At 05:28 PM 5/27/2010, Jameson Quinn wrote:
Correct strategy in APV when the two frontrunners are ideologically
distinct is to disapprove one and everybody worse, prefer the other
and everybody better, and approve everybody in between.
Eh? That forces favorite betrayal, doesn't it?
No.
Okay, by "approve," you must mean "approve or prefer." This is also
"correct strategy," i.e., maximizes expected outcome, with any
Bucklin method I've seen. The more a third candidate approaches
parity with the others, the less obvious it becomes. With a runoff as
a possibility when there is majority failure, it is possible to defer
making the decision to approve a frontrunner, such that one will only
do it if the preference strength for more-preferred candidates is
low. With three major candidates, the probability that voters have a
good understanding of all three goes down. Most voters will still
have a first choice. I can say that when I come to a race on a ballot
where there are only unknown candidates, I skip it, unless I know of
a good write-in.
And I recommend that behavior. If one is not willing to defer the
judgment to the rest of the electorate, one can write in "Someone
Else, 27 West 57th Place, Nowhere, MA." (Local rules ask for an
address for write-ins and the clerks tend to disregard write-ins
without an address. But they are still reported as "write-in," and
still for part of the basis for a majority, and are therefore a vote
against all other candidates.)
Wo what this strategy does is to, by default, seek a majority for one
of the frontrunners. It's likely to do so unless there are more than
two frontrunners. The supporters of minor candidates normally know
that they are minor, so they are the most likely to add additional approvals.
"Correct strategy" presumes that a particular goal is "correct."
What is it, in this case? Presumed here is an assumption that
ideology is the issue.
I give a more precise and general definition below for the shorthand
"ideology", which makes your objections moot. Perhaps you should
finish a paragraph before writing several in response to the first sentence.
Your "should" presumes a behavioral model here which is inaccurate. I
use the comments of others as grist for generating my own comments. I
frequently respond as I read. I risk sticking my foot in my mouth.
You get to see my reactions from *before* you have completed your
argument. Some of them will be "moot," in which case you can thank me
for effectively agreeing with you. I.e., for making an objection,
say, that you would see as needing argument, which you supplied. My
goal is discursive, not generally polemic. When I move into polemic
mode, you will see my responses become far shorter. These are, for
me, discussions, explorations, not finished argument in a debate. As
this proceeds, though, for me, the issues become clearer, and the
background generated becomes part of the foundation of my continuing
positions (or shifts those positions).
This isn't for everyone. It is for me, and for you and others if you
care to participate or read. If you don't, no obligation. There is no
presumption, with mailing lists, that anyone has read anything,
unless they respond.
If voluntary and honest. But one dishonest strategic expression can
"poison" a number of honest expressions. Moreover, even semi-honest
strategy creates two classes of voting power - strategic and
nonstrategic - which hurts legitimacy.
I would encourage all voters to vote strategically and honestly. In
a Bucklin system there is no advantage to dishonesty that is worth
the risk. I.e., from a game theory point of view, net zero or
negative expected gain.
I happen to agree. But some voters might overestimate their capacity
to predict behavior, and the fact that they're wrong doesn't stop
the harm they do. In my system, where there is never more and almost
always significantly less payoff from dishonest strategy, this is
less of a danger.
The harm they do is mostly to themselves, not to others. The supposed
rational strategy for these voters, if based on overestimation of the
accuracy of their knowledge, results in their exclusion from the
decisive electorate. In other words, the method will maximize the
utility of everyone else. Alternatively, if they cast a
"turkey-raising" vote, we do have the possibility that a majority
raise that turkey, and it becomes the national flag. When a majority
makes a mistake, it's done until the next opportunity. It is
impossible to prevent the majority from making mistakes through
voting systems! If a majority want to vote with a stupid strategy,
and turkey-raising with runoff methods is, at least, very dangerous,
they can do it.
I find it practically inconceivable that a normal electorate would do
this in large numbers. So such a strategy can only afflict small
groups, and affect close elections. In Lizard v Wizard, did some of
the voters favoring the Lizard vote for the Wizard in the primary?
It's not impossible, but awfully unlikely for there to have been more
than a scattering. Most voters were, I'm sure, just figuring out whom
they most supported. The Lizard had a strong political base, and one
which would be *very* opposed to the Wizard. No, this was just
classic center squeeze, and if the method had been Bucklin, Roemer
would have leapt into first place, and quite probably would have
gained a majority in the primary, finishing the election. If not, it
would have been Lizard v. Roemer in the runoff, and Roemer would
probably have creamed the Lizard. Or not. The problem woudl be
preference strength. The runoof that was Lizard v. Wizard had huge
turnout, exceeding the primary turnout (which was a general election
primary, as I recall). Lizard v. Roemer would have been much lower
turnout, because fewer would have cared so strongly.
(For those who don't know this election, I recommend Poundstone,
Gaming the Vote. The Lizard was a corrupt Democrat, and the Wizard
had been the Grand Wizard of the KKK. Because the Wizard was on the
ballot, turnout among people inclined to support the KKK in some way
probably turned out heavily in the primary. In the runoff, support
for the Wizard barely increased, and the Wizard had been in second
place in the primary anyway. There was a similar effect in the French
presidential election which is also often given as an example of
center squeeze. Extremist candidate, probably high turnout for
supporters in the primary, same turnout in the runoff, somewhat
increased because now The Forces of Truth and Justice finally have a
chance! -- but basically done. In ordinary runoffs, a dark horse can
come up to second place and now has a chance and this is where runoffs shine.
Anyway, you didn't respond to my critique of semi-honest strategy.
In APV, naive human nature strategy is closer to being the same as
optimal strategy, so the difference in voting power is less. This
means more legitimacy.
This is important: the math hasn't been done, but my intuition here
is that the rational strategic Bucklin ballot is a Range ballot with
these restrictions: the candidates are divided into two sets,
approved and non-approved, and range ratings are best as sincere
ratings *within these sets*.
I vigorously disagree. The rational strategic Bucklin ballot is, to
first approximation, an approval ballot. In some cases (which I
don't quite have a handle on) it might be rational to move a single
candidate down from maximal to minimal approval, or to add a minimal
approval to a single candidate who would not have made the cut under
approval. Intermediate approved rankings are never rational if all
voters are purely rational, though if there are some honest voters,
it may become rational to use intermediate approvals occasionally.
Unapproved rankings besides the bottom are used for turkey-raising if at all.
A Bucklin ballot is a kind of approval ballot, yes. But it allows
ranking within the approved class, and rational strategy for the
ranking is sincere Range equivalent, within the approved range. That
range can be narrow (one candidate fits in it) or broad (many
candidates, but all of which the voter is willing, under the
conditions, to approve. That's a separate issue, how to decide who
fits into the approved class.) The argument about "intermediate
rankings" would apply to Range voting as well, and it's bogus there
as well as here. It's based on shallow analysis that makes
assumptions about what voters want that aren't accurate as to real
voters. The addition of unapproved rankings to a Bucklin ballot is a
new idea, and should not be mixed up with criticism of basic Bucklin,
including Bucklin/runoff as a general proposal, replacing top two runoff.
Note that if we think that the rational strategy for ranking is
"approval style," no intermediate rankings, we must, logically, think
the same for Range voting. I've done the math on that, you know.
Whether or not pure approval strategy is best is an issue dependent
upon voter knowledge as well as voter preference strengths and the
difficulty of making decisions. Decisions in the presence of high
roundoff error become more difficult, not easier. I.e, if I have
trouble deciding whether to put a candidate in top-approved or
bottom-approved, I can quickly resolve this by putting the candidate
in middle-approved. The strategic difference would be small, thus the
ability to make an intermediate decision is helpful.
Essentially, the middle-approved rating, which Mr. Quinn thinks
useless or even harmful, has a real function to assist voters in
categorizing. Ini general, the arguments for limiting expressivity
are similar to the argumewnts for Approval vs. Range. But Range
*allows* voting approval style, if the voter thinks that easier!
This qualification "if there are some honest voters" is useless. Most
voters are and will be relatively honest within customs and their
understanding of possibilities. Most voters who would greatly prefer
an unnamed candidate for an office do not therefore write in that
name unless they have reason to believe that others will do so, or
they really do have no significant preference between the candidates
on the ballot.
Middle ranks were used. Mr. Quinn thinks, apparently, that the voters
were strategically stupid. Okay, if that's true, they will learn and
usage of the middle rank will decline. I do predict some level of
decline, but it will not stop happening.
Note that "approval" (distinct from "preferred") is really "extra"
from this black-and-white strategic viewpoint.
That's why adding levers and knobs to your voting system is
dangerous if they can be used strategically with impunity.
I've seen no cogent example of this. In evaluating strategy, I'd
encourage Mr. Quinn and anyone else to *start* with utilities.
I do.
But he has not disclosed them, numerically. He has, I'd guess, some
seat-of-the-pants concept of utilities and how they motivate voters.
But by not being quantified, it can then easily lead to contradictory
conclusions that are not recognized as such. A lot of error in
analyzing voting systems is caused by this.
Voters will bullet vote, commonly. It is a rational and sensible and
*sincere* strategy, properly understood.
Absolutely true in many, but not all, cases.
I didn't assert that it was for all cases. However, I'm quite
suspicious of facile assumptions that a voter will "really" approve
of A, but will not vote for A becasue the voter prefers B. To me,
this means that, because of the presence of B, the voter does *not*
approve of A, and the voter will only approve of A relative to
another option, C. Approval drove the ranked voting anaysts nuts,
because ranking can be imagined to be a quality of the candidates,
whereas approval is not. In an election with many candidates, there
are very many possible sincere votes. Bullet voting is sincere, it is
a sincere and accurate division of candidates into two classes, with
every candidate in the approved class being preferred to every
candidate in the unapproved class.
Thus, I'll claim, unless it's just a plain mistake, bullet voting is
always sincere. This would take us into the old debate about whether
or not Approval Voting satisfies the majority criterion.
I'd guess that mostly it's rational and sincere; sometimes it's
rational and insincere; and rarely it's irrational and sincere.
Mr. Quinn's proposal is indeed simpler,
Simpler; and better at harmonizing naive, individually optimal, and
socially optimal strategies. Both are important advantages.
So we "treat" naivety by hobbling evreryone else?
That is, a solid majority coalition might elect its more radical
member, not the centrist. "Solid majority" means that the median
voter is a member of that coalition, supporting the "radical" on
that side over all other candidates. Unlike closed primaries, if
there's a majority but it's not solid, the centrist from that side
is probably elected.
In the example shown, there was a drastic difference between the
winner and loser.
And it was an artificially-constructed example, one which both the
naive and the correct strategy (which are the same in this case)
would tend to discourage from ever happening.
In other words, you are attempting to prevent stupid voters from
negatively influencing the outcome, while still helping them to get
what you think they want.
If you're relying on it working, people will manipulate it, and that
manipulation will be arguably biased; that is, one side will
arguably be doing it more than the other. (Whether there truly is a
bias or not doesn't matter; the mere appearance of bias undermines legitimacy.)
What I have not seen is a manipulation scenario that makes sense
*for the manipulators*, when risks are considered along with
possible gain. As I've mentioned, though, it is possible that with
full knowledge, any voting system can be "manipulated," but, if it
is a utility-maximizing system, the "damage" is limited to the
voting power of the manipulating faction. It's, in fact,
questionable if it is damage at all, and if that faction directly
uses its power, it would not be bothering with "turkey raising" as
Mr. Quinn proposed.
Again, want to bet? You program your agents to vote your strategy,
I'll program mine to take them to the bank. All agents have random
preferences, except that each candidate is either "Jameson-style" or
"Abd-style", with a small bonus to the utility of all respective
agents for that candidate. We can do any reasonable set of
pre-election imperfect information, though of course zero
information is by far the easiest to program for.
Otherwise, this is just hot air.
I know that Bucklin *did* work. I have no reason to believe that it
wouldn't continue to do so. The changes I'm suggesting simply
improve it to reflect modern voting system theory, they are not drastic.
The "manipulations" as designed would be somewhere between difficult
to impossible. Mr. Quinn did not show an exact scenario that
reflected how the method would actually work. Basically, it's
possible that a faction of voters, speaking roughly, could improve
results, from their perspective, *a little*, using a complex
strategy that could backfire, easily. Many theorists have proposed
voting strategies that were like this. In fact, serious voting
strategy, that requires voters to vote with reversed preference,
seems to be quite rare, that we would see it in nonpartisan
elections seems vanishingly possible, to impossible. The strategist
is asking voters to state on the ballot what they don't believe.
As I've mentioned before, if my favorite candidate suggested that to
me, the candidate would no longer be my favorite.
Ever heard of Limbaugh's "operation chaos"? It's not the candidates
you should worry about, but their loose-cannon allies.
Thus promoting a turkey-raising strategy, in this context, would be
very hazardous. And I doubt that voters would do it individually.
This is a red herring.
The basic error that Mr. Quinn makes is in assuming that bullet
voting will be a natural and practically universal strategy.
Where on earth did I say that? In fact, I said several things which
contradict that: that Bucklin would encourage (strategically
misguided) extra ranks, and that correct strategy would find a CW in
one round if non-supporters cared about the distinction between the
two frontrunners.
You have not established that they are strategically misguided, then
you build further assumptions on top of that. If you could show that
middle ranks were contrary to the interests of the voters, should
they use them, you would have a case for rejecting them. Unless it
happens that "contrary to the interests of the voters who use them"
results in better social utility. In other words, these voters by
being "foolish" are helping the society to make better choices. I
wouldn't call that foolish at all. I'd call it beneficial and for
voters to do it, truly altruistic, not foolishly altruistic. This is,
in fact, the general debate over Range voting, and we have good
reason to believe -- and I have mathematical reason to believe --
that even a few voters voting intermediate ratings causes the overall
performance to improve. Even one, in fact. It dithers the result.
Definitely, bullet voting will be common. It's common with IRV where
it's allowed. It's a sensible, rational strategy for a voter without
sufficient information to do more than vote for their favorite, and
Lewis Carroll invented Asset Voting to enfranchise these voters with STV.
Then, to the contrary, he posits some clever, conniving strategy
Oh, I get it, calling your system design a "trick" (later clarified
to mean not evil but unstable) is not fair, but calling mine a
"clever, conniving strategy" is OK.
No, that was not the system design, it was the turkey-raising
strategy, and I think you agree that this is not exactly
"straightforward." It's possible to do it in Bucklin without Favorite
Betrayal, which isn't true with top two runoff. But that's no
improvement from the point of view of sincerity.
[...]
Let me list the ways I find my proposal better than yours, in order
of importance.
1. Simpler to explain.
2. Naive, rational, and socially-optimal semi-honest strategies are
closer to each other.
3. My system has stronger reasons not to use dishonest strategies
(turkey-raising).
Okay, let's work on explanations, ballot instructions. Plurality has
the simplest ballot instructions. Approval next to that, I'd say.
Ballot instructions, however, don't include "strategy." I've seen an
exception, where it was claimed in the proposed Vermont IRV
legislation that adding a lower ranked vote could not hurt your
more-preferred candidate's chances of winning, and that was a
mandated ballot instruction. And it was false. Way to go, Terrill! (I
think he wrote this one, in the time he put it up.) That's because a
true majority was required. And if there was no majority, the top
three were tossed to the Vermont legislature for decision. So by
ranking your second choice, you could cause the election to complete,
whereas if you didn't do that, there would have been no majority and
your candidate would have had a chance. (But as the third of the
three in votes, well, it better be center squeeze!)
The second reason is an argument for plurality, taking it to the
extreme. Or, then, for Approval. Or, then, for Range 2. Etc. There is
a point where additional range resolution provides declining benefit,
but Range experts like Smith want to see high-resolution range, at
least Range 99 or 100. It's clear that lowering Range resolution
causes loss of social utility, unless, of course, everyone bullet
votes. But we know that Range, with mixed strategy, is better than
Approval. (Approval is Range 1).
You're arguing against reason 3 by saying your system's
anti-dishonest-strategy properties are strong enough. You may be
right. I still prefer to be doubly safe. But that's my weakest reason anyway.
Turkey-raising strategy would apply to two-rank Bucklin or even
simple Approval, if a runoff is required with majority failure, and
especially if it's a naive top-two runoff. It gets really difficult
with top three, because the goal, to knock the likely winner out of
the runoff, gets much more difficult. That likely winner is really,
in Bucklin, quite likely to win the primary. To knock him or her down
to third place is hard, but not impossible, I'd say. To fourth place,
it gets ridiculously difficult for a strategy that is dicey and
difficult to promote in the first place, you can lose support just by
advocating it.
What are your system's advantages? To me, it's a lot of rules - for
nothing that my system can't accomplish using a nonbinding poll and
a write-in runoff.
Don't confuse the basic system with tweaks that are possible later
improvements. While I'm proposing is basic Bucklin, three-rank, with
only the no-overvoting rule completely tossed from all rounds, as a
replacement for top two runoff. I'm proposing further refinements for
later implementation if justified by the already-good ballot data
that would be collected. I've arranged them in a hierarchy of precedence. So:
1. Context: jurisdiction with top-two runoff.
2. Proposed first reform: Traditional (Duluth) Bucklin primary, with
only the rule requiring ballots to be disregarded in an overvoted
rank or lower -- which only affects first rank and second rank, since
original Bucklin allowed unrestricted voting in third rank already.
This is actually simpler to implement than Duluth Bucklin.
2a. Options: top three runoff, Bucklin runoff. Or top two runoff,
write-ins allowed in the runoff, Bucklin runoff (but maybe two-rank).
Less preferred by me: simple top two plurality runoff.
then
3. Add disapproved rank for data collection. The ballot is now a
Range 4 ballot, straight, with explicit approval cutoff at midrange.
(Actually, it treats midrange as minimum approval.)
4. Use Condorcet analysis of the ballots to make the method guarantee
that an expressed Condorcet winner makes it into the runoff. In this
event, the runoff should be plurality with only two candidates
allowed, or a condorcet compliant method, there are various
possibilites that could exist and still retain the benefits of
(almost complete0 social utility maximization. Other rules might be
developed, based on analysis of election history, that could avoid
unnecessary runoffs.
5. Increase the range resolution if needed. It's prossible that
performance improves a bit to the point where all candidates can be
fully ranked, and even beyond that point. (Even though Range 2 allows
full ranking of 3 candidates, performance increases when more ranks
are allowed, because then full ranking can be done *and* better
expression of preference strength is possible.)
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