At 09:07 PM 12/2/2008, Kevin Venzke wrote:
> This is the "relatively objective method of
> assessing" election outcome. When it's easy to
> determine, in a real situation, the absolute individual
> voter utilities, "fully sincere Range Voting"
> implements it as a method. That is, if the voters are
> honest, or if their "votes" are determined for
> them by some objective method -- such as a measurement of
> tax impact based on, say, the previous year's income tax
> return -- this obviously would produce an objective result
> that could be considered ideal. In real elections, of
> course, determining absolute, commensurable utilities may
> not be possible. (There are voting systems involving
> lotteries and real bets made by voters that should encourage
> the voting of absolute utilities, but these aren't being
> considered here.)
In your previous message you seemed content to say that voters can't
vote "accurately" under Range because they don't know how and because
the ratings have no inherent meaning.
The two considerations should be kept rigorously separate. We can
study voting systems using absolute utilities that are *assumed* in a
simulation. The absolute utilities allow the prediction of voter
behavior under various models. We can convert absolute utilities to
Range Votes. Want to actually maximize overall voter satisfaction.
Somehow arrange for absolute utilities to be voted. The "ideal"
winner may be determined using absolute utilities, in a simulation.
Then voting systems, with various "strategies" -- read "methods" --
used by the voters to translate their real preferences, including
real preference strengths -- i.e., the simulated ones -- into votes
in a voting system, and Bayesian regret is defined as the difference
in overall, summed absolute utilities generated by the difference
between the voting system winner and the best winner from the summed
absolute utility standpoint.
This regret is not minimized by normalized Range, which is how we
imagine most voters will vote, because of the normalization, which
equates the votes of voters with *overall* weak preferences for the
entire candidate set, with those with strong preferences over this
set. However, we get reasonably close, because the normalization
error more or less averages out. And we preserve "one person, one
vote," which is politically desirable.
That's an objective method of studying voting system performance.
Strategy comes in when translating voter absolute utilities into votes.
From the absolute utilities, we can generate preference lists, even
more accurately than a voter could. (If the voter would have trouble,
the simulator still detects any preference within the accuracy of the
assumed utilities -- which are sometimes generated from issue space
assumptions.
Ideally, the utility models would be correlated and corrected by
their predictions in real-world circumstances, but little work has
been done on this; at this point, we simply have reasonable
approximations being used for the models.
With the simulation models, "fully sincere Range votes" have a
precise meaning. They are simply, under one of two assumptions, votes
that are the utilities, normalized by some means, to the voting
range. What is usually called "absolute sincere Range votes" would be
the absolute utilities, with the same normalization factor for all
votes, on the Heaven-Hell scale, voted. Nobody expects voters to be
comparing Obama with Jesus Christ in Range votes, rather they will
compare Obama with the other candidates, and will rate max if he's the best.
So the next kind of "fully sincere vote," which is what we normally
mean by "sincere Range vote." These are utilities normalized to the
candidate set. And then a "strategic voter" normalizes to the
*possible* candidate set's range of utilities, not the full one. I
won't address the complication of a strategic voter in a three-way
contest, but the difference in utility between an accurate Range
vote, but normalized to the possible candidate set, and the
approval-style one, is, unless the voter has very, very good
knowledge of how the other voters will vote, minor if it exists at all.
Now, voters would have difficulty voting with high accuracy. They can
approach it, however. Voting Range 2 or Range 3 or 4 style, for
example, will give improved fidelity to the true utilities, and is
easy to do. And the voting rules can provide some real incentives to
do this: for example, if there is preference analysis on results,
with a preference winner then going into a runoff against the Range
winner, the voters are incentivized to maintain preference order. In
low-res Range, this incentive gets fairly high, but only for real
candidates. I.e., possible ones. Where this would improve results,
possibly, is with three-way races. It would encourage those who
prefer one candidate to down-rate their alternate, if they care about
the victory in that race. It's a balancing decision, but with low-res
range, it gets easy.
High-res range can be voted as low-res range, it's only about how
much the voter wants to express in fine distinctions. Further, in
real elections, with real voting strategy, the most common, I assume,
the voter will first rate a favorite and the worst. That's usually
fairly easy! (At least among those the candidate recognizes.) Then
the voter rates the frontrunners. If the method is hi-res, the voter
now makes the first real strategic decision. How much vote strength
does the voter put into the pairwise election between the favorite
and the favored frontrunner? Fully strategic: no points, except that
then there is no opportunity to influence the pairwise analysis. So
one point does it. In high-res Range, that is practically no cost in
the major election. It can be made fully no-cost by allowing voters
to rank within ratings, but that's a complication I won't address. I
want to keep the actual voting system pretty simple! Voter strategy
can be complex as long as there are easy strategies that are "good
enough," i.e., reasonably effective. And there are.
But if I want to increase the accuracy of the vote, which may not
maximize my personal utility (it's not likely to harm it much, if at
all), then it's harder. I've suggested thinking about -- and maybe
actually making -- campaign contributions. I won't go into details,
but, in theory, with three candidates, if I'd spend the same to
promote one pair, zero knowledge, as another pair, my preference
strength in those pairs is the same. If the pairs are pairs within
the frontrunners, and there are only three, that's enough to give me
a sincere midrating for the middle-preferred candidate.
I might just do it by the seat of my pants. *It's only about one
vote.* I'm *not* a dictator. A lot of voter guesses about sincere
ratings will average, probably, to something close to sincere
ratings. ("Sincere" with real people is tricky to measure, for sure,
but it's reasonable to assume that people have a transitive internal
utility scale, and not making this assumption leads us into
complexity that, at this point, is probably impossible to address.
Simply insisting on discovering a majority turns very poor voting
methods into quite good ones. Think of it as a binary detector,
making a series of pairwise comparisons, but it's even better than
that, for preferences shift between ballots, based on preference strengths.
In other words, we already know how to do sincere Range voting. It's
deliberative process with an engaged and active electorate, those who
care, and those who do not care not participating!
This is why top-two runoff is probably far better than we have
estimated based on fixed-preference analysis. Range information
enters into it as well. Runoffs do not simply confirm expressed
preferences in the primary! They shift, and voters shift, favoring
those who have stronger preferences *in reality.* Not fake ones, or
pretend ones. You either get up and go to the polls or you don't.
I'm assuming we don't introduce external incentives into the election
method.
Yes. It can be done in a positive way, though. I won't go there for
now. One external incentive is important, though, which is showing
support for a third party. Range allows this without harm.
> In real elections, voter behavior will deviate from those
> "fully sincere" votes. (Fully sincere means
> disclosing true preference strength, within the resolution
> of the method.) It deviates from it for two reasons: (1)
> voters don't care to put that much effort into rating,
> it's easier to rank, generally, because it only involves
> pairwise comparisons; however, voters usually only have
> meaningful preferences between a few of the candidate pairs
> involved. And (2) voters are accustomed to elections being a
> choice, or a set of choices, and choices are normally made
> within a context that considers outcome probabilities where
> choice power is used to choose between realistic
> possibilities, not merely to compare the value of each
> outcome.
This seems pretty different from your explanation previously.
Consistency is the hobgoblin of little minds.
I'm exploring. I may explore new ideas today, or restate old ones.
My position grows like a hologram, based on the sum of all these
"explanations."
> So: How does Range, with realistic voting patterns, compare
> with other methods. Range does *not* produce zero regret. It
> produces relatively low regret. If fully sincere voting
> could be somehow guaranteed -- probably impossible -- it
> would always choose the ideal winner (within certain
> restrictions, basically normalization). So there are two
> deviations from the ideal. The first is from normalization,
> and the second is from strategic voting.
>
> Range *with strategic voting* is better with respect to
> regret than any other method that has been simulated, to my
> knowledge.
If this is true it can only be by comparing strategic Range to strategic
(insert rank ballot method), which is at the mercy of Warren's
understanding and implementation of rank ballot strategies.
Yes. Except that it is only at Warren's understanding if others don't
exercise themselves to confirm the approach. Given that this is the
only approach that has any hope of being objective, and that little
additional work has been done, apparently, it shows how much people
care about objective comparison of voting systems. Not much. They'd
rather plump for their favorite, perhaps.
The comparisons have been done, by Warren. His work is published and
should be verifiable. If not, I'm sure that reasonable questions
unanswered by his publications could be addressed here or on the
Range Voting list. If they couldn't be answered, that would radically
impeach his work, wouldn't it?
Essentially, poor simulation -- if it is poor -- is better than none.
If the simulation were designed to make Range look good, that would
be one thing. But it appears that the reverse is true: Warren went
for Range Voting because simulation work -- as well as theoretical
work -- showed it to be ideal, with sincere votes (it must be! --
with the right definitions of sincere). He didn't set out to prove
Range was best, he wanted to know.
And he wanted to answer the question of "how much." How much is, say,
IRV better than Plurality? Or Approval than IRV or Bucklin? Voting
systems criteria don't even begin to approach this.
The only superior approach would be a study of actual voter behavior,
with far more information needed than we can normally obtain.
The theoretical work behind Range Voting (such as the Dhillon-Mertens
publication) has been done in the field of economics, which studies
the same problem: how a group of people can make decisions. Arrow was
an economist. The political science people -- Brams excepted -- have
mostly looked down their noses at this approach.
Hang "objective," I want what I want, and Criterion X is the most
important. I gotta have Criterion X, and anyone who disagrees with me
is an idiot, it's intuitively obvious.
What we can now do is to study voting system behavior with, at least,
some model of what motivates voters to vote as they do. Utility
translation to preferences is pretty easy, it's strategic voting
that's more complex, but we can assume that if preferences are weak
(low differential utility), voters will not be exercised to use much
strategy. It's too much work, and get it wrong, you can seriously
regret your insincere votes! I don't think that Warren's work covered
this difference: voters who vote strategically are likely to be those
who have stronger preferences. Not those who almost don't care! These
are more likely, in a system that allows it, to rank equally. Which
is more expressive of true preference than a strong ranking, and
improves results overall.
> There is an exception: Top Two Runoff Range
> Voting beats Range. That's not surprising. It would
> detect and fix some of the deviations due to normalization
> and strategic voting.
I'm not sure what this method is but it sounds vulnerable to clones.
Sure. However, the simulations don't generate clones except rarely.
In real politics as a strategy? Dangerous, but I won't go there.
Instead, I'll point out, I have *not* suggested that the runoff would
be between two top Range winners, but between a Range winner and any
candidate preferred to that winner by a majority. This is *not*
vulnerable to clones. It would produce a close Range race, that's
all. It's not going to suppress a Condorcet winner, who would make it
into the runoff. Then it's up to the voters.
I've suggested a runoff whenever a majority choice isn't clear. So,
sure, two clones might make it to a runoff, but highly unlikely that
any other candidate would be a better winner than one of them. Range
winners, if the ratings are sincere, have an advantage in runoffs. We
want a runoff to detect, among other things, the rare situations
where the ratings weren't sincere, or possibly just inaccurate. There
is normalization error as well, which a runoff fixes to a degree.
If you're open to introducing mechanisms to fix problems caused by Range
strategy, I wonder why you would keep it to just this.
I wouldn't. I prefer Asset Voting, which can use a Plurality ballot
quite effectively. Choose between Range and Asset? Hands-down, Asset Voting.
> Now, to prevent the advantage that knowledgeable voters
> would have from being able to vote accurately, should we
> damage the outcome averaged over all voters?
How is it even clear that it would be damaged?
That's what the simulations show, and nobody has controverted that
result. It's quite reasonable, by the way, it's not likely to be
generally wrong. How carefully have you looked at this work, Kevin?
It should be understood that the simulations are measuring average
Baysian regret, considering a large number of simulations for each
method. Each method then can be assigned a rating based on average
Baysian regret, and compared with other simulations using the same
input data (i.e., the same underlying voter utilities). Method
results using various voter strategies can be compared; for example,
there are experiments that compared various Approval voting strategies.
You've presented an idea
of what people are doing when they go to vote, and trying to vote
accurately wasn't part of it. People are making sincere, strategic
decisions.
No, that, as well, is only part of it. People also simply vote as
they feel. Further, in a Range voting system, people will know
exactly what the system is doing. It is collecting preference data
from all the voters, and using it to optimize overall, summed,
satisfaction, treating all voters equally. They will know that if
everyone provides accurate information, the system will produce the
best result as to overall satisfaction that is possible. They will
know that, if they have good information, they can push the result a
bit -- not a lot -- toward what they personally prefer, but at a cost
to other people.
They will know that if everyone votes sincerely -- read accurately --
in all elections, everyone will benefit from this. What goes around
comes around. Voting strategically is the Tragedy of the Commons, a
variation on it. However, in this case, it is a *relatively harmless*
variation, the damage done by it is small. *Punishing* the
miscreants, those "selfish voters" -- or the simply lazy ones -- is a
very bad approach, because it will do much more harm than good. Try
to prevent people from freely deciding *how much* they want an
outcome, mistrust them, and we get worse results, not better.
The healthier the society, the more we will see Range votes trend
toward full sincerity. We'll never get it totally, because it's too
difficult to be really accurate. I have no idea what level of Range
we will settle on. Range 2 might be just fine! -- and Range 2 is
quite simple to vote. Depending on the exact rules.
But want simple and maximally powerful? Asset Voting. Terminally
simple as a voting method. Ideal strategy: identify the eligible
person (could be yourself!) whom you most trust to make a good
decision in your absence, because you will be absent, as a voter,
until the next election. Vote for that person, period. There is no
reason to vote for anyone else, at all. Can't decide between two?
Vote for both, the system will divide your vote between them. But I
suggest that only to avoid tossing out the vote, I see no other
reason to put that in. We are deciding *representation*, not a final
decision. If we were limited to a small candidate set, then we'd want
to be able to create virtual committees by voting for more than one.
But we need not be limited to such a small candidate set.
The persons receiving votes in Asset become public voters, I usually
call them electors. There are a lot of uses for this, and it goes far
beyond single winner elections. Asset was first designed as a tweak
to STV, by Lewis Carroll, to deal with the very serious problem of
exhausted ballots. It was a much better fix than the Australian one
of requiring full ranking, which essentially coerces votes out of
people who don't have the knowledge to do deep ranking. And who
clearly would rather not, as we see where full ranking is optional,
as with Queensland, for example.
Once you have public voters, electors, though, it becomes possible to
do much more than simply resolve one election. This becomes a fully
representative "electoral college" -- no compromises at all -- which
can handle many different kinds of problems. Filling a vacant office.
"Hiring" a President instead of electing him for a fixed term, a
practice which is guaranteed to occasionally produce massive
deviation from democracy.
Runoff elections? Not necessary. Instead, we have deliberative
process among the electors, who can, partly, meet in person, but in
any case can handle an election by many different means. Because they
are public, their votes are public, and security problems are
minimized and cost is minimized.
If we must have a determinate result, in one ballot, some form of
Range is clearly the best. So far, I think the best is a hybrid of
some kind. But allowing a single runoff is a small deviation from
deterministic, and a big step toward deliberative process. That's the
biggest improvement, it may even swamp the improvement from Range,
but we have no work comparing them. (The simulations that have been
done have assumed fixed preference and the same voters, which doesn't
apply at all to real runoff elections, which run closer to Range
results than would be expected, I'm sure.)
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