Abd ul-Rahman Lomax wrote:
At 01:38 PM 12/5/2008, Kristofer Munsterhjelm wrote:
Abd ul-Rahman Lomax wrote:
Ballots do not ask for the voter's sincere opinion. They ask voters
to make a choice or choices.
I think that is incorrect. Ranked methods ask for the sincere opinion of
the voter, and that opinion can be well defined.
Understand that before writing this, I actually looked at some real
ballots. Quite possible, some real ballots ask for ranking in order of
preference. But the RCV ballots in the U.S., just like the name implies
(Ranged Choice Voting) asked for "First Choice," "Second Choice," etc.
Which leaves it up to the voter how to vote.
In my view, to ask for "First Preference" on a ranked ballot would be
just as offensive as asking voters on a Plurality ballot to vote for
"their favorite." It would generate a political bias, making "Core
Support" the standard in elections. Plurality tends to choose a
Condorcet winner because voters strategize and make their compromises
based on information about each other. "Strategic voting" is how voters
can improve the performance of a voting system. The problem, of course,
is that when the voting system gets very good, strategic voting can
sometimes reduce the overall voter satisfaction. However, my contention
is that when it does this, it does not do it to any great extent, and I
have yet to see an example, of any reasonableness, that contradicts this.
Plurality voters have to be strategic all of the time because Plurality
is a bad voting method. Ideally, there would be a "vote for one" method
where people *could* vote their favorites. Repeated balloting might come
close, but it incorporates feedback to the mechanism and thus isn't a
single voting method unless voters mechanically translate ranked votes
into plurality-style votes (first vote favorite, then vote
next-to-favorite next round, etc).
Consider Plurality, again. Voting with strategy improves the situation
when compared against a situation where everybody else is using strategy
and you don't. However, if everybody were sincere (had zero knowledge),
the result would be better. By Bayesian regret (which I assume you find
valid), this is true for Plurality and for many other methods, perhaps
all ( http://rangevoting.org/BayRegsFig.html ), unless Warren's strategy
simulations are too simple.
That voters in Plurality (most likely) can't vote for their favorite is
not a property of the ballot input of Plurality. It's a consequence of
that no voting method is strategy-proof, and that Plurality is
particularly egregious in this respect.
Now, you may say that only order reversal is insincere. This sounds a
bit like a ranked vote advocate saying that only altering your first
preference is insincere, and therefore, ranked methods that pass FBC
are strategyproof because altering your subsequent preferences is mere
optimization.
That's correct, about order reversal. It's a reasonable statement,
because equality is a judgement that does not require any specific
precision. "Equality" means "below some threshold of difference
considered significant." "Sounds like" is a personal statement, a
subjective impression.
(We focus on "exaggeration," but it's equally valid to focus on
"minimization," which in Range is rigidly correlated with exaggeration.
In ranked methods which allow or require truncation, "exaggeration" by
ranking in the presence of little or no preference takes place, and
minimization of preference takes place by truncation, whether voluntary
or forced.
The similarity is that you define a ballot to have some sort of data
that's "really important", and leave the rest up to optimization. If you
think that ordinal values (preferences) are defined externally with
respect to the voter's interaction with the voting method, then yes,
preference reversal is insincere. If you think that cardinal values are
defined externally with respect to the voter's interaction with the
voting method, then exaggeration is insincere too. And if you think one
but not the other, why the inconsistency?
Methods that permit truncation accept ranks over subsets of the
candidates. Most Condorcet methods handle this by ranking the remainder
equal-last, but it's not inconceivable to have a method that simply
treats it as if no decision as to whether A's better than B was done if
A was ranked and B not - a ranked version of Warren's Range tweak. The
point of this is that truncation is the submission of a partial ranking,
out of convenience. A strategic use of truncation would have a voter
considering, based on LNH* properties, how far to rank to maximize the
chance that his vote will lead to his first preference winning (and
failing that, maximizing the chance that his vote will lead to his
second preference winning, etc).
Election methods in general are thus algorithms that take individual
opinions as input and returns a good common choice, or a social
ordering. What is a good common choice may be defined by criteria (e.g
Condorcet) or by utility.
Okay. However, the definition by criteria was never widely accepted,
beyond certain simple ones, such as the Majority Criterion, and Arrow
blew the whole thing out of the water. Paradoxically, Arrow rejected
ordering by utility, based on alleged indeterminacy or other incomplete
consideration; but it turns out that it's possible to satisfy the
Arrovian criteria, that are allegedly incompatible, with a minor tweak
to IIA, which has often been considered the weakest link in Arrow's
chain. The substance of IIA is preserved. See Dhillon and Mertens,
Relative Utilitarianism, Econometrica, May 1999, pp 471-498. See
http://rangevoting.org/DhillonM.html
Okay, but I can't make use of that. I don't know what CONT is (or their
weaker version of monotonicity, for that matter), and the notation from
hell deters me.
Also, I'll note that the page mentions a version of Range where the
favorite gets score 1 and the most-hated gets score 0. If this input is
used for Range, and voters would try to optimize their votes and vote
Approval-style, would that constitute insincerity in your view?
As for Range, either Range, the method, has a well defined input or it
has not. If it has, then incentives to misrepresent the input is bad,
and would count as strategy. If it has not, then how can it make sense
of the input to find a good output (choice or social ordering)?
The input is well-defined, it's provided by the voters. What cannot be
done is to define the input exclusively by a preference profile,
additional information my be incorporated. "Preference profile" is
clearly inadequate information to allow utility optimization; preference
strength information is also necessary, and, for practical decision
making (even by individuals, and voting systems involve individual
decision-making), lottery probabilities are also necessary. The voter is
making choices in a lottery, and to do this intelligently requires
estimating the lottery probabilities for each option.
Is there such a thing as a preference strength information in a vacuum?
If there is, then altering that information (beyond rounding errors)
misrepresents the input. If there isn't, then the voting method is
resistant to strategy simply because strategy is no longer strategy,
it's just part of finding which of the set of "potentially correctly
represented inputs" that maximizes the chance that you get what you want.
A strategic Range vote does not "misrepresent the input," because the
input to the system is a product, in the voter's estimation, of the
relative utility of the outcome and the probability that the outcome is
relevant.
That means that there'll be a feedback loop in the system; the voters
vote in mock elections (that is, polls), then take the output of those
to further refine their next input. Now, in the ideal situation for
ranked vote methods, there is no feedback loop, and what loop exists in
practical situations exists because no method can be strategyproof.
When I say this, I'm excluding external feedback loops, like ranking a
candidate for re-election lower because he didn't fulfill your
expectations the last time around. Those are parts of democracy. But
let's say you froze time just before the election. The voters shouldn't
need to use mechanisms external to the voting method to get a good
result, or run feedback loops within that frozen world. If they're
absolutely necessary, have a computer do it as part of the method itself
and let voters vote.
I.e., the full preference profile consists of a rank order, with a
preference strength in each adjacent pair in the order. The preference
strength is then adjusted according to the probability that this pair is
a relevant one, that there is some finite probability that the vote in
that pair will improve the outcome. Further, there is a constraint: the
sum of all the adjacent pairwise preferences must equal one full vote.
In this social welfare function, preference order is preserved with two
exceptions: where the probability of relevance is zero, the preference
strength in the pair goes to zero, thus equating the two outcomes; as
long as there is nonzero probability, no matter how small, the
preference order is maintained. It will be noticed, I'm sure, that this
sets up independence from irrelevant alternatives, IIA, because if an
irrelevant alternative appears in the full candidate set (which
Dhillon/Mertens also define), it does not have any effect on the other
preference strengths. Only relevant alternatives can do that.
Again, is Approval-style insincere under this welfare function?
Further, if the preference strength is below the resolution of the
voting system, the preference may be lost. In pure RU, there is no
resolution limit. I don't know of any significant opinion that a
resolution beyond 1/100 of a vote is needed in practical systems.
Granted. That's kind of like truncation in a system that has infinite
write-ins; the latter's a quantization of a set with regards to another
set, and the former's an uniform (but not total) quantization of the
data of all candidates.
The problem here is that estimating probabilities is "strategy." Thus
what we may call "strategy" is part of the system.
And since strategy involves adjusting opinions based on others, this
implies the need for external feedback systems.
[snip]
The large majority of people with Open Voting will, under anything
resembling current conditions, Bullet Vote. *That is a strategic vote*.
Yes, it is. My simple example here is the Nader-Gore-Bush case. If this
was Approval, most Nader voters would vote Nader only in the first
"round" (poll round). Then they'd see that they're splitting the liberal
vote, and would vote Nader-Gore afterwards. In my opinion, a voting
system should permit the Nader voters to say Nader > Gore > Bush and not
have to deal with the iteration. Range can do this, sort of; if you're a
Nader voter and vote Gore higher than (Bush margin over Gore)/(number of
Nader voters), and all Nader voters do this, Gore wins. But if the
voters are adamant about optimizing their votes, they're going to vote
Approval-style.
Strategic voting generally *improves* outcomes, in real voting
situations. When the voting system gets very good, such that "fully
sincere and accurate" voting will choose the optimal winner, this
becomes untrue, but it never goes to the point of serious damage.
Then why is the Bayesian regret of strategic Plurality greater (worse)
than that of honest Plurality? Plurality is by no means a "very good"
method. (Of course, BR could be wrong - a bad metric.)
And we have to remember that "fully sincere and accurate" voting with a
Condorcet method can sometimes choose a very poor winner, *in realistic
social choice situations.* It's not common, but it happens.
I'm not familiar with that. Which situations were you thinking of?
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