[EM] The path to election reform, was Re:

[Abd ul-Rahman Lomax]

At 02:13 PM 12/6/2008, Kevin Venzke wrote:
>Hello,
>
>--- En date de : Jeu 4.12.08, Abd ul-Rahman 
>Lomax <abd at lomaxdesign.com> a écrit :
> > > Ok, so sincerity doesn't matter. It's a red
> > herring, it's something not
> > > to be dwelled upon.
> >
> > My, my, is this an appeal to the common meaning of
> > "sincerity"? After all we've done to point out
> > the technical meanings and to respond to others who have
> > called these words "terms of art," i.e., not to be
> > taken in their common meanings?
>
>No, it was almost certainly me trying to summarize something you had
>said. I'm pretty sure you have said yourself that sincerity is a red
>herring. Whether you were then using a different meaning of "sincerity,"
>or a different context, is difficult for me to tell.

Sincerity is a red herring when it comes to 
expressing preference strength. It's not a red 
herring when it comes to preference reversal. 
Preference reversal implies a substantial 
departure from preference order, which is 
explicitly violates. Preference equality (the 
extreme) does not violate this, it merely does 
not express a preference that the voter indicates 
is not significant, for whatever reason. Rather, 
it reflects the indeterminacy of rank that 
offends so many. Kevin, you are certainly not the first!

> > Voting is a choice, not a sentiment. Consider a voting
> > method as a black box. It has some controls on the outside.
> > You manipulate the controls and you influence the result.
> > How the controls translate to influence is well known, with
> > simple methods, not necessarily with complex ones.
>
>I'm starting to wonder whether this viewpoint is of any use to you.
>It seems to me that perhaps all you can do with it, is argue that the
>placement of the Approval cutoff need not correspond to any absolute,
>abstract preference.

That's correct, but that's not a small thing. As 
real human beings, we set the Approval cutoff by 
considering the realistic possible outcome set, 
which includes a consideration of possibility. We 
can imagine some kind of absolute preference, 
I've described it in other posts in this series: 
it is the  zero-knowledge assessment of probable 
outcome. This is "strategy" but it isn't 
dependent upon the knowledge of how other voters 
would vote, and even though it could be 
considered theoretically optimal, it's not clear 
at all to me that I would vote that way. First of 
all, restrict the candidate set to candidates the 
*voter* immediately rejects as impossible. No, 
Santa Claus is not going to be elected. Probably 
all write-in possibilities are excluded except 
those the voter thinks might actually get some 
other votes. Then, N candidates remain, and the 
voter has no assessment of relative probability, 
except that they are all, for the voter, nonzero. 
Assign a probability of 1/N to each candidate, 
and multiple the relative utility estimate by 
this. (If assessing the relative utility estimate 
is too hard, assume that rank order spreads 
relative utility. This turns the vote into a kind 
of Borda vote, or based on a Borda vote.) The 
expected outcome is the sum of all individual 
expected utilities, and the voter would then 
approval all candidates with higher expected 
utility than that, or possibly equal to that.

Nobody expects anyone to vote that way. However, 
note that I've suggested that rating higher than 
midrange be considered an acceptance of the 
candidate for purposes of determining majority vote. This is equivalent.

Defining midrange as the approval cutoff, then, 
with the likelihood that nearly all voters -- 
except in elections with small N -- will 
truncate, not expressing a vote for all 
above-midrange candidates, and having a majority 
requirement, will encourage but not require "more 
sincere" voting, i.e., more expression of all candidates considered acceptable.

But it is much easier to vote by looking only at 
candidates with *significant* election 
probability, the "math" can usually be done in 
one's head, particularly when there are only two 
frontrunners. In Approval, those determine the 
votes for the rest of the candidates. In Range, they constrain those votes.

> > Certainly a voter may push the buttons
> > "insincerely." But that would mean, to me, that
> > the voter does not seek to maximize the outcome. A vote for
> > a frontrunner in a Plurality election, if the voter would
> > prefer someone else, is that "sincere"?
>
>Either answer is possible.

That's correct. Which means that sincerity in 
this meaning is basically meaningless as applied 
to votes. Technically, the voter has reversed 
preference if the voter does not write in the 
name of every candidate the voter prefers to the 
election set. However, we normally restrict our 
consideration to the set of candidates on the 
ballot, and allow that a voter may consider the 
election probabilities of all non-ballot 
candidates to be zero. Ahem. The voter votes with 
consideration of realistic election 
probabilities. Thus strategic voting, as it has 
been often defined, is inevitable, it's only a 
question of what *kind* of strategic voting. 
(Disallow write-ins, and then demand that the 
voter express all preferences within the set of 
candidates on the ballot, you can then return to 
some discrimination between strategic and 
non-strategic. But that's contrary to higher 
democratic norms. Write-ins are, I understand, 
generally not allowed outside the U.S. That's one 
aspect of democracy that we got right. Other 
countries got other aspects. (Note that I don't 
consider registration requirements, that all 
candidates be *registered*, to be inferior, as 
long as registration is simple, can be done up to 
the day before the election, and is so low-cost 
that the cost is negligible, it would not impeded 
any serious candidate -- nor a voter in Asset who 
wants to represent himself or herself in 
subsequent process. San Francisco has a 
"write-in" system like this, in the primaries. It 
used to have the same in the runoffs, but, folks, 
politics is everywhere. Use it or lose it, defend 
it or it *will* be gone. That rule change 
excluded a specific candidate, it was challenged, 
and the California Supreme Court, a bit to my 
surprise, defined a runoff election as being 
"part of the same election." That was a possible 
conclusion, but a poor one, when we look at 
standard deliberative process, which clearly 
wants a series of independent elections, and 
which allows the electorate, by majority vote, to 
postpone the result. The Court clearly followed 
the principle that the runoff *must* terminate 
with election, no matter what, a principle which 
has been raised higher than that of majority 
rule. There is a word for this, which I apply 
technically: fascist. Mild, to be sure, and 
generally moot. It is rare that the write-in 
possibility is effectively used in serious contested elections.

> > We can call a vote concealing preference
> > "insincere," but that does, indeed, take the
> > meaning quite away from the common meaning. Note that if the
> > voter bullet votes for the favorite, the voter is similarly
> > concealing other preferences within the rejected category.
> > If equal ranking in the presence of a preference is
> > insincere, then *every Open Voting vote is insincere.*
> > It's *impossible* to vote sincerely, under that view.
> > Which is why the view is actually preposterous.
>
>Well, that's not how I would argue that Approval encourages "insincere"
>voting. But that's a separate issue.
>
>So, one would rather say that every strategic vote is at least at the
>same time sincere.

In Range methods, yes. Not so with ranked 
methods, and there's the rub. Yes, if we avoid 
calling the choices voters make "preferences" -- 
which is actually done, that is, on RCV ballots, 
for example, they are called "choices" -- then 
the concept of sincerity doesn't apply at all, 
except that we can still assume that the voter is 
"sincerely" attempting to influence the result in 
some way, even if it is just to show contempt or 
silliness. Yes, I deliberately voted for Mickey 
Mouse. That shows what I think of the choices presented to me on the ballot.

But this isn't useful. What is useful is to 
consider preference reversal "insincere," and to 
allow that there are many different sincere votes otherwise.

These sincere votes may be chosen according to 
improvement of expectation strategy, but this is 
different from strategy that reverses 
preferences; in particular, this strategy, either 
partial or fully optimized, averages over many 
voters to approach what would be the average 
fully sincere vote (positive expectation 
Approval, or accurate relative utility Range.) 
Preference reversal has weird effects that I won't go into.

"Strategic voting" in Range corresponds to 
ordinary real-life decision-making process, 
where, faced with multiple choices, we assess 
which ones are reasonably possibilities and 
assign our assets to those, considering relative 
probabilities, to one degree or other. It's not 
some strange new thing that voters have to learn 
in order to be able to vote intelligently.

>One could say that this is a bit of a trick. We can say that Approval
>doesn't have "insincere strategic" votes, due to the way the method works.
>But clearly it can only work this way by lacking a great degree of
>expressiveness.

Of course. But pure ranked methods also lack 
expressiveness, sometimes as much as Approval. 
You want full expressiveness, you want high-resolution Range.

Note that Relative Utilitarianism -- a method of 
preference amalgamation, strictly, not a voting 
method in itself -- uses von Neumann-Morganstern 
utilities, which preserve preference order unless 
there is zero probability for an outcome, in 
which case the preference strength involving that 
outcome goes to zero. Preference is never 
reversed even with a zero probability. Turned 
into a voting system, RU implies Range, and the 
authors, Dhillon and Mertens, specifically 
suggest Approval as a practical appplication 
where the voter decides between 0 and 1 for each 
candidate, maximizing expected outcome.

The decision of where to set the approval cutoff 
is specifically left to the voter, and likewise 
how to weight the votes in higher resolution 
expression. Given sufficient resolution, I would 
preserve any discernable preference, Range 100 is 
more than enough unless there were a ton of 
candidates. (And with a ton of candidates, it's 
highly unlikely that I could knowledgeably rank that many.)

This constrains the Range votes and, with broadly 
distributed candidates, makes them *relatively* deterministic.

> > The question before us is really this: is it better that
> > voters vote "strategy free," which is equivalent
> > to voting "zero knowledge," or is it better that
> > they adjust their votes according to their understanding of
> > the context, i.e., what other voters think.
>
>First of all I don't know what you mean when you say that voting
>"strategy free" is the same as voting "zero knowledge."

This was developed through this discussion. Zero 
knowledge means that the voter cannot use an 
expectation as to how others will vote, because 
the voter does not know. It's a standard concept, 
and a definition of strategic voting using it is 
reasonable, if perhaps misleading, improperly applied.

Pure ranked methods, particularly if equal 
ranking is allowed, allows easy zero knowledge 
voting. Order the candidates in sequence by 
preference of election. (Strictly speaking, it is 
the election that is preferred, not the 
candidates, and the difference affects where I 
rank unknown candidates.) If there is no 
discernable preference, equal rank. Note that 
forced ranking, equal ranking not allowed, does 
not allow sincere voting, because it forces the 
expression of a preference where not exists. If 
we want sincere voting to be possible, we *must* 
allow equal ranking. And that makes the method 
into a form of Approval! -- because it can be 
voted that way. (Though other aspects may make this undesirable to the voter.)

(In general, I prefer allowing the voter to 
choose the "voting system," to a degree. I.e., 
equal ranking should be allowed. A voter should 
be allowed to cast a Later No Harm compliant 
vote, in substance if not in full effect. For 
example, any method which requires a runoff with 
majority failure is not LNH compatible, strictly. 
But in substance, it can be. Terrill Bouricius' 
bill in the Vermont legislature explicity 
claimed, in the ballot instructions, LNH 
compliance, though it wasn't strictly true, 
because a majority was required or the top three 
went to the legislature for resolution by secret ballot vote.)

Range with approval cutoff and sufficient 
resolution can be voted as ranked, including 
using a Borda-type distribution of ratings, 
Approval, or even Plurality. The ballot is the 
most expressive of any that I've seen proposed. 
That freedom of expression, of course, means that 
we cannot derive the voter's vote simply by 
knowing the voter's preferences and preference 
strengths. The voting is a possibly complex 
decision, unpredictable. But very usable!

>My answer to this question is that I'm not sure; I think it depends; I
>also think it's probably a moot point.

It's not moot when words like "sincerity" and 
"strategic voting" are bandied about as if they 
had fixed moral implications! That's what I keep hammering down....

> > Any method which satisfies Later No Harm must not provide
> > this information, or, at least, must not use it. This is why
> > Later No Harm is actually, itself a poor election criterion.
>
>I think that is premature. Of course this makes sense if we're only
>discussing FPP and IRV, and there aren't many other choices. But the
>methods MMPO and Woodall's DSC method satisfy LNHarm, and it wouldn't
>be true to say that they don't use the lower preferences. They just
>are careful to not use those preferences against the voter.

Later No Harm can, in some conditions, remove one 
cause of bullet voting, causing votes to become 
more expressive. I'm not saying that it is 
valueless. But election criteria, in general, are 
analyzed as absolutes, and any voting system 
which contains what I consider essential for true 
result optimization must violate LNH. It's the 
rigid requirement that is a problem. Those 
methods, if they satisfy LNH, must sometimes make 
seriously poor decisions, because the information 
they need to optimize results is missing, and 
*they do not allow it to be expressed.*

Using lower preferences of a voter is not 
"against the voter," and that's part of the LNH 
myth. It is "for the voter." Just not exclusively 
for the voter's first preference. If you would 
not be pleased by an election result, don't vote 
for it! Demand, instead, that the voting system 
require a majority vote to complete. You are then 
essentially consenting to the inconvenience of a 
real runoff by truncating and not expressing 
lower preferences. It's your choice.... Depriving 
the voter of reasonable options, and, in 
particular, depriving the majority of the ability 
to cause election failure, is a serious violation 
of democratic principles, we have too long and 
too often tolerated in the name of efficiency, a false dichotomy.

> > Voters may desire to vote Later No Harm, but this is the
> > kind of concealment of preference that reduces election
> > efficiency. It is a concealment of true preference
> > strengths, so, again, any method which follows Later No Harm
> > has *required* the concealment of preferences. We avoid some
> > level of strategic voting by *requiring* all voters to vote
> > that way.
>
>Ok. That is an interesting argument. It seems to work in favor of Approval
>against both IRV and Range.

This would be Saari's argument for Borda as well. 
Note that this isn't *my* argument, I consider it 
specious and anti-democratic. In order to avoid 
the harm of strategic voting, we require all 
voters to vote strategically, thus 
institionalizing that inaccuracy. It's not 
terribly harmful, though, because Approval votes 
do average out, normally, to results approximating Range results.

> > But if some voters conceal preference, and others do not,
> > with a good method, the results are better than if *all*
> > voters conceal preference. Further, a good method allows the
> > expression of all significant preferences without harm to
> > the voter. "Harm" must mean, not that the voter
> > fails to get their first preference, but that the preference
> > strength between that candidate and the winner is not
> > minimized. Since IRV is not monotonic, as an example, it can
> > seriously harm the voter's interest if that is expressed
> > sincerely. The only reasonable defense against this
> > criticism of IRV is that this is rare.
>
>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!

I'm not *specifically* offended by monotonicity 
failure, in the same way, but it would depend on 
the social utility damage caused by the failure. 
Monotonicity is an Arrovian axiom, and for good 
reason. It's a sign of something seriously wrong with the method.

Here we see an example of the criterion-based 
judgment of voting systems. It's a fundamentally 
flawed and subjective approach, devoid of and not 
susceptible to measurement (except as to 
frequency assessment, given enough ballot and 
poll data, or simulations). That is, we might be 
able to objectively predict how often IRV would 
violate monotonicity, but that gives us no 
objective way to assess the *seriousness* of the failure itself.

But there is a way, which is Bayesian regret, 
which is itself founded on the old utilitarian 
concept, the greatest good for the greatest 
number, converted to a sum of utilities approach. 
Contrary to so many shallow claims, it is 
possible to define interpersonally compatible 
utilities of a kind useful in social choice, and 
that's what Dhillon and Mertens show, and further 
that these utilities can be used in the only 
Social Welfare Function that is compatible with 
the Arrovian set (excepting only that IIA is 
redefined in a reasonable way to apply it to a sum of ratings method).

Allowing voters discretion to vote these 
utilities, then, allows them to approach, through 
their free choices, an ideal voting system. The 
system simply takes their votes *as if they were 
sincere*, and optimizes the results. "Insincere 
voting" in this system simply means not troubling 
to -- or deliberately concealing -- express fine 
preferences. It's foolish to conceal a major 
preference in such a system, unless it is a moot one.

> > Yet that this does harm can only even be perceived if we
> > have sincere Range votes, for all voters, to compare the
> > results with. Range strategic voting does not harm results
> > to the point where they become as inefficient as those of
> > less accurate methods.
>
>If you're talking about simulations now, this doesn't seem to be true.
>"Strategic" Approval (however that was defined) was worse than the
>sincere Condorcet method. You can say that it isn't fair to compare
>strategic Approval to sincere Condorcet, but there aren't any serious
>alternatives for comparison. It's an "unknown" at best for Approval.

First of all, normally the Condorcet Criterion 
works. That's one reason why it has such appeal. 
The simulations show average results. No, it's 
not "unknown," the simulations show comparisons. 
It's true that it is possible that some kinds of 
optimized Approval, possibly those used in the 
simulations -- it's totally unclear to me what 
"strategic Approval," but presumably this means 
applying certain fixed strategies, may 
underperform, on average, sincere Condorcet, but 
I'd want to look at the nature of the failures. 
I'd be surprised if the differences were large. I 
should look at the simulation results again. Note 
that I was describing Range Voting, not Approval, 
but Range with full strategic voting fades into 
Approval, so, sure, a totally unrealistic extreme 
of Range could possibly underperform a Condorcet 
method. But that's not in the simulations, and 
while Approval is a Range method, it's the 
absolute extreme in the unexpressive end.

>I'm not sure we really need simulations for this. I try to imagine how
>insincere Condorcet voters would have to be, to reduce the quality of
>the method to the equivalent of only having two rank levels.

You want lots of rank levels, you want Range or 
Borda (almost equivalent, but Range fixes some 
Borda problems.) Approval works better than you 
might expect because those rank levels are chosen 
by many voters and average out to show much more 
information about the voter set than individual voters can express.

(How insincere? Preference reversal is black and 
white, it happens or it doesn't. The difficult 
with Condorcet isn't that, it is that trivial 
preferences are necessarily equated with large 
ones. Now, if the Condorcet method allows equal 
ranking, it is really a more sophisticated form 
of Approval, or perhaps you'd prefer to say Range, just as Bucklin is.

>What I am unable to get past, is that there is no theoretical reason
>for Range voters to vote "accurately" other than that we can agree that
>we would like them to. So the accurate, non-strategic Range voters are
>either voting in error, or they are choosing to play nice.

Choosing to play nice is a strategic vote that 
one accomplishes, in Range, by voting, as closely 
as possible, a measure of one's satisfaction with 
each candidate. The theoretical reason for voters 
to do this? That it works, that many or even most 
people will do it, quite likely, that it's easier 
than deciding pure rank, what else do you need.

Absolutely, voters will deviate from the 
"accurate" vote, with or without intention. They 
will approximate. They will bullet vote. They 
will spread. They will do it all. And all of it, 
together, is more expressive of the true position 
of the electorate than is possible with a pure 
ranked method. Take Borda, allow equal ranking, 
it's the same. Range defaults, with full-on, 
high-knowledge strategic voting, to Approval. 
(The voter will vote for the candidate where it 
is possible for the voter to improve the outcome, 
which, the voter will know with high precision, 
even certainty. (total:knowledge: it's a tie 
without the vote or the vote will create a tie). 
Why call this Approval and not FPTP? Because that 
voter can still vote, in addition, for any 
candidate preferred to the effective maximizer, 
and I think almost all such voters would. 
Otherwise their vote is not sincere, it would 
reverse preference but since it is harmless to 
express that preference, and is, in addition, 
insurance against being wrong about the true 
frontrunner(s), voters will do it. Why not be more sincere if it is harmless?

Strategic voting in Approval is actually easier 
to predict than so-called sincere voting. For the 
majority of voters in real election situations, 
most will know who the frontrunners are.

>I think it would be reckless to just assume we would get this, so I
>cautiously view Range as exactly the same as Approval. Approval is in
>my top 5 list, if I were able to propose something. But I have
>reservations about it, and think we can probably do better without losing
>anything.

But that's actually silly, Kevin. Every 
indication we have is that some fraction of 
voters will vote intermediate ratings; for many 
of them, it is strategically harmless or even 
advantageous (as "insurance.") Further, the 
existence of unpredictable numbers of fractional 
votes dithers the result, making ties much less 
possible, and we can assume that intermediate 
votes are *relatively* sincere. To consider 
higher resolution range as "exactly the same" as Approval is preposterous.

Now, Approval is in your "top five" list. Various 
methods have various social and political costs 
to implementation. Which one is more accessible? 
Which one costs practically nothing and, 
remember, for a very low-cost reform, the issue 
is whether or not it could cause serious damage. 
Approval's alleged "failures" are that (1) it can 
reduce to Plurality, allegedly. Except that this 
isn't the case when there is a spoiler candidate, 
we will almost certainly substantial numbers of 
additional votes from supporters of the spoiler. 
And, compared to Plurality, this result is 
clearly harmless, it hasn't made the situation 
worse. SU estimates show very substantial 
improvements, comparable to much more expensive 
methods. It's probably the 
biggest-bang-for-the-buck method. Comparing 
Approval to Condorcet is the wrong comparison 
and, in fact, there is no real conflict.

Start with Approval, you'd go to 
equal-ranking-allowed Condorcet, which is more 
accurate than pure ranked Condorcet. I'd be 
astonished if it were not higher SU than pure ranked Condorcet.

Further, allowing equal ranking will certainly 
reduce the number of spoiled ballots. While some 
of that information is bogus, on average counting 
it reflects voter intention better than 
discarding it. (Consider Florida 2000; if the 
votes which had overvoted Gore and Buchanan -- as 
a rather obvious result of bad ballot design -- 
had been counted, Buchanan would have gotten some 
extra votes, which would have been totally 
harmless. Gore would have gotten the same number 
of additional votes, *most of which were 
doubtless the intended vote.* It's a bit of a 
shame that the U.S. courts don't allow the use of 
statistical methods to recover intended votes, 
but rather insist on the pure examination of each 
vote individually. If there is a hanging chad on 
some other punch than Gore, for example, and Gore 
is clearly punched, or even equally badly 
punched, there is a certain probability that the 
vote was intended for Gore. It *wasn't* intended 
for Bush, unless Bush had the hanging chad. If 
so, the voter was abstaining, if the vote was 
intentional, from the real election, and it's 
moot. You could count both, as I would do. It 
could be argued that such votes should be counted 
fractionally, but some counting is better than 
none! Politics, unfortunately, affects all of 
this, so that the issue doesn't become what best 
discerns the intention of the electorate, as 
expressed by the votes and the method, but who 
wins. Anyone here who thinks that the U.S. 
Supreme Court in late 2000 made its decision 
purely on the basis of legal principles, please 
raise your hand! (Some who supported the decision 
have even written, you are surprised that the Court is political? Get over it!)

> > In an election like this, I'd always have a runoff.
>
>If you simply have a runoff, what's to stop clever candidates from running
>with a clone? Do you think these candidates' supporters would become
>offended by this behavior?

Hello? A clone would not affect the Range winner, 
essentially. Range satisfies clone independence, 
under reasonable assumptions. Remember, clones 
impact campaign costs, very much of successful 
campaigning is as simple as gaining positive name 
recognition. Divide that among two candidates? 
Bad idea, quite likely to cause a loss. In any 
case, cloning would not affect whether or not the 
clone or cloned candidate would beat the Range 
winner pairwise. I have *not* proposed top-two 
Range. What I've proposed is a method where 
majority failure, i.e., the failure of a majority 
to approve of a winner (which could be defined as 
voting above a set "approval cutoff," and the 
voters know that. For example, in Range 3, with 
votes of -1, -1/3, +2/3, 1, it could be defined 
that any positive vote was approval. (which with 
standard approval strategy makes perfect sense).

If a runoff is forced, it would not be among the 
top two Range winners. That would be vulnerable 
to cloning, though only in a very narrow sense. 
(It could be argued that in this case, either of 
these candidates is the best winner, this is pure 
Range, so cloning is really moot. If you can get 
there, you don't need cloning, and you just made 
the campaigning harder.) No, it would be between 
a Range winner and any candidate who beats the 
Range winner pairwise, who, with fixed 
preferences assumed and the same voters, would 
win a runoff. If there are two of these, ideally 
they would all be in the runoff, but I'd pick the 
Condorcet winner among them, and if they were 
members of a cycle, I'd pick the one with the highest Range rating.

Pretty difficult to game this system in a truly 
negative way. It encourages voters to express all 
sincere preferences except possibly the truly 
moot, provided that the Range method has 
sufficient resolution. Low-res range would have a 
preference marker. I called Approval with 
preferred marker A+, and if this was used in 
determining the winner, I called it A+/PW, PW for 
pairwise. But there is no advantage to this, that I can see, over ER-Bucklin.

The immediate election reforms I recommend are 
(1) top two runoff, or specifically keeping 
runoffs where they exist. (2) Approval or 
Bucklin, and particularly one of these as the 
primary in TTR, and possibly the secondary, where 
they might be plurality methods, which I still 
don't like, personally. I'd use Asset to resolve 
a continued problem. Far more efficient, and fully democratic.

In any case, allowing equal ranking is essential 
to allowing a fully expressive vote. Range 
without that is simply Borda count, a good method 
on its own. We really wonder why Saari seems to 
have not realized that Range is just Borda with 
some tweaks allowing fuller expression. I never 
cease to be amazed by election reformers who 
think they know better than the voters how voters 
*should* vote. They do *not* trust democracy.

> > The point is that, yes, if the isolated voters are
> > exaggerating their expressed preference, the overall result
> > has not been optimized. But by how much did it fall short?
> > Very, very little. In the Range 100 example, overall
> > satisfaction, assuming that the isolated voter really had
> > the same preferences as the others, only reversed, has been
> > damaged by 9999 minus 9801 = 198, which is 2.0%.
>
>I'm not sure how you can tell whether this is big or small. Typically
>one's vote makes no difference at all.

It is a ritual. We are talking possible results. 
After all, Keven, you are concerned about Later 
No Harm. How much of a consideration is that? How 
likely is it that the voters' additional vote -- 
which must be taken as a kind of approval unless 
you force full ranking -- will harm the voter? 
The most it will do is produce less benefit! The 
whole concept is confused, in fact.


> > Indeed. What I've been pushing for is precision in the
> > definition, not just the sloppy use of a very hot-button
> > word without careful definition and application. Many
> > writers, early on, noted that "sincere vote" with
> > Approval did not have a clear meaning, that there wasn't
> > just one "sincere vote," there were many.
>
>By "writers" are you talking about published articles, or EM participants?

Here, published articles.

> > Within
> > that many, though, most didn't define some as
> > "sincere" and others not. That came, I think,
> > later, where writers started to assume that the voter had
> > some absolute approval cutoff, and was concealing that by
> > voting differently. This is underneath most of what I've
> > seen as criticism of Approval on the basis of
> > "vulnerability to strategy."
>
>The criticism could rather be that Approval *requires* strategy, which
>means it isn't clear how to translate sincere preferences into an
>Approval vote, which means that, once you have identified the Approval
>winner, it is extremely difficult to explain why that is a good winner,
>in terms that relate back to the original sincere preferences/utilities.

Not difficult at all, actually. *If a majority 
was found.* This is why if I have my choice 
between TTR and Approval, in spite of the 
theoretical advantages of Approval, I'd go for 
TTR, it is closer to an even more intelligent 
method of aggregating preferences. Of course, TTR 
gets even better with an Approval primary, and 
probably even better with a Bucklin one. It even 
gets better with a 2-winner STV primary, with a 
single winner determined if that candidate gains 
a majority. But Bucklin is much easier to count, 
and the practical difference, in terms of outcome 
quality, might hinge on how often LNH influences 
Bucklin voters to avoid adding second or lower 
preferences. I think it would, in fact, have little harmful effect.

We had, in the U.S., and still have, in some 
places, a method which is Condorcet compliant and 
which is almost exactly what Robert's Rules of 
Order actually recommends, instead of the IRV 
that FairVote asserts. It's top-two runoff with 
write-in votes allowed in the runoff. The primary 
is a convenient and *non-binding* way of 
determining ballot position, when needed. There 
are two elections (not one as the California 
Supreme Court asserted in ruling on the San 
Francisco exclusion of runoffs -- which only 
affected, I think, one election.) The winner must 
gain a majority in the first election or a 
plurality in the second, and almost always that 
is a majority, not a mere plurality, which is why 
I call it close to the RRO recommendation. They 
recommend repeating the election, which might 
mean new nominations, withdrawals, compromises. 
No eliminations. If write-ins are allowed, there 
are no eliminations, actually; if there was a 
Condorcet winner in the primary, by significant 
preference strength, a write-in campaign is set up to be successful.

But we can clearly do even better. For now, 
though, we should keep the best system we have in 
the U.S., TTR, (setting aside STV in Cambridge), 
and work on making it better. Just allowing Open 
Voting would make it a lot better, using Bucklin, 
with it's noble history, even better.

> > We need to define "sincere vote," as it applies
> > to voting systems, using a uniform definition that applies
> > to all methods, or we cannot determine whether a method
> > encourages "sincerity," or treats sincere votes
> > properly. What are sincere votes?
>
>I don't think we will be able to define it. I don't think we need to,
>on this list. We can define what we mean when we make the claim.

Sure. My goal here is to point out that it is 
often used without that precision, and then knee-jerk conclusions are derived.

>If we could agree on what "sincere vote" means, then yes, we could go
>around advertising our methods as certified as Strategy-Free. And this
>would help us gain followers.

Approval was called that, in peer-reviewed 
publications. So ... they changed the meaning of 
"strategic voting." Clever, don't you think?

> > What we need to do is look at how systems treat (1)
> > preference reversal, i.e., clear insincerity, (2)
> > concealment of preference, and (3) fully sincere votes.
>
>I think you are breaking this down more than is desirable. I'm not sure
>these categories are useful. #3 is probably meaningless under Approval,
>so that gets us nowhere. Regarding #2: Isn't there (or couldn't there
>be) a qualitative difference between IRV's treatment of lower preferences,
>forced compression under Approval, and, say, truncation?

It can be given a meaning. There is a way of 
defining a "sincere approval cutoff," as positive 
election expectation. But it's not necessarily 
the best actual voting pattern, if the voter has 
zero knowledge, even though it is an optimal 
strategy. Rather zero-knowledge situations, where 
the initial poll is all that voters have, and 
where further process will follow if there is 
majority failure, encourage tighter approval, 
even bullet voting. Approval theorists worked 
this out long ago, actually, particularly on this 
list, conceiving of Approval as a series of polls culminating in an election.

I defined a Range method where approvals cascade 
down the ratings, starting with the highest, 
shifting an approval cutoff down one step at a 
time until a majority is found. Is there a name 
for that? Seems someone else may have proposed 
that. If the voter specifies it, substantial LNH compliance can be gained.

>Though, when you aren't aware of the assumption that voters may play
>nice under Range, saying that "strategic voting can harm results"
>is happily not very meaningful.

It's been precisely defined. If you define the 
ideal result as the absolute SU maximizer, or, 
alternatively, as the normalized SU maximizer, 
then concealing the preferences on which this is 
based necessarily makes it possible to miss that 
winner. Thus Range doesn't have zero Bayesian 
regret. If we use absolute utilities (which may 
be the soundest approach, perhaps defined on the 
"universal candidate set" that Dhillon and 
Mertens talk about), normalized, we can get a 
true optimization. Voters may optimize their 
personal expectation above that vote, though, as 
D/M note, they even suggest it and name it: Approval voting.

So, it's reasonable, in fact, to say that 
Approval voting "requires" a kind of strategy. In 
fact, though, it only requires that to maximize 
personal impact on the real election. Voters can 
provide useful information short of that, and, as 
all the information provided is sincere, it 
helps. It simply doesn't help all the way.

>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?

You are right. Existing methods don't allow that 
kind of communication, so, of course, you've not 
even though about the possible value. I may think 
a candidate not ready for prime time, but up and 
coming. If the candidate is moot, though, I might 
rate the candidate higher than otherwise, and 
there are lots of possible reasons for doing 
this. That I prefer one candidate and would not 
like to see my vote for another reduce the 
election chances of that candidate, hence I don't 
"approve" of the second candidate, surely you 
understand this. That's the legitimate thinking behind LNH.

> > If we want optimal results, we need to find ways to
> > encourage sincere voting, that's true. But we need that
> > preference strength information to optimize results.
>
>What if you can't get it? I think you can only get it indirectly, by
>forcing voters to make strategic decisions.

Perhaps. However, we get *some* of it from 
looking at the Range vote patterns, and simple 
summation does a pretty good job of it. 
Preference analysis extracts an additional 
increment, and a runoff actually tests sincere 
preference strength. This keeps being overlooked, 
maybe I need to mention it more!

> > Only with Range, though, does it even become possible to
> > exaggerate preferences. And the meaning of
> > "exaggeration" is unclear, we have to define what
> > a "fully sincere" range vote is, and that is not
> > particularly easy.
>
>Well, I think it's fairly easy. Especially since you are totally free,
>as far as I can see, to declare that normalized ratings are sincere.

Yes. Usually that's allowed, though these ratings 
are not "fully accurate." Absolute utilities 
would be fully accurate, but could not be used 
unless we have an auction system or similar. 
Politically, as Dhillon and Mertens note, 
one-person, one-vote is a necessity. Hence 
normalized utilities are as close as we can get. 
In simulations, we can still study using 
non-normalized utilities (they must still be 
normalized in some sense, but only with a 
universal candidate set, that is the Dhillon-Mertens approach.)
> > But we can say, as with Approval, that
> > any vote that does not reverse preference is not insincere.
> > And then we say that "fully sincere" means that
> > preference strength is expressed with reasonable accuracy,
> > fidelity to true underlying utilities, and thus useful for
> > finding compromises assuming that further information cannot
> > be obtained (as with a runoff).
>
>You can do this, but as soon as critics realize that in order to speak
>your language they need to use the concept of "fully sincere," you'll
>find you haven't gotten very far from them.

I didn't invent that language, Smith uses it. It 
means with accurate disclosure of preference 
strengths, which, of course, must be defined, and 
it is generally defined to be zero-knowledge. 
It's not modified by probabilities. It is the raw 
data on which VNM utilities are determined by application of probabilities.

(Dhillon and Mertens use a lottery approach, 
voters are voting on lotteries, which is sound. A 
vote has a certain probability of affecting a 
result, one "invests" one's vote in that probability and utility combination.)


> > Range makes it *possible* to move beyond the assumption of
> > fixed preferences.
>
>Well, the Range *ballot* does.

Yup. That's what I mean.


> > It does not guarantee that we will, but I
> > don't see that, when it does not, it has therefore been
> > a net harm over fixed preference systems.
>
>Certainly difficult to say for sure.

I've never seen an actual assertion. FairVote 
gives an example where Range works just fine, and 
simply assumes that it is a preposterously bad 
outcome because Plurality with sincere voting, 
zero knowledge, would result in 99:1 for one 
result; but Range gives the other result. 
However, real deliberative process, with the 
stated utilities, would be quite likely to come 
up with the second result as well, hence my 
thinking that it is very important to remember 
that we only tolerate advanced election methods 
because we think we need to make a decision in 
one ballot, which is a *severe* constraint; 
fortunately for us, perhaps, Plurality usually 
gets the right one! -- because of pre-election 
process. Have a truly open election like 
California's election of the Terminator, it's a 
mess. But he might have won with IRV, for 
example. The Plurality leader usually does. (And 
he might have won with any non-majority required 
method that is on the table. He was very popular, 
really. I even like him, he's not so predictable by knowing he's a Republican.)

> > Plurality is generally considered to satisfy the Majority
> > Criterion. (Actually, I think Woodall may have concluded
> > differently, but I don't have the reference handy.)
>
>Well, I have told you at least twice that the reason Woodall says
>Plurality fails Majority is because his "Majority" criterion is not
>the same.

I knew that. I wasn't repeating it for your 
benefit, but for the general readership. In this 
case, I didn't want to repeat what I knew, 
because I was not certain of the details.

>Here is an example.
>
>7 A
>6 B>C
>5 C>B
>
>According to Woodall's Majority criterion, the winner must be B or C,
>because more than half of the voters are solidly committed to the set
>of candidates {B,C}. Plurality elects A and thus fails the criterion.
>
>It would be misleading to say that Woodall says that Plurality fails
>the Majority criterion without clarifying that he doesn't use the same
>definition of the criterion.

That's right. I certainly didn't say the opposite! I said "may."

> > So why is Approval considered to fail the M.C.? Believe me,
> > I've been around and around this in other discussion.
> > It's because multiple approvals are considered sincere
> > votes, so the voter has voted sincerely. And voting
> > sincerely has been considered the necessity in deciding MC
> > compliance. Why was that the definition?
>
>Actually most of us define criteria to avoid referring to sincerity at
>all. The real question is how to interpret the approval ballot as a
>rank ballot.

Which, of course, can only be done in an 
extremely limited way. It is a rank ballot, with 
two ranks, equal ranking allowed. (Plurality is 
the same, but with the top rank being exclusive, 
hang the preference strength, and the bottom rank requiring equal ranking.)

>It is certainly possible to say that Approval satisfies Majority, but
>it is at least as possible to say that it doesn't. It you interpret
>the approval cutoff as something external to the underlying rank ballot,
>then it surely doesn't.

That's right. Except that then you are stuck with "sincerely."

The voter expresses rank. The wording of the MC 
was "If a majority of voters rank A above all other candidates, A must win."

Then we have the unstated assumption: the voters 
vote this rank "sincerely." They do not conceal it or reverse it.

If a method allows them to express it -- both 
Plurality and Approval allow the same expression 
of it -- then it would seem that we'd consider 
Approval to satisfy the criterion.

As I've said, we've gone around and around on 
this. This is why we need to examine sincerity. 
In order to consider whether or not a method 
satisfies a criterion that depends on something 
other than the votes, we need to specify how the 
other thing is translated to votes.

If we claim that the voter may have a preference, 
conceal it in Approval, and therefore the 
preference does not prevail, and the method 
fails, we then have a problem: No method can 
guarantee that the voter expresses a necessary 
preference. So every method would fail.

Definitely, the problem can be solved, one can 
make up a definition of the criterion such that 
Approval fails. But wait a minute? Weren't voting 
systems criteria supposed to be objective methods 
for comparing voting systems. If we can flip 
compliance by manipulating the definitions, we've 
lost the objectivity. And that, in fact, 
happened. And the whole voting system criterion 
approach to comparing voting systems, while 
useful in some ways, is thoroughly defective in 
terms of practical assessment of systems.

Criteria are absolutes, they are pass/fail. A 
method may fail a criterion, but it is moot if 
this is effectively impossible in real elections. 
So criterion failure is no proof of method 
unsuitability, and it becomes your important 
criteria vs my important criteria, and there is 
no resolution. And with ranked methods, of 
course, we run headlong into Arrow's theorem.

But with sum of ratings systems we can move beyond that.

I'm saying that we should, in fact, agree that 
there has been only one method (or family of 
methods, more accurately) proposed for assessing 
voting system quality, and that is the sum of 
voter utilities approach of Smith et al. This 
approach can produce *measures* of voting system 
quality. While it could theoretically be done 
with real elections, practical limitations leave 
us with simulations; simulations are far more 
powerful than constructed scenarios to show 
system failures, because the constructed 
scenarios do not address frequency, simulations 
do. Sure, the models used in simulations should 
be examined for reasonable correspondence to real voter behavior.

But it's all we have.

This approach, however, gives a natural edge to 
Range Voting, because the method is, itself, a 
means of estimating the social utilities, and 
thus it is pratically by definition, more likely 
to be optimal. That is, of course, not the end of 
the question, and my own work has led me to the 
conclusion that hybrid methods can improve on 
pure Range by encouraging more accurate 
expression of relative utilities, and testing the 
preferences when there is a clue that they 
haven't been sufficiently expressed. Condorcet 
failure is such a clue. We cannot distinguish, 
without a runoff, unless we find a different and 
better way of encouraging accurate utilities, 
between a true Condorcet result with significant 
preference strength, and one based on small 
preferences and hence safely disregarded in 
choosing the Range winner. A runoff tests that.

I've claimed -- and this is, I think, original 
with me, that a genuine Range winner, the 
absolute utility maximizer, has an edge in any 
runoff. To my knowledge, no one else has 
confirmed this as a reasonable hypothesis, but 
the theory indicates it pretty clearly.

Weak preference strength equals less motivation 
to turn out, and higher possibility of voter 
change of mind. Both of these effects favor a 
genuine Range winner over the Condorcet winner.

What we want to discover is the situation, 
relatively rare, where preferences come up with a 
clearly poor result, a Condorcet winner, perhaps, 
but by weak preference strength, such that the 
net "happiness" of the society is significantly 
better with another winner; I've used the Pizza 
election to show this. Quite simply, healthy 
societies do not operate by pure majority or 
plurality preference, they take preference 
strength into account, they must. Hence the 
Condorcet and Majority criteria, taking without 
reference to preference strength, must fail in 
any method which optimizes results accurately.

(Examples have been adduced which show this, with 
situations where nearly everyone would agree that 
the majority preference is far short of being the optimal winner.)

> > It wasn't mentioned in the early definitions. In fact,
> > those definitions did not even mention the possible gap
> > between voter preferences and voter votes.
>
>They should not mention them, in my opinion.

So do you define the criterion purely on the 
votes? You are aware, of course, that this would 
imply that Approval satisfies the Majority Criterion?

Without some specified method of converting voter 
preferences (i.e., mental states or underlying 
utility converted to ranks) and actual votes 
based on them, we cannot assess method compliance.

> > Why is all this important? Because these terms are bandied
> > about as if they condemn a method. "Rewards insincere
> > voting!" "Fails the Majority Criterion!"
> > "Vulnerable to strategic voting." I just saw
> > someone write that, sure, with "sincere votes,"
> > range is an ideal method, but "because it is vulnerable
> > to strategic voting, I cannot support it for public
> > elections."
>
>I don't really see what the big problem is. Even if you don't like the
>terms being "bandied about" you can at least understand the criticism
>being made.

Sure. And I can criticize it as unfounded, based 
purely on a knee-jerk response to a behavior 
*assumed* to be bad. It's not a matter of not 
liking people's writing or speech. It's a matter 
of the harm it can do. People are influenced by 
this language, they make decisions based on it. 
Majority Criterion failure, for example, with 
Approval, is a common reason for rejection. Yet 
Approval doesn't fail the MC in real-world 
political election scenarios unless we are 
extraordinarily lucky. In Florida 2000, for 
example, it would take a significant number of 
voters, more than those who vote for neither Bush 
nor Gore, to approve both of them. I'd say that 
would be just about impossible. It's an example 
of how strict criterion compliance can be very 
misleading. Multiple majorities is not a major 
problem with approval; but if we think it is, 
it's easy to fix. Hold a runoff, just as with 
majority failure. But we already have Approval 
voting in limited circumstances in the U.S., and 
the precedent is that when there are multiple 
majorities, the one with the most votes wins. 
That's law in at least a few states.

>You don't need the term "Majority Criterion" to understand the criticism
>that Approval can fail to elect the favorite candidate of a majority
>even when the voters are not being fools. Won't happen often? Doesn't
>matter. That's how criteria work, as you know. It's not a wording problem.

The question is the damage done when it happens. 
The "damage" is that a candidate is elected who 
was, in spite of not being preferred by a 
majority, was "accepted" by a larger majority. 
That is quite arguably a better result. The 
assumption is that MC failure is a bad result, 
the criterion wasn't really designed to deal with multiple majorities.

And you are correct. How often it happens is 
irrelevant to voting systems criteria. My point. 
Could be one election out of a billion, no 
matter. It fails because we can construct a 
totally ridiculous scenario that it fails in. 
And, now, in a real, and actually practical 
Social Welfare Function, such an outcome is 
actually irrelevant. It would not affect the 
real-world value of the voting system, as long as 
the probability is so low that we have far more 
to worry about with the alternatives.

The wording problem is that criterion success or 
failure depends on the wording, and the 
interpretation as well. Or criterion failure 
becomes meaningless. There was a purpose behind 
the Majority Criterion, which is Majority Rule. 
It is assumed that the first preference of a 
majority must prevail, because this is implied by 
Majority Rule. Except that a real majority in the 
real world may choose to set aside its first 
preference for a higher goal. And real majorities 
do this quite well, when the system allows it to 
be negotiated; currently we mostly see this in 
small groups, but the principle is universal and 
does not depend on scale, negotiation simply 
becomes more difficult, we think, on a large scale. That problem can be fixed.

Approval satisfies the purposes of Majority Rule. 
That's why it's offensive to insist that it fails 
the Majority Criterion. If we return to the 
original purpose, we see that it is more useful 
to define the MC to refer to expressed votes, and 
to require that the majority have a means to 
express that preference, if they choose.

Again, we can look at standard deliberative 
process. It's certainly possible that the 
majority does not obtain its first preference, 
but this *must* fail with an explicit acceptance 
by a majority. I.e., the majority considers it 
more important to gain a decision than to 
absolute gain its first preference. Overall, we 
must interpret this as the majority actually 
preferring the result that they voted for. It was 
just a simplified, possibly uninformed preference 
that was the alleged "first preference."

In real, practical, non-political decision-making 
systems, preferences are not fixed, they shift 
during the process, they can reverse, especially when they are weak.

Why should politics be different?

>I know you dislike the term "vulnerable," but it seems to me that the
>criticism that Range is "vulnerable to strategic voting" is at least
>quite clear in what it refers to.

Once we defined it well, sure, but then the world 
"vulnerable" is the use of a loaded term as a 
term of art. Bad Idea. Misleads those who don't 
know the field, and you can be sure that spin 
doctors will use it that way. They won't provide 
the definitions and restrictions.

> > > Ok. So Range ballots could permit the collection of
> > information needed
> > > to provide an "optimized outcome," if the
> > voters are accurate, which
> > > they won't be, because there is no specific
> > meaning to the ratings they
> > > can give.
> >
> > That's not true. It's just that there is not *one*
> > specific meaning. It's like Approval in that way.
>
>Ok. How far do you think this realization would get us? It seems to me
>that even if everyone agreed that Approval and Range allow multiple
>sincere and meaningful votes for a given set of sincere preferences,
>the criticisms would still be exactly the same. Only the terminology used
>might change.

No, some criticisms would disappear, because they 
are *only* based on assumptions about the 
importance of certain criteria failure. Being 
strategy-free is of higher importance when 
strategy involves preference reversal, than when 
it merely means choosing how to express 
preference strengths, but not violating 
preference order. Being "vulnerable" implies 
pathology, when reducing a result, in rare 
circumstances, from ideal to almost-ideal, isn't pathological.

>Surely all this discussion isn't just to get people to change the terms
>that they use...?

It's to expose the hidden assumptions underneath 
the terms, so that when these terms are used in a 
misleading way, it can easily be seen, exposed.

> > Or we could just start with Bucklin. Simple. Allows the
> > expression of preferences (up to three in Duluth Bucklin).
> > Phases into Approval as a majority winner is not found with
> > a canvassed rank. Add in the next rank votes. Preferential
> > voting method that incorporates Range-like characteristics
> > and is not vulnerable to Center Squeeze. At least not as
> > seriously as IRV. We still see Center Squeeze if all the
> > voters really want Later-no-Harm and insist on it by not
> > ranking anyone else.
>
>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?


> > (I've proposed, yesterday, a hybrid IRV/Bucklin method
> > that allows voters to insist on LNH compliance with their
> > votes....)
>
>I'll have to find this as it's not clear to me how this would work.

I'd have to look back, I don't remember clearly at the moment.


> > > In this discussion we probably should not use the term
> > "strategy-free"
> > > except in cases where there are no meaningful
> > decisions.
> >
> > My point is that it was used that way, in peer-reviewed
> > publications, with a lot of agreement, re Approval.
>
>Did anyone use it that way who was not advocating the method?

I'm not sure. I do know that it wasn't just 
Brams! And if Approval were "obviously 
vulnerable," Brams would not have gotten away 
with it. It took a process of redefining 
strategic voting, which, I'm sure, including some 
rapid response that the claim wasn't true, in 
order to raise the idea that it was vulnerable.

I still don't see clear examples of what 
"strategic voting" in Approval means, except 
being Approval votes determined by the voter's 
understanding of what candidates are the important ones.

> > > Well, none of this matters much as long as we use
> > consistent terms
> > > when having a discussion.
> >
> > Perhaps. But a discussion will also be read by many others.
> > It's tricky to use words with a specialized meaning when
> > a larger audience will read the text with generalized
> > meanings. Hence "accurate," which itself needs
> > definition, is far less a loaded term than
> > "sincere." Accurate raises the immediate question
> > "accurate to what?" And that's what a reader
> > would need to know.
>
>I want to note that I'm only interested in the terms used, in order
>to understand the underlying issues. I'm not interested in discussing
>what terms *ought* to be used.

I'm interested in, not only understanding issues, 
but communicating the understandings.

> > The point is that the additional preference information
> > available in Range does not harm the outcome over not
> > allowing that information.
>
>However, this argument is only useful when you're talking to an Approval
>advocate.

Yet critics of Range use the alleged harm as an argument against Range.

>My feeling lately is that it might be better to arrange the incentives
>of a method so that a third candidate is likely to be able to gather
>enough support, as opposed to simply getting rid of all barriers to
>entry, which could tend to leave the two frontrunners unharmed.

The best way I know of is to allow the method to 
terminate with majority failure. This, then, can 
allow a third candidate who can make it into the 
top two -- which can be better defined than 
simply the top two in first preference votes -- 
the opportunity to convince the electorate in a 
head-to-head contest with the other major 
candidates that he or she is the best.

And that runoff tests a lot. If you can really 
get the two best candidates into it, you've 
eliminated a whole series of possible election 
pathologies. I contend that we have two different 
approaches to "best": Condorcet winner, on the 
one hand, and expressed voter satisfaction 
optimizer, on the other. If the method collects 
both kinds of data, which is easy to arrange with 
a Range ballot, we then can determine a result: 
normally, large majority of elections, I believe, 
the Condorcet winner is also the Range winner. 
But it's the exceptions that are interesting, and 
it's not difficult to test for the exceptions and 
to consider these as ambiguous results, hence the 
need for more voter attention to the election and to those specific candidates.

Could we agree that an ideal winner would be 
either a Condorcet winner or a Range winner? Yes, 
one could quibble about two candidates who beat 
the Range winner pairwise, but this would be 
extraordinarily rare; one of those two would have 
higher Range summation, and, unless we want to 
expand the runoff to three candidates, it would 
seem to be overkill to go for more than one 
member of the Condorcet cycle. But I'd be content 
to use Schulze method, for example, to determine 
the winner on the Condorcet side. We are talking 
very rare that this wouldn't be moot. Normally, 
if there is a candidate who beats the Range 
winner, which is known to be relatively rare, 
there would not be two or more. If we are using 
sum-of-votes. Average Range is a little trickier.

There is no theoretical basis for Average Range, 
it was a wild idea that sounded good to some 
Range advocates, not to others. Unfortunately, 
Warren is one who likes it. He is *not* politically sophisticated.