compromises
outside of the actual voting. IRV can make it worse. In that
situation, IRV is worse than Plurality, because it holds out a false
promise of being able to vote sincerely without damage.
Some IRV activists, being "progressive," think that IRV must be the
greatest thing since sliced bread, since Kiss won as a Progressive.
But that's a product of the fact that the Progressive Party is the
strongest in Burlington, followed by the Democrats, followed by the
Republicans. It's quite unusual.
I'm not thrilled at the idea of partisan elections at the town or
city level. It's divisive and often irrelevant.
And the voters will do best if they can choose that vote
themselves, if they can express preference strength themselves
without being forced into some specific model that constrains their
votes without necessity.
A voting system should be simple to vote. Range voting does require
some more complex thought,
yup.
but the simplest Range method is quite simple, and the strategy is
usually quite simple as well,
what is that? Approval? it is *not* simple.
A voting system can't be simpler. It's simpler than Plurality, in fact.
More later.
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