At 08:57 PM 12/13/2008, Kevin Venzke wrote:
--- En date de : Lun 8.12.08, Abd ul-Rahman
Lomax <[email protected]> a écrit :
>> What you're talking about here isn't even "playing nice," it's more
>> like using lower ratings as loose change to toss into an (inadequate)
>> street musician's hat. I'm not clear on what motivates that either.
>> I don't think I've ever wanted to communicate to a candidate that they
>> aren't acceptable (i.e. worse than what I expect out of the election
>> after considering both frontrunners' odds), but should keep trying.
>
>Why did voters vote for Nader in 2000? Were
they purely stupid? You may >never have voted
this way, but other real people do. Why do
voters bother >to vote for minor parties, ever?
Do you think that most of them imagine >that candidate could win?
I would say that they voted for Nader because they wanted him to win.
Mmmm.... Sure, they would *prefer* to see that
candidate win. But that avoided the issue. Did
they think the win was a realistic possibility?
Were they naive? I don't think so. I think they
knew that their vote would have no effect on the
outcome. (They did *not* cause Bush to win, if
they sinned, it was a sin of omission, not of
commission. If, in Range, they voted zero for
Gore, *then* we might say that they would have
caused Bush to win, perhaps. But it depends on
method details and the rest of their votes. If
they bullet voted for Nader, then their vote
would probably have been moot, not causing Gore to lose.)
It
is not relevant whether he could or not.
It's relevant to most voters who would otherwise
support a minor candidate. In fact, because of
the election method, it's quite likely that quite
a few more voters would prefer minor candidates.
They don't even go there because they don't want
to waste their time with false hopes. Give them a
better voting system, they would, indeed, tend to
become more politically sophisticated. Warren
Smith is right, to a degree: Range Voting would have an "incubator effect."
The phenomenon I'm scratching
my head over, is where you give a lowish but positive rating to someone
who isn't good enough to be elected, but good enough to "encourage" in
a sense.
It's not about the candidate, necessarily, though
candidates can grow and mature. Giving a small
but positive rating to a candidate could send a
message: you've got something. Work on it and
maybe next time I'd give you a higher rating.
It's also about the party. Giving some positive
rating to a minor party could encourage your
major party to shift in that direction.
But never give an approval rating (if that means
anything in a method) (in Range it might be above
50%) to a minor party unless you'd like to see
that party win. That's my suggestion. The
exception would be under serious
lesser-of-two-evils conditions, which, I'd argue,
would cover U.S. Presidential 2000, definitely
2004 and probably 2008. Those are just my
opinions, of course, and don't affect the principles here.
I would certainly have preferred Obama over any
of the libertarian candidates, including Ron Paul
(the libertarian "Republican"). But I'd have
given Ron Paul some serious rating strength, were
he on the ballot, because I want wider
consideration of libertarian principles, and
because I don't think he'd be a disastrous
President, and thus if it happened that, by some
rare constellation, he were to win, I'd not have been distressed.
Range Voting allows far more sophisticated
expression. Many wouldn't use it. That's not a
problem. It seems that many *would* use it. With
good voter education, they wouldn't use it
stupidly. If they care who wins the election,
they would know to vote high, perhaps max, for at
least one frontrunner, and low or even min, for
the other, and that it isn't, in any but the
rarest and weirdest of circumstances, which can
safely be neglected, advantageous to vote
reversed preference. If you prefer one candidate
to another, rate the one higher than the other,
or rate them equally if you don't want to waste
any vote strength. But don't reverse rate them, thinking this might help you.
>> I'd rather "start" with MCA (two rating levels plus the option to
>> not rate at all) and stay there, as I think MCA is at least a little
>> better than Approval.
>
>How is it counted?
There are three slots (the lowest of which can be expressed through
truncation). If any candidate has top-slot ratings from more than half
of the voters, then the one of these candidates with the most, wins.
If there is no such candidate, then elect the candidate who has the
most top-slot plus middle-slot ratings. (Which is the same as saying:
Elect the candidate truncated by the fewest voters.)
This is Bucklin-ER with two ranks. I've been
recommending it. The only difference between it
and, say, Duluth Bucklin is that the latter had
three explicit ranks, and overvoting was prohibited in the first two.
I see no reason at all to prohibit overvoting in
the second rank, and little to prohibit it in the
first. Duluth Bucklin allowed unlimited approvals in the third rank.
I have criticized this method (and Bucklin and median rating, to which it
is similar) for not offering any great basis on which to decide whether
to rate a candidate top or middle. But I do guess that it is more stable
and more Condorcet efficient (in the abstract sense) than Approval. (In
my simulations it was definitely more stable, though it was difficult
to devise the strategic logic for it, so there could have been a flaw.)
I'd start with an assumption that most voters
would bullet vote. That's what happened with some
Bucklin elections. We should look at the ballot
images for IRV in San Francisco; bullet voting
isn't reported, because most bullet votes will be
for the top two, generally, and those votes aren't ever considered exhausted.
I expect that 3-rank Bucklin and 3-rank IRV
voting patterns would be practically identical,
for most voters. But, of course, strategic voting
patterns could differ. Most voters won't vote
strategically, in both systems. Except that they
will mostly try to rank, at some rank, a
frontrunner, when they have that information.
Otherwise they will simply vote "sincerely,"
which in this case means a bullet vote for a
favorite, to start. Then they would add in votes,
ranked down if there is significant preference,
but not to the extent that they rank everyone
above some mean expectation. And that's why
runoffs might still be a good idea. Expect
majority failure. It's normal with IRV, when
runoffs are needed. And it would be slightly less
common with Bucklin; the difference would be
significant with nonpartisan elections. With
partisan ones, fewer voters would approve both
frontrunners, thus there would be less of a fix
of majority failure, by Bucklin, than with
nonpartisan elections. IRV, of course, never discovers these hidden votes.
>> That's not very generous. I can think of a couple of defenses. One would
>> be to point out that it is necessitated by the other criteria that IRV
>> satisfies. All things being equal, I consider LNHarm more desirable than
>> monotonicity, for instance.
>
>I, and certainly some experts, consider LNH to cause serious harm.
>Absolutely, it's undesirable in deliberative process, someone who insists
>on not disclosing lower preferences until their first preference has
>become impossible would be considered a fanatic or selfish. That's a
>trait I'd like to allow, but not encourage!
Well, I said "all things being equal." All things being equal I think it
is a positive thing that by providing more information, you don't have
to worry that you're worsening the outcome for yourself. Maybe something
else gets ruined, but then all things are not equal.
You don't add the information if you reasonably
fear that the damage to your desired outcome
would be serious. You provide it if you think it
will increase your expected outcome.
Where I would agree is that it would be ideal if
a voter could control LNH compliance. It is
possible. This is equivalent to the voter taking
a very strong negotiating stance. But I would
not, myself, want to encourage this unless the
method tested majority failure and held a runoff
in its presence. And it's a general truth that if
there is a real runoff, with write-ins allowed,
total LNH compliance is impossible. Unless you
truly eliminate the candidate. Never again can an eliminated candidate run!
Basically, so that I can't "harm" my favorite by
abstaining in one of the pairwise elections
involving him, the *method* eliminates him! I'd
rather be responsible for that, thank you very much.
Again, you seem to describe LNH as though it is synonymous with the IRV
counting mechanism. MMPO and DSC do not render preferences "impossible"
thereupon "disclosing" more preferences.
I think this is correct. LNH, however, is
strongly associated with sequential elimination
methods. It's possible to reveal lower
preferences but to not use them in the pairwise
election with the additional approval. I've not
studied all the variations, there is enough to
look at with forms of Approval and Range.
When Bucklin is mentioned to knowledgeable IRV
proponents -- there are several! -- LNH will be
immediately mentioned as if it were a fatal flaw.
But the "harm," as I've noted is actually not
harm from the ballot but only the loss of benefit
under one particular condition: the voter, by
adding a lower preference, *if* there is majority
failure in previous rounds, has abstained from
that particular pairwise election while
participating in all the rest. It should be
possible, by the way, to leave the second rank in
3-rank Bucklin empty, thus insisting on LNH for
one more round. That shouldn't be considered an
error, but a legitimate voting pattern.
>Entirely neglected in Kevins consideration here is the possibility I've
>mentioned: that the very fact that voters can express intermediate
>ratings, and the near certainty that some do so, improves the method
>performance.
There is a possibility. But even if voters do provide them, this isn't
sufficient to say that this would improve method performance, because we
can't deduce that the intermediate ratings we collect mean the same thing
as the mind-read utilities we can see in simulations.
Of course not, and we make no such assumption.
However, they do express sincere preferences, we
*can* assume. Further, there is the dithering
effect. More work is needed, but adding even one
intermediate vote causes all voters to have an
increased probability of altering the result,
thus increasing the expected utility for all
voters. This took me aback when I discovered it
in an analysis of absolute voting utilities in
Range 2, but if all voters vote approval style,
one vote can, at most, change a tie into a win or
a loss into a tie. If we assume, say, a coin toss
as a tiebreaker, this means that the most that
the vote can effect with the vote is one-half the
expected utility for a full shift. With the
prevote being Range, and it only takes one voter
to do this, and with many voters, we can expect
that the prevote totals are *not* integers, the
vote, if it affects the result, will do so
flipping a loss to a win for the candidate favored with a vote.
That is, the method being Range, even if all but
one voter don't use it, improves the expectation
for all voters, that their vote will make a
greater positive difference. Since nobody has
explicitly confirmed this result -- nobody has
denied it, either, and I've made the claim many
times -- this must be considered unconfirmed.
The "mind-read utilities" are used to judge
election outcomes, not to determine them (except
for the technical curiosity, "fully sincere
Range." However, rational voting strategy can be
based on those utilities, in a far more accurate
and sophisticated way than without them.
The most powerful voting strategies with Range
involve Approval style voting. However, they
aren't the safest strategies, from my study. The
variation is higher, they can produce a better
result, but, get it wrong, and the voter may
regret the vote. Another way to look at it is
that "strategic voting" in Range can optimize
your personal expectation. "Fully sincere" voting
-- i.e, attempting to accurately disclose
preference strengths -- allows the method to
optimize overall satisfaction. If everyone does
it, the optimization is perfect. If none do it,
we get the same results as optimal Approval (i.e,
assuming everyone in Approval uses a decent
optimizing strategy -- which for most voters in
most elections under anything like current
conditions would be bullet voting, simple). Which
isn't a bad result. Each voter who votes with
full sincerity brings the result closer to an
overall satisfaction, so, by voting that way, we
might be voting for the principle of maximal
distributed satisfaction. At small personal cost.
I'd probably pay that cost, myself. If you would
not, that's your choice, it's respectable and it
is not lying. "You pays your vote and you takes your choice."
(The result will usually be the same! Because
Approval voters tend to average out to vote a net
vote, over many voters, as if they had voted Range.)
>> Warren's approach could be useful when:
>> 1. they simulate realistic voter profiles (and some of them apparently
>do,
>> but again, anyone can argue about whether they really are realistic)
>
>I've pointed out that they don't have to be realistic, only unbiased, not
>warped against one method and for another.
I don't agree. If certain scenarios are realistic for public elections,
then those are the profiles we care about.
Yes. However, we do get useful information from
simpler scenarios. If a method doesn't work
reasonably with a unidimensional preference
space, it seems a tad unlikely that it would work
well with a multidimensional one. Sometimes, in
some elections, the preference space is
unidimensional. In others, it's far more complex.
The idea of scoring each method according to an average of all possible
election scenarios, is not on its face very promising.
Not if the "average" doesn't consider frequency!
But the simulations do that. They do not consider
"all possible election scenarios," but quite a
limited set of them, those which came up in the
simulations. Thus a very rare scenario may not
occur at all. And unusual scenarios occur only
rarely and so impact average results only a little.
However, the variation should be reported. A rare
election outcome that is a disaster is of
interest. Again, the questions that we can answer
through simulations are "how much, on average."
And "how often." These are questions that are
utterly missed through the criterion approach,
where clever voting systems theorists dream up
election scenarios that are (1) highly simplified
and (2) often preposterously rare. Further, if
the result seems to violate some criterion deemed
important, the result shown is considered a
disaster, even if the actual harm is small, compared to possible alternatives.
To understand whether a result is a disaster or
not, we need to know more than preference
information, we need to know preference strength.
So ... if some election scenario violates a major
criterion, it's possible that the outcome is
actually an *improvement* over satisfying the
criterion. What we'd want to do is to find a set
of voter utilities that would create, with some
appropriate voting strategy or mix of strategies,
the problem election scenario, then look at the affect on summed utilities.
It's important that voting systems theorists
start paying attention to preference strength.
The habit of simply writing A>B>C and assuming
that this tells us enough means that a great deal
of thought and analysis is being wasted. It's
quite possible that A>B>C tells us less than
A=B>C, in terms of what is significant to the
voter. It's possible that the A>B part was
forced, the voter was actually unable to
distinguish a preference. So, okay, most experts
seem to agree that allowing equal ranking is
better than not. Saari excepted, and he is one
bizarre holdout, practically incoherent. My claim
is that giving voters more freedom is *generally*
desirable, other things being equal. So Range is
simply allowing voters to not only rank equally,
but to specify preference strengths, within a
certain restriction: the sum of preference
strengths expressed must not exceed one full
vote. This *forces* a certain kind of strategic
analysis, if the voter wants to be strategically
effective, and it happens that this analysis
involves the generation of von
Neumann-Morganstern utilities, which would be
terrifing if it weren't already instinctive for
us. We discount irrelevant alternatives, we don't
spend our vote on them. If Adolf Hitler gets on
the Range Ballot, so to speak, and Bush is on the
ballot, I don't waste part of my vote raising the
rating for Bush to discriminate him from Hitler.
That's if the goal is an election for office. If
it is an attempt to figure out the worst figure
in history, everything gets inverted and I'd put
some voting strength into that pair. How much?
I'd have to think about it! And it depends on the alternatives.
>> 3. they simulate voter strategy that is customized to the method
>
>That is relatively easy, and has been done.
No, this is the hard one! I don't know if Warren has even implemented
this for Approval and Range. I don't remember, whether the strategic
voters simply exaggerate, or actually approve above-mean.
Various strategies have been used.
"Above-mean" is an *awful* strategy, unless it's
defined to mean something other than the mean
utility for all the candidates. "Exaggerate," with Approval, is meaningless.
That strategy was indeed used: from Smith's 2001 simulation run:
16. Honest approval (using threshhold=average candidate utility)
17. Strategic range/approval (average of 2 frontrunner utils as thresh)
18. Rational range/approval (threshhold=moving average)
Strategy 16 is awful. That's what Saari assumed
as a strategy when he gave his example in his
paper, "Is Approval Voting an Unmitigated Evil?"
How's that for a nice, academically objective
title? The paper does not disappoint.
Strategy 17 is better. Strategy 18 is not
described enough that I could figure out what it
means. 17 is adequate, but better strategies can
be described, and it's possible to devise a
zero-knowledge strategy (where the voter doesn't
actually know the frontrunners) that would work
better than bullet voting or only approving
candidates "almost indistinguishable" from the
favorite. The last strategy, except for the
possibility of equal ranking effective clones,
reduces to Plurality Voting, which isn't a
terrible system as long as there aren't too many
candidates and the configurations are those
common in settled Plurality voting environments. (Hint: two party system).
For rank ballot methods Warren has implemented the same strategy for all,
and it is the biggest problem, with the least clear solution.
This doesn't seem to be true. I'm looking at his
old simulation run, which describes the strategies briefly.
http://math.temple.edu/~wds/homepage/voFdata
But, absolutely, Warren's simulation approach needs much work.
>> 4. they simulate pre-election information
>
>This is necessary for Approval and Range strategy, for sure, so I believe
>this has been done.
I don't believe Warren's simulations do this for any method. All
strategy is either zero-info, or (for rank ballot methods) based on
random arbitrary info provided uniformly to all voters.
No. Simulations using "poll strategy" involve, as
described by Smith, simulated polls answered by
random voters pulled from the complete voter set.
That's not "random arbitrary info." It's a simulated poll of the voters.
The most common Approval Voting strategy is to
vote for the preferred frontrunner, then for any
candidate preferred to that candidate. This
leaves out intermediate candidates, i.e.,
preferred to the worst frontrunner, but the best
frontrunner is preferred to that candidate.
However, these votes are mostly moot, unless the
election is close between that candidate and the
frontrunner, which would require that there be
something close to a three-way tie.
In any case, to apply this strategy, the voter
needs poll data. I've argued that the voter can
*estimate* this from the voter's own opinion,
either alone or together with the voter's general
estimate of where the voter sits in the
electorate. This is technically zero-knowledge,
I'd assert, but it uses the voter's own opinions
as a sample to estimate election probabilities.
This has to be right more often that not! -- and
this strategy would knock Saari's silly Approval
voting scenario upside the head!
It's really crazy to expect that most voters will
approve above the mean candidate, with no regard
at all for anything else. That strategy would
make Approval highly vulnerable to clones, when
it probably is not. It would make Approval highly
vulnerable to irrelevant alternatives, when it probably is not.
>It can actually be done, in the simulations, with perfect strategy,
>though, obviously, if you take this too far, you could run into loops, so
>I'd guess that the best strategy used would assume some uncertainty and
>would only iterate so many times, simulating polls and then shifts in
>votes as a result, then another poll, etc. The "polls" would solicit how
>the voter intends to vote, and the model can assume that the voter can't
>hide the information. After all, just how complicated do we want to make
>the model?
Yes, my simulations are based on polls. Polls are a great idea.
Smith used them....
How complicated do we want to make the model? Sufficiently complicated
that we can compare methods in realistic situations. Personally I only
care about public elections.
I care about all of them, but I agree that public
elections are important. I agree that we should
make the models as realistic as possible;
however, we should remember that the models need
not be fully realistic, as long as they are
reasonable. The problem would be if the models
preferentially select voting scenarios that
improperly favor or denigrate a method. I think
that this has happened with Plurality, for
example, where candidates aren't random, they are
preselected to appeal to large numbers of voters,
and given cachet from this selection. Likewise,
the neglect of preferential turnout, and write-in
possibilities, has made Top Two Runoff look worse than it is.
>Heavy use of serious strategization is pretty unlikely with ranked
>methods, in my opinion, most voters will simply do as the method implies,
>rank in preference order, and they can do this a bit more easily if equal
>ranking is allowed.
Yes. I agree with both of these comments. The
problem with ranked methods is that, sometimes,
they come up with a poor result *from sincere
rankings,* but this is hugely ameliorated, I
expect, when equal ranking is allowed. Still,
there is still the problem of the defective
assumption of equal preference strength for each
ranking, and that limits the performance of ranked methods.
My opinion is that all the benefit of ranked
methods can be realized within a Range method,
with appropriate rules. This is best done with an
additional round when necessary, and this
dovetails with runoff voting, then, and the
desirability of explicit majority approval of any
result. In other words, voting systems theory,
the theory of democracy, and the long-standing
understanding that top two runoff is a major
election reform, all come together here. It's
amazing to me that this wasn't being considered
when I arrived on the EM list, it's not like it's really complicated....
Warren's implementation would suggest that he strongly disagrees with you
on this.
No, I don't think so. But Warren is quite quirky
and sometimes cranky. Further, I don't see that
he's doing serious continuing work on the
simulations. He pretty much has said to others
who criticize his simulations: "Fix it, then! Do
your own damn simulations, my IEVS engine is
published, you can use it and tweak it to your heart's content."
He has a point.
>> Some of this isn't difficult, it's just again a question of how far you
>> take it. Strategic voter behavior needs to be made less ridiculous.
>> But what kind of strategy should be allowed, for (let's say) Condorcet
>> methods? If everyone votes sincerely, then Range will look bad. So
>> clearly the line has to be drawn somewhere else.
>
>No, you'd have to compare sincere Condorcet with some kind of sincere
>Range.
Look at it this way: To compare methods fairly we need to know how
strategic voters attempt to be, in the same situations, under whatever
methods we want to compare. Why compare strategic Method A with strategic
Method B, if Method B voters would never vote that way in reality?
Well, maybe you are right. To synthesize this,
the probability of voters using some voting
strategy must be included in the simulation. In
fact, with proper ballot design and voter
education, I think we would see *more sincere*
Range voting, than just popping a Range ballot in
front of them. For starters, voters should be
encouraged to maintain preference order, where
it's distinguishable. *How much vote strength*
they give to this is another matter. They should
know that voting Range Borda style may not be optimal!
I think that there is room for some creative work
here, in ballot design and in how Range is presented.
Practically speaking, though, I'm not pushing
Range immediately. I'm pushing Approval (lowest
cost, biggest bank for the buck, by far, because
the cost is almost zero) and Bucklin (low cost,
probably comparable performance to Approval, or
better, satisfies clear voter desired to be able
to indicate a favorite, maintains Majority
Criterion compliance, avoiding that political can
of worms, and several other reasons, including a history of use in the U.S.)
(Why aren't we *outraged* that race and
red-baiting were used to torpedo STV-PR in New
York? That Bucklin was extremely popular, widely
considered fully constitutional, never produced
bad election results -- compared to Plurality --
but was removed or even outlawed, as in
Minnesota? One of the worst things a politician
can do is to manipulate voting processes to
ensure the politician's continued power. Voting
fraud is obvious, but legal manipulation is just
as damaging. We've had better systems in the
past, and we lost them because we did not defend
them! And now we are losing top-two runoff, a
system known to favor healthy multiparty systems,
in favor of IRV, known for the reverse, based on
propaganda from hucksters, selling it on spurious claims of cost savings?)
What if, in real life, Condorcet voters just don't use any strategy?
And what if it's also true, that Range voters in real life turn the
method into Approval?
Well, the first is reasonably likely. The second
isn't. Rather, real voters will push Range toward
Approval, which isn't a bad result! But it won't
go all the way there, probably not even close.
Under present conditions, rational Range strategy
is, indeed, practically Approval strategy,
*except for some minor candidates." And that's
where Range makes a big difference over Approval,
though the effect works to some degree with
Approval (as it should! -- Approval is a Range method.)
Mostly minor candidates are to the fringes in the
U.S., so Range strategy, for most voters, would
be to vote Approval or Almost-Approval style, for
the frontrunners and the favorite. But it's
intermediate candidates that are interesting: for
the most part, the voters are free to rank these
with full sincerity, with no significant loss of
expected utility. Thus a minor party candidate
can rise in the ratings without harm; only when
the candidate approaches parity does something
else start to shift, as voters need to start
taking this candidate into account in strategic
voting (i.e., the two-frontrunner model becomes
inadequate, one needs to use a three-frontrunner strategy to maximize utility).
There is probably lots of time to prepare voters
for that, and certainly in such an election there
would be lots of commentary and suggestions on
how to vote. Some of it would actually be good
advice, and, as always, the most important skill
we might need, politically, is to be able to
distinguish good advice from bad! Otherwise we are sitting ducks!
In that case, the only useful comparison to be
done by the simulations, would happen to be sincere (or strategic, no
difference) Condorcet vs. strategic Range/Approval. And according to
Warren's simulations, Range doesn't win, in that case.
Depends. Do you have a page reference? Mostly
what I've seen doesn't disclose enough details to make that conclusion.
http://math.temple.edu/~wds/homepage/rangevote.pdf
This is the full original paper, written in 2000.
First of all, we should realize that advanced
voting systems encourage more candidates to run.
This can cause some systems to experience
seriously increased regret. So I'm going to look
at the maximum number of candidates used, five.
Honest Copeland seems to do the best of the
Condorcet methods, in the five-candidate
elections, average regret of 0.14181. (This is
the run with issue-based utilities, 50 voters).
Sincere Range, by the way, seems to do better
with more candidates. Given that San Francisco
sees more than twenty candidates in the ballot on
their elections, this is interesting.
However, here we are comparing with strategic
Range, though: 0.23232. Strategic Range does
worse with many candidates (like Copeland),
probably because of the oversimplified votes that
result. Now, that is *fully* strategic Range,
i.e., all voters vote that way. This is highly
unlikely. I think I recall seeing that some work
has been done with mixes. However, I'd assume
that real Range Voting would roughly in between
fully sincere, what Smith calls "Honest," and
fully strategic. Honest Range with 5 candidates has regret of 0.05368.
While this may not be accurate, if 50% of the
voters vote honestly, and 50% strategically, we
might expect regret for the mix of the average:
about 0.14. Roughly the same as Honest Copeland.
Now, Smith examined strategic Copeland. The
strategy was to max rank the preferred
frontrunner and to min rank the worst
frontrunner, and to order the rest honestly. This
is a simple strategy, I don't know how effective
it is for the voter, but it's certainly easy to
apply, and I think it does increase the voter's
expected utility. Some voters will use it, if it
is reasonably rewarding. (I don't know if that is
true). (But some voters do tend to think this
way: they elevate their preferred frontrunner to
practically a kind of god, and the worst
frontrunner is equated with the devil. Even if in
other situations they would think better of that
devil.) Strategic Copeland came up with 0.5443 as regret.
I'd say, on balance, Range is superior, overall.
If you make the maximum favorable estimate of
percentage of strategic voting for Copeland
(i.e., total sincerity) and the minimum for Range
(total approval-style voting with frontrunner
strategy), sure, Copeland looks *a little better*.
It should be realized that these are all low
regret values. Honest Plurality is 0.48628.
(Except note that strategic Copeland was worse
than that!) Note that fully strategic
Range/Approval, which is implemented by simply
dumping the no-overvoting rule, i.e., this is the
cheapest possible reform, is quite good!
(0.23232) Almost as good as Honest Copeland.
Honest Bucklin was 0.22931. Slightly better than
"strategic Approval" and Bucklin probably
encourages sincere voting; however, I do expect
high truncation rates with Bucklin *and with a Condorcet method."
Realize that "Honest Copeland" means no
truncation. That is *highly unlikely.* Truncation
is common, very common, with IRV, from many
sources, for example, and is reputed to have
occurred commonly with Bucklin. Truncated votes
aren't "insincere," but they don't fully disclose
preferences, and that behavior, in fact, is quite
similar to strategic voting in Range.
I'd say that these results do favor Approval, as
the first reform. And Bucklin may be better than
Copeland, in practice, because the strategy of
ranking one frontrunner is quite likely to be common.
>> I wonder if you have ever been curious to wonder what a "strategic"
>>voter is, for a rank ballot method.
>
>Nah, curiosity killed the cat.
>
>I've done a fair amount of reading on this, but who remembers anything?
>Often not me.
Actually this question was specifically about the simulations.
Read the paper. Smith describes it explicitly.
>> Some six months ago I wrote a strategy simulation for a number of
>> methods. One situation I tested was Approval, given a one-dimensional
>> spectrum and about five candidates, A B C D E.
>>
>> In my simulation, once it was evident that C was likely to win, one of
>> either B or D's supporters would stop exclusively voting for that
>> candidate, and would vote also for C.
>
>B and D voters are motivated to ensure that C wins if their favorite
>doesn't. Hence Approval will tend to find a compromise. If B or D are not
>relevant, can't win, they *may* also vote for B or D, so I'm not sure
>that the simulation was accurate.
I'm not sure what you mean by this. Voters that prefer B or D to C have
no reason to not continue voting for B or D.
The issue is that when all the D supporters (for example) *also* vote
for C, then it isn't possible for D to win. And the more that D voters
"give up" and vote for both, the less sense it makes strategically for
the remaining D-only voters to not "give up" as well.
I think something has been missed here. The votes
for C are added, not when C becomes a
frontrunner, but when C becomes a frontrunner
preferred to another frontrunner. If B or D are
frontrunners, with C, and if the voters prefer B
or D to C, they won't vote for C in the most
common strategy. The example is incompletely
explained, I don't know if something was missed by me, or it just wasn't there.
No. If the D voters prefer D, they won't vote for
C unless there is another candidate more likely
to win if they don't vote for C. The only
situation where this breaks down is a three-way
tie (three-way close race) between their
favorite, with C and another candidate less
preferred than C. In other words, if their
candidate can win, most voters will not add an
additional approval for a likely and
significantly less-preferred rival. They might do
it with Bucklin, where it's more like insurance and an easier decision.
My simulations involve polls. When the polls find that the winner will
either be B or C, then it's strategically unwise to not approve one of
them.
That's correct. However, you were talking about B
or D voters. If it's a B voter, the strategy
means "don't vote for C." If it's a D voter, it
means "Vote for C," assuming that C is preferred
to B. But in that case, the C vote is probably
harmless to D, who isn't likely to win anyway, with or without the vote.
At first, the polls report that C will win a lot but (due to bullet
voters for B and D) there is some chance that B or D will win. Eventually
the polls (which are subject to some randomness) will produce a prediction
that D's odds (or B's) are abnormally poor. This causes D voters to stop
voting only for D, and also vote for C. This almost immediately makes D an
unviable candidate, and the bullet voters for D disappear.
You mean that they stop indicating in polls that
this is how they will vote. I don't think that
real voters will iterate in polls like that.....
not with significant differences. Most Approval
studies of iterative voting start with bullet
votes. Then approval thresholds are gradually
adjusted. If the bullet voters for D disappear,
it must mean that the voters have concluded that
D can't win, hence they go for the compromise, C.
They will only do this if they think that the
real pairwise election is not between C and D,
but between B and C, and they prefer C.
But remember, it starts from bullet votes, pure
favorites. Plurality has a fairly good ability to
predict what a preferential voting system -- or
Approval system -- will come up with, and it only
breaks down under certain conditions. If the D
voters have a significant preference for D over
C, they will hold out longer, and some of them
will never compromise. Remember, not all voters
will follow frontrunner strategy. They don't with
Plurality, why should they start with Approval?
To summarize this, the scenario makes sense only
if B, C, and D are in a near-tie. If both B
voters and D voters prefer C over the other of B
and D, then C is, indeed, their compromise
candidate! It's perfectly rational that the B and
D voters, iterating over polls, increase their
support for C, but it will never go all the way.
The behavior described seems reasonable, proper,
and is effective for finding a compromise winner.
Is there some problem with it?
Bucklin allows them to maintain their sincere
preference, but, effectively, vote this way. Some
might add C in the second rank, some in the
third, depending on their preference strength.
But some will always bullet vote, perhaps even
most. Real voters don't give up so easily as your simulated ones!
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