[EM] Why I think IRV isn't a serious alternative 2

[Abd ul-Rahman Lomax]

At 10:26 PM 12/2/2008, Kevin Venzke wrote:

> > I've responded to this in a prior post, the first part
> > of it. I did not make the claim that Range Voting was
> > "objective." It is a voting method and does not
> > automatically choose the best candidate according to overall
> > utility, neither in simulated elections with practical
> > methods, not even if we assume "fully sincere
> > voting."
> >
> > It simply gets closer than any other single ballot method.
>
>Can you come to this conclusion without the assumption that voters
>will vote accurately?

Yes, of course. That's what the simulations show. Range is better 
than, or roughly the same as, other methods, with total usage of 
strategic voting. (I should look again, by the way, but this is my 
impression. It is *not* assumed that Range voters need vote with full 
sincerity. We do assume that they express preferences, suppressing 
only minor ones. They may vote full Approval style. In which case, 
obviously, the method functions as Approval, which is a very good 
method. Look at the simulation results. I'll do it and put up a URL.

>So I guess you must not just assume but *hope* that voters can vote
>accurately. In that case it seems fair to criticize that voters don't
>have incentive to vote accurately.

No. Voters not voting with "accuracy" still contribute well to the 
result. The quality of the results increases with the degree of 
sincerity, but the *worst case* is still very good. And we absolutely 
do not expect the worst case. There will be intermediate votes, and 
these, so to speak, raise all boats. Just not their own as much.

(In my exact utility study, i.e., not a simulation but a 
zero-knowledge study of true expected utility for Approval style 
votes vs. "sincere" votes in a Range 2 election where the true 
utilities were 2, 1, 0, the sincere vote for the middle candidate of 
1 had the same utility as the votes of 2, 2, 0 and 2, 1, 0, with many 
votes. Interestingly the votes of 2,2,0 had a higher expected utility 
than 2, 0, 0, when there were few voters. This disappears with many 
voters. I generalize that when one can vote accurately, the sincere 
vote has the same expected utility, zero-knowledge, as an appropriate 
Approval-style vote. But I haven't proven this. Obviously, when there 
is very good knowledge, a voter may flip a vote more easily by 
applying full voting strength even if this is not "sincere," i.e., 
accurate to true utilities. That is dangerous when there is zero 
knowledge. In the study, the accurate vote had less variation: it was 
less likely to produce the voter's best outcome, but also less likely 
to produce the voter's worst outcome. Often critics of Range have 
focused only in the improved positive outcome from an "exaggerated 
vote," neglecting the risk of a more serious negative outcome. The 
risk, of course, declines with improved knowledge, until it's zero 
with full knowledge of the other votes.)

> > So let me be specific, though we will get back to this.
> > Range Voting isn't perfect. It does not always choose
> > the best winner. When it does not, it is sometimes possible
> > to detect the situation and fix it; that is why Range Voting
> > with Top Two runoff gets lower regret results than Range
> > alone. It detects the relatively rare situations that cause
> > Range to fail to find the ideal winner.
>
>We're talking "honest" simulated Range, yes?

In that case, I'm not sure which was actually done. Top two runoff 
Range would fix errors due to strategic voting, but it also fixes 
some normalization errors. I'm not sure which was involved. I think 
the original studies were done with pure sincere voting, probably 
normalized on the candidate set for each voter.

> > And in my opinion,
> > Runoff Range is not as accurate in the simulations as it
> > would be in real life; that's because real runoffs test
> > *relative absolute preference strength,* free of strategic
> > considerations (when write-ins are involved, this isn't
> > totally true.) This effect is something which has been
> > largely overlooked. Or even totally, as far as I know.
> > It's original with me, but it's likely someone else
> > has written about it somewhere. I don't consider it
> > rocket science, just something obvious that's been
> > overlooked.
>
>If you're talking about the idea that two-candidate elections are
>strategy-free, then yes, that has been noted.

Yes, that's known, for sure. The likelihood of voter changes of 
opinion based on better information about the candidates, that's 
known. However the effect of preference strength on that is original 
with me. It could be predicted, to a degree. Further the turnout 
effect, I'm not aware of any publication of this, but it's certainly 
possible, there is a huge amount of work that I haven't seen or even heard of.

It's clearly been overlooked, though, even if it has been published. 
I've not seen any discussion of it that I did not originate. Even 
now, my comments on this are being largely ignored.

> > > At the same time you want to defend Range against the
> > charge of
> > > susceptibility to strategic voting, essentially by
> > denying that the
> > > Range voter is supposed to be mapping his true,
> > absolute preferences
> > > onto the ratings.
> >
> > That's right. Range results shift, and they shift to
> > increase regret, when voters vote "strategically."
> > This is well know, but it's an error to consider this a
> > reason to avoid Range. If, with realistic voting profiles,
> > they shifted results to make Range worse than other methods,
> > it would be one thing. But they do not, if the simulations
> > were accurate.
>
>Well, if the simulations were accurate, then strategic voter behavior
>wouldn't even vary for different rank ballot methods. Everyone would
>apply Borda strategy according to randomized polling data. It is not
>very surprising that strategic Approval can outperform a method with
>this kind of behavior.
>
> > Nobody has challenged Warren's results.
>
>What do you mean no one has challenged Warren's results? What would you
>interpret to be "challenging" the results?

Showing that they were misleading. That his assumptions were 
distorted, replacing them with more reasonable assumptions. Or 
showing that the whole approach is defective. Unlikely. Most people 
who understand his work think the approach is sound, as far as I've 
seen. If there are exceptions, they aren't speaking up and revealing 
what they know that we don't.

> > The voter *does* map his true, absolute preferences onto
> > the ratings.
>
>Really? Ok.

That's right. The voter, however, doesn't map them linearly, but 
still monotonically. We have been considering a "sincere" vote to be 
linearly mapped so that it accurately reflects relative preference 
strengths. That enables the method to predict -- this is one way of 
looking at it -- how the voter would respond to compromises in 
negotiation. Strong preference, less likely to compromise, weak one, 
more likely.

And this (the nonlinear but monotonic mapping) is exactly what we do 
in ordinary decision-making. Instinctively. We can easily determine 
preferences between outcomes, but we shift the preference strengths 
-- corresponding to the investments we make in them -- according to 
likelihood of success.

> > Kevin, you are not being careful. There is, in
> > theory, a one to one, continuous, monotonic transformation
> > of absolute voter utilities (not "preferences") to
> > Range votes (neglecting roundoff error, which makes the
> > function a step function, still monotonic.)
>
>Ok. So my sincere ratings of candidates A B C can be accurately recorded
>as, let's say, 1 4 and 9.

Only partially accurate, I'm sure. But probably good enough!


> > That's why
> > we can, with a reasonable definition, still call these votes
> > "sincere,"
>
>I'm not sure what you mean by "still." I guess you mean, in spite of
>roundoff error.

No. Roundoff error is there, but here, I was referring to monotonic 
votes. If you rate a candidate higher than another, you prefer that 
candidate, and the same in the other direction, i.e., lower rating 
equals less preferred. Equal rating, though, does not tell us that 
there is no preference, though we may still be able to place limits 
on preference strenth. I.e., with ratings of a series of candidates, 
we can determine that the preference strength between two candidates 
does not exceed a limit, otherwise the candidate would have been 
rated differently. This, by the way, is why Borda sorta works. It 
makes an assumption that the candidates are evenly distributed 
through the utility spectrum, so A>B>C indicates a equal preference 
strength in the A>B pair and in the B>C pair, thus A>C, we can infer, 
is a preference twice as strong as the closer ones.

In Range, then, if we have A, 100, B, 100, C, 80, D, 20, E, 0, F, 0, 
we can assume that the preference strength in the A>B election is not 
more than 20 points, otherwise the voter would have rated C at 100, 
or one of A or B at 80, or something like that. It's likely less than 
20 points. If this is a two-frontrunner election, and C is not a 
frontrunner, we can assume that the C vote is reasonably accurate, so 
the preference information is pretty strong. Likewise, we can assume 
that the sincere rating of E or F would not be higher than 20. Thus 
we know that the preference strength between A or B and E or F is at 
least 60 points, and probably higher -- average 80 points. That's 
useful! We can guess from this vote that the two frontrunners are 
quite likely in the set A, B, E, F, but not necessarily, if this is a 
sincere vote. If it's a sincere vote, then we know the voters 
estimate of the true preference strength between the A/B clones and 
the E/F clones. It is 100 points, a full-one honest, sincere, vote.

> > since they do not violate the derived
> > preference profile of the voter. All that they do is to,
> > possibly, equate the vote of some candidate pairs when there
> > is a non-zero preference strength between them, and that is
> > larger than the Range resolution. In other words, the voter
> > thinks that, given all the conditions, the voter exercises
> > more effective voting power elsewhere and -- presumably --
> > will not regret the abstention from voting in that candidate
> > pair.
>
>But under Range this probably isn't much of an issue, if the resolution
>is somewhat high.

That's right. The voter can probably vote a sincere preference with 
very low risk of harm, provided it is done in connection with a 
strong vote or votes exercised in the frontrunner pairs. Usually two, 
easy-peasy.


> > This is quite what we routinely do with real world
> > choices under analogous conditions. We do not bid on things
> > in auctions based merely on cost, when we have a limited
> > amount to bid. I won't go into describing such an
> > auction, but we factor in the probability of success, and we
> > put our limited auction dollars into the preference pairs
> > that seem more likely to be a good investment. But we never
> > try to pay *more* for a candidate that we prefer *less.
>
>Ok. But didn't you claim that the concept of "sincerity" is flawed in
>Range? If it *is* possible to map real preferences to the Range ballot,
>then what on earth is wrong with the concept of "sincerity" in Range?

It's possible, but it's not necessarily easy. The easiest way to vote 
in Range is with a certain degree of "strategy." I.e., decide on the 
favorite and the worst, max and min rate them, period. Then look at 
any frontrunners different from these, and max and min rate the 
favorite frontrunners, or some small level away. Or some large one, 
if you don't give a hoot about your personal influence on the 
election. Zero knowledge, you'll try to estimate real preference 
strengths. I wouldn't advise anyone to lose sleep over it. It's just 
some fractions of a vote you are deciding. In any case, the simplest 
voting pattern here is Approval or next-to-approval style. With some 
variants on Range, that is about all that voters do.

> > The transfer function, thus, is monotonic but not linear.
> > With "sincere absolute preferences normalized to the
> > voting Range," we'd get a limited regret-minimized
> > result, and there may be some voters who decide to vote this
> > way. I'd not advise it, though it's relatively
> > harmless. It improves the overall outcome at small cost to
> > the voter. (By definition, if the cost is large, the sincere
> > preference is large.) In real world collective decision
> > making on a small scale, we often do exactly this: we reveal
> > our sincere preferences in absolutes, where possible, or, at
> > least, in terms of preference strength across our personal
> > profile.
> >
> > So is Range Voting "vulnerable" to strategic
> > voting? What does that mean?

It means that voting which is altered from the best effort of the 
voter at accurate relative preferences because of knowledge of how 
the rest of the electorate is perceived as being likely to vote. This 
can change the result in Range, and a *small* change is not difficult 
to anticipate and may be fairly safe to vote. A *big* change, quite a 
different story. Very difficult and hazardous. Get it wrong, serious regret.

Part of the problem is that, for some people, "vulnerable to 
strategic voting" is a synonym for "utterly unacceptable." That's a 
serious mistake. The "vulnerability" of Range Voting to strategic 
voting is quite confined and limited.

>It means that given a certain understanding of what an "accurate" vote
>is under Range, typically an inaccurate vote is the strategic one.

That's right. Imagine a hundred voters, any voting method. If the 
hundredth voter can change the result in his favor by voting without 
accurate expression of preference strengths, under any circumstances, 
the method is "vulnerable to strategic voting."

That's a definition tailored to Range Voting. Anywhere else we would 
just say "insincerely," i.e., reversing preference. You can get an 
intimation of Arrow's theorem here. If the voter *can't* change the 
result, in at least some configurations, the voter may be powerless 
over one of the election pairs..... at least that's my intuition here.

An inaccurate vote with Range isn't necessarily insincere, at all. 
The voter has decided not to put more effort into determining 
relative utilities. The voter simply has not considered other than 
two frontrunners. The voter has simply decided that full-on Yes and 
No are adequate expressions.

Accurate utilities will allow a Range system to optimize the winner, 
accurately. Approximate utilities will allow the system to optimize 
accurately. Not complicated. The key in Range is that strategic 
votes, as some want to consider them -- and by some definitions of 
strategic, including the very common meaning of "with consideration 
of the goals of the actor," legitimately so, are approximations of 
accurate votes, and these votes averaged over many voters tend not to 
deviate greatly from what the average of accurate votes would be.

We can construct artificial scenarios where it can seem otherwise, 
but these scenarios require constructing very unusual or rare 
situations, and, even with allowing that, what I've seen proposed as 
Range "failures" were actually decent decisions, with the famous 
FairVote example, purportedly showing bad behavior, elects the 
candidate that is almost perfect, as distinct from one who is simply 
more perfect (deviation from unanimous satisfaction, 2% for the "bad" 
result, 1% from the supposedly ideal result had there been no 
"strategic voting.) And that scenario requires extreme conditions. 
Probably someone who actually took the time to understand Range 
voting and the theory behind it could come up with something worse 
and more reasonable. But every other election method, we see greater 
deviations from the ideal, with more reasonableness of the scenario.

FairVote likes to claim that IRV only rarely violates major criteria 
like monotonicity and the Condorcet Criterion, and they are fond of 
demanding that critics of IRV come up with real elections that 
violated them. However, the criterion violations aren't common in a 
two-party system, where the election is really a binary choice. When 
faced with a choice between two candidates, naturally, many election 
methods do well, including Plurality. The extensive experience with 
IRV is with it in a two-party context, without many elections where 
there was a real three-way race. IRV is highly erratic when 
confronted with a rough three-way tie. This is where truly massive 
Condorcet failure can happen. Yes, it's rare, even in nonpartisan 
races. But what's "rare?"

 From fairly scanty evidence, because of the small sample size, it 
appears that nonpartisan elections in the U.S. choose, roughly one 
election out of ten, a candidate who would lose in a direct runoff 
with one of the other candidates. Because a runoff is a separate 
election, we cannot distinguish between this being a Condorcet 
failure or a result of differential turnout or of voters changing 
their minds. The latter are likely effects, and beneficial ones on 
the quality of the results; voters changing their minds is oft-cited 
as a benefit of real runoffs, you get better-informed voters in a 
runoff, albeit fewer of them. The "fewer," I claim, also improves the 
results, maximizing voter satisfaction over the entire electorate, 
not just those who showed up in the second election. That's because 
it effectively discounts the votes of those who voted in the first 
election, but who had -- and who maintained -- low preference 
strength. This is a genuine Range effect, based on sincere 
preference, not on strategy. A real runoff would confirm the 
preference differentials expressed in a Range election, hence Range 
plus runoff if a majority choice is not shown can be expected to 
improve real Range results, even in the presence of major strategic voting.

>  In practice, it is used as a
> > voting system criterion and a black mark against Range
> > Voting. But the "harm" done is simply
> > institutionalized by other voting systems, and the possible
> > improvement through accurate expression of absolute
> > preference strengths (within the limitations) is made
> > impossible.
>
>"Possible improvement" must be the important thing about it all.

Sure. Consider this: most election methods will choose the same 
winner. Plurality, I'd guess, gets it right almost 90% of the time, 
because of strategic voting by the voters. So when we are talking 
about election reform, we are only going to improve the results in a 
few elections. It's a "possible" improvement.

This is an important point to notice: strategic voting is a method by 
which informed voters improve election results. Yes, they improve 
those results according to their own preferences, but, presumably, 
there are many such, and in a true contest, there are informed voters 
on each side, capable and willing to make the compromises to get the 
best results. So, again, Plurality takes advantage, probably, of 
another Range-like effect.

Voters who don't care very much about results will vote their sincere 
preference in Plurality. Why not? It's the easiest way to vote. 
Consider those Nader supporters. From the arguments of their 
candidate, they did not believe that Gore would be better than Bush. 
Nader still argues that, I saw him in an interview continuing the 
argument: Obama isn't really any different, he's an "Uncle Tom for 
the corporations." The interviewer either was or pretended to be 
aghast. Nader really sees things through some kind of black and white 
filter, so to speak.

(To be fair, Nader may have said something more like "He won't be any 
different if he is just an Uncle Tom for the corporations, which 
technically isn't so bad, but which politically is just as bad. The 
guy was, and remains, unqualified for high office, with gaffes like 
that, he and his agenda would be slaughtered. Choose a better 
standard bearer, Greens and progressives! He's not it. He could have 
solidified the voting power of the Green Party, but chose instead to 
pursue a narrow and practically suicidal agenda, and the result has 
been massive damage: eight years lost in starting to deal with a 
possible environmental disaster of monumental proportions, bigger 
than anything we've known so far, a huge cost in lives and property 
from an unnecessary and foolish war, a packed Supreme Court that may 
make change difficult for a long time, and more. And certainly no 
better approach to the problems of corporate power. I'd say that the 
Nader approach is totally bankrupt.)

The Nader supporters, to return to my point, didn't care about the 
result of the pairwise race between Gore and Bush. Would they have 
turned out to vote in a runoff? Would Nader have endorsed one of the 
candidates, encouraging his followers to turn out? *What would have 
happened if there had been a real runoff in Florida?* They could have 
done it, you know. The states determine how the electors are chosen, 
they could toss a coin if they wanted to. They could divide up the 
electors. They could join the National Popular Vote Compact, which I 
consider somewhat foolish but constitutional. (Foolish as written. 
Basically, there are better ways to do it that would be more likely 
to be implemented quickly, that could improve election results 
*without* having states with a majority of electoral votes sign up. 
One big state could fix every spoiled election that the U.S. has 
had.... All by its lonesome, simply by deciding to award all their 
votes so as to approach, for the overall electoral vote, the national 
popular vote results, with, as other states join this process, they 
back off to assigning electors proportionally, thus making the 
electoral college actually function instead of mindlessly making it moot.

Are my ideas crazy? Maybe. But where is the process that filters out 
bad ideas, while giving good ones maximized opportunity? What we've 
seen, in electoral reform, is that some idea gets "momentum," because 
of certain initial conditions, and then co-opts the field, possibly 
preventing real reform for a generation or more. We have no 
institutional memory. IRV has been tried before in the U.S. How did 
it work? STV, we know, works, and when it was rejected in the U.S., 
it seems to have been for purely political advantage. New York STV 
was daring to elect a few Socialists and, horrors, Negroes. So much 
for democratic values. *The U.S. power structure often doesn't give a 
fig about democracy.* It simply wants what it wants, and the people are asleep.

IRV, it's far from clear. It was rescinded in Ann Arbor for political 
reasons, it not only elected a Democrat, but an African-American, to 
boot. But, we might as, where were those supporting democratic values 
in the initiative election that rescinded it? It was politically 
timed to be voted upon when students were away, Ann Arbor is a 
university town. Why didn't the reformers simply put up another 
initiative, timing it better? One reason is that the Human Rights 
Party was fading at that point. It's hard to build lasting political 
power with a student base, they keep rotating in and out. They did 
not build roots in the general community. The place to institute 
major reform was probably within the Democratic Party, not purely 
independently. Fusion Voting. That would have allowed the HRP to have 
its fun, keep ballot position, and possibly grow to the point where 
they might safely run a candidate here and there. This is a more 
solid reform than IRV! And we have it in New York, now. It failed in 
Massachusetts, two years ago I think it was. But it was poorly 
promoted. It is as if progressives imagine that all they have to do 
is come up with a good idea, and the public will flock to it.

No, support for reform must be built, one brick, one person at a 
time, spreading out, and to be effective at bringing real change, it 
must be flexible and open. Otherwise it's likely to fall into the 
FairVote trap. If FairVote had decided to promote *education*, to 
promote the general increase of real knowledge regarding election 
systems, instead of becoming an advocate for one form, it would be, 
by now, I'd suggest, more effective, not less. As it is, in its drive 
to "win," it found a vulnerability with top-two runoff, it could sell 
IRV as saving money and reducing voter inconvenience. In so doing, it 
has been chipping away at the best voting system in use for single 
winner elections, quite arguably better than IRV, and clearly 
producing different results, something that IRV promoters aren't 
likely to mention. They sell IRV as a "simulation" of runoff voting. 
It is very much not. One nonpartisan election out of ten, different 
result, roughly. And it's pretty certain that the different result is 
a worse result, due to either Condorcet failure or a lack of adequate 
public knowledge about the top two. Or an IRV result based on weak or 
even accidental preferences, as another possibility.

Any good system will have to factor for most people being asleep to 
political reality. That fixing the system depends on people becoming 
politically active is an error that reformers often make. People, 
need, instead, good advice, it's that simple. How can people get 
trustworthy advice? That's the problem that I set out to address, and 
it actually isn't difficult.

No, instead of being difficult it almost seems impossible. But that 
is an appearance. Little by little, the concepts are becoming widely 
understood, and little by little, they will be implemented. I have no 
idea if I'll be remembered as a pioneer in this field. And it's not 
important to me. We have roughly five or six independent inventions 
around the world of Delegable Proxy over the last decade. Delegable 
proxy is extraordinarily simple, in structure, but the reality of it 
would be highly complex and sophisticated. It's hard for people to 
visualize, that's one of the problems, but actually functioning 
within the system would be very simple. You *don't* need to see the 
whole structure, and just need to deal with a few people directly.

Delegable Proxy would make what have been called "starfish 
organizations" able to rapidly find consensus and distribute 
trustworthy advice on a large scale. I've been writing about starfish 
for many years and thinking about them for thirty, though not under 
that name. Free Association is the name I come to use recently, with 
the clear model being Alcoholics Anonymous, an organization that 
continues to be spectacularly successful in its field, more than 
sixty years after it was founded. Without any central control, it 
became, almost, the only show on the road in its field, and the way 
it functions makes competing organizations redundant and practically 
unnecessary. This is not necessarily understood: Rational Recovery is 
an atheist version of AA, promoting "responsible drinking," as I 
recall. Yet that position is one found within AA. If AA members are, 
in fact, prohibiting people subscribing to Rational Recovery tenets 
from, say, organizing an AA meeting where members talk about these 
tenets and attempt to apply them for their own sobriety, they are 
themselves violating AA traditions. (Which does sometimes happen, AA 
certainly is not perfect, even as an example of its own traditions. 
Some members, essentially, don't really understand the AA traditions deeply.)

> > The simulations answer the questions of "how
> > much" and "how often," which cannot be
> > answered through the prior approach, the use of voting
> > systems criteria. Approval Voting fails the Majority
> > Criterion, according to the usual interpretations (which had
> > to be modified to apply to Approval Voting, and, clearly,
> > the modifications were designed to *cause* Approval voting
> > to fail, because the students thought, intuitively, that it
> > failed. That's what I mean by subjective analysis! See
> > James Armytage-Green's study and application of the
> > Majority Criterion to Range Voting).
> >
> > Okay, how often? It would be extraordinarily rare in real
> > public elections, because it requires a significant number
> > of voters to vote for both frontrunners, which is the
> > opposite of standard Approval strategy and is, normally, a
> > foolish vote if the voter does have a significant preference
> > between them. And if the voter doesn't have a
> > significant preference, well, there you go. See the second
> > question!)
>
>How long has it been since I noted that this is not correct, unless you
>want to assume that Approval won't have more than two viable candidates.

Kevin, I make no such assumption. Sure, that's what I stated, just 
above, because that is, by far, the most common situation, even in 
nonpartisan elections. It's unusual to have first preferences be 
equally divided among three candidates. That was the French election 
in 2002. FairVote argues that because Approval doesn't satisfy Later 
No Harm, voters will be reluctant to add additional approvals. I'd 
counter that this depends on preference strengths. A three-way race 
is equivalent to zero-knowledge. What's the optimal Approval vote in 
a zero-knowledge situation.

A game theory approach would suggest that one would average the 
utilities of the three candidates, then approve those with utility 
above that average. Let's suppose that the situation is really 
symmetrical, what happens?

Full symmmetry here means that there is a Condorcet cycle, I think. 
Let's suppose one-third A>B>C, one-third B>C>A, one-third C>A>B. With 
some kind of even distribution of sincere utilities, voted as such, 
we'd get half of each faction approving the second preference, and 
half not. Thus each candidate would get half the votes, we'd still 
have a very close three way race, which seems correct. However, if 
voters do think Later No Harm is important, and some will, the votes 
will be distorted toward bullet voting. And any distortion toward 
bullet voting pulls the votes away from a majority to less than that.

And that is with a Condorcet cycle. What if there is no cycle, rather 
there is a standard political spectrum.

The left is one-third, with the A candidate in the middle of that, 
the B candidate is the middle third of the spectrum, and the C 
candidate is the other third. This is actually quite a reasonable 
distribution, though political reality pushes the A and C candidates 
toward the center. If we look at this distribution and predict 
utilities from it, we get that accurate Range Votes -- which, rounded 
off, become sincere Approval votes, would be we get:

(I'm going to assume, at first, that voters are linearly distributed. 
In fact, there will be a bell curve. I'll come back to that. This, by 
the way, is more of an intuitive analysis than any kind of rigorous 
one. I'd invite someone to look at it with more rigor, correcting my 
errors, and I expect there is more than one, i.e., besides true 
mistakes, more than one improper assumption.)

Position on political spectrum:
A: 0.166
B: 0.500
C: 0.833

A voters: all vote for A
         distance from voter to B < half distance to C, one-half of A 
voters vote also for B

B voters: all vote for B
         voter closer to A than to C, we could assume that half the B 
voters also vote for A, and one half also vote for C; however, as the 
voter approaches the exact position of B, the loss from the election 
of the candidate on the other side becomes less, and at some point 
voting for the favorite outweighs the increase in utility by avoiding 
a loss to the other side. So I'd assume that the B vote for A is less 
than half. Likewise in the other direction.

C voters: all vote for C, similarly less than half vote for B.

So we have A vote total equals 1/3 plus less than one-sixth. I.e., 
less than 50%.

B vote total is 1/3 plus 1/6 plus 1/6, or 5/6.

C vote total is the same as A.

A multiple majority is unlikely. *But even if there is a multiple 
majority, that candidate is still the obvious best winner, better 
representing the overall electorate than the candidate on either side.

However, of course, the center candidate's "core support" tends to be 
smaller, because the left and the right party tend to move their 
candidate toward the center. However, in that case, avoidance of 
adding additional approvals increases. While it's not nearly as clear 
as with two major candidates, even when there are three evenly 
balanced, natural strategy -- zero knowledge in this case, the 
outcome cannot be predicted, that's the definition of three-way -- 
leads to avoidance of multiple majorities. And a balanced election 
like that is itself rare. I consider it highly unlikely that we would 
see multiple majorities in public elections. If we did, great! 
Something is coming up with better candidates, when you have more 
than one with a majority willing to accept him or her. In tightly 
partisan races, where people place very high value on their party 
winning, and less value on avoiding a poor outcome -- they may even 
claim to not care which of the other two candidates wins -- what we 
are more likely to see is majority failure, *no* candidate gets a 
majority, and then, in this situation, we could have a top two runoff 
-- or decide it on Plurality. Note that what I'd support most 
strongly for U.S. implementation is Bucklin, which allows all those 
voters to first express their support for their favorite, if it 
matters that much to them. Then they can add an additional approval 
in second rank. It is quite unlikely, again, to see a multiple 
majority in the election, because many voters will not add second approvals.

 From experience, what we are quite a bit more likely to see is 
majority failure, not multiple majorities. That's what actually 
happened. It would be interesting to know if any Bucklin election 
produced multiple majorities. All of the ones I've looked at -- which 
is really only two where I saw the votes, as I recall -- there was 
only one candidate who obtained a majority. FairVote has claimed that 
Bucklin was discontinued with its use for primary elections because 
it was failing to find a majority (same as apparently happened with 
IRV), so this would confirm that multiple majorities would be rare. 
Primaries are really nonpartisan elections in that candidates can't 
be conveniently grouped, especially not into two major parties with 
easily predictable "vote transfers" in IRV or possible additional 
approvals in Bucklin.

What I expect with Approval is that only a small number of voters, 
maybe 10%, will add approvals. Same with Bucklin, only a relatively 
small number will add additional ranked candidates, though probably 
more than with Approval, because of a lesser possibility of "harm to 
the favorite."

Thus it is quite unlikely that we will see multiple majorities. It's 
a red herring. Approval will almost always satisfy the Majority 
Criterion. Bucklin always will, it's fully MC compliant.


>If two candidates obtain majority approval, most likely one of them was
>not a frontrunner, but a compromise choice.

That's correct, if "frontrunner" refers only to first preference. If 
it refers to overall popularity, predicted approval votes, it's a 
different matter, and one that I did not consider above.

Yes, and this is why a runoff between the top two if there is a 
multiple majority makes sense, rather than simply choosing the one 
with the most votes. I'm not sure this will be as easy to explain: consider:

The winner will be the candidate with the most votes.

Add majority requirement:

The winner will be the most votes, provided that this candidate 
receives a vote from a majority of voters. If there is no such 
candidate, there will be a runoff election between the top two with 
the most votes each.

Add multiple majority runoff requirement.

If more than one candidate receives a vote from a majority of voters, 
there will also be a runoff election between the top two.

The real question here is whether or not it is worth worrying about 
the multiple majority, simply to comply with a defective criterion, 
the Majority Criterion. Approval approximates Range, reasonably well. 
If there are multiple majorities, choosing the one with the most 
votes is unlikely to damage overall satisfaction much, if it damages 
it at all. It may not be worth having a runoff, often enough, just to 
avoid that situation. I still prefer it, though.


>This baffles me because I can't imagine why you like the Approval method,
>if it doesn't occur to you that a non-frontrunner compromise choice
>could conceivably obtain majority support.

No, that's not the likely additional "majority winner." It's one of 
the non-compromise choices, the other two that would be unusual. A 
true compromise winner will get a majority in approval, or there will 
be majority failure, almost certainly. Be baffled, then. It's good 
for the soul.

Remember, in a three-way race -- if it's based on first preference -- 
we have only one-third "core support" for each candidate. In 
Plurality, this spells majority failure. Approval shifts results 
toward finding a majority, but mostly additional votes come from the 
left or right adding a security vote for the center, and fewer come 
from the center adding a security vote for the left or right. The 
result is that only the center is reasonably likely to reach a majority.

It would be nice to have some real election data, wouldn't it? Some 
enterprising student could look up old records of Bucklin elections. 
If a multiple majority showed up there, my guess is it would have 
been reported in newspapers. "Smith gained a majority of votes but 
did not win because Jones got even more."

We *really* need some study of real Bucklin elections. Bucklin voting 
and Approval would resemble each other, except that additional votes 
are a bit more likely in Bucklin. Hence the Bucklin experience 
indicates, with common majority failure, low likelihood of a multiple majority.

My main point (don't you agree with it, Kevin), is that Majority 
Criterion failure in Approval is a red herring. It's quite unlikely, 
one, and more to the point, even, is that if it happens it is not a 
Bad Thing, it's actually a good sign, we should be so lucky as to 
have this happen. The only way this would be a poor outcome is if a 
public was massively duped into voting for a second preference who 
really, without the deception, had no chance to win. And for this 
deception to take that candidate all the way to the top -- very 
unlikely. Especially with Bucklin. Getting up to second place is more possible.

> > And how much damage from failure? Little. When the Majority
> > Criterion fails, we have multiple majorities. The majority
> > has Approved another candidate as well as their favorite,
> > and, together with other votes, this less-preferred
> > candidate has broader support. Is that bad? Many would argue
> > it's good, and this again points out the subjective
> > nature of the use of voting systems criteria to judge
> > election methods.
>
>I think it's probably good for frontrunners, since they have an easier
>time getting that many votes.

Yup. However, top two runoff works better than IRV because getting to 
second place, causing majority failure (due to other candidates) is 
easier for a dark horse than getting all the way to the top. And then 
this candidate has a chance of convincing the electorate that cares 
that it's worth voting for him or her instead of the frontrunner in 
the primary. Look, it's quite clear: around the world, when top two 
runoff is used for partisan elections, there are strong, persistent 
multiparty systems. Look at that French election with the top three 
being Chirac, Le Pen, and Jospin. The *leaders* got roughly twenty 
percent each. This situation is going to cause majority failure with 
just about any voting system that cares about real majorities.

There has been an issue raised here that we have not addressed: Range 
strategy depends on an understanding of who the frontrunners are. 
What is a "frontrunner?" Is it defined by first preference, or by 
likely vote in the election? We've mostly looked at first preference, 
but actually, it's probability of success in the actual election that 
would be the basis for proper strategy. We'd want to look at Range 
polls to determine the latter. Better than Approval polls, even if 
the method is Approval, but you'd want both if you could get it.

> > Quite simply, to make sound decisions from preference
> > profiles, we need to know preference strength. Preferential
> > ballots can, sometimes, approximate this (Borda does that,
> > and works better if there is a broad spectrum of candidates
> > on the ballot, thus creating, in the real preference pairs,
> > an approximation of preference strength), and usually the
> > majority preference will also be the ratings winner. But a
> > Range ballot directly expresses this.
>
>Well, that is subject to your interpretation of what the Range ballot
>signifies. It certainly *could* be used for that.

What I meant is that preference strength can be expressed directly 
with a Range ballot, not with any other kind. We can, from a Range 
ballot, as well, derive reasonable assumptions about true 
preferences, better information from some voters than from others, 
even in the presence of strategic voting, which is or approaches 
binary votes (0 or 1) for each candidate. The voters who provide 
little information -- other than, at a minimum, a categorization of 
candidates into two classes, most preferred and least preferred -- 
still, when averaged together, will provide information about average 
preference strength, which is what we need for amalgamation anyway. 
I've mentioned many times that one can measure an analog voltage 
accurately by making a series of binary comparisons with a random 
voltage. If the randomness is evenly distributed, it can get very 
accurate as an average of many measurements. It won't be evenly 
distributed, but within a range of preferences, it will be close to that.

Look, lots of exploration of theory. It's all trumped by the 
simulations. Warren's approach was brilliant. I don't think he really 
invented it, but he publicized and popularized it, to a degree. It's 
an approach that comes out of economics and game theory.

And he asked a fundamental question that deserves much more 
attention: how can we objectively judge the performance of a voting 
system. What does "good performance" mean? Voting systems criteria 
were designed to indicate that, but they didn't *measure* it. They 
only gave pass-fail results, with no consideration of frequency of 
failure, nor with any objective measure of the value of each 
criterion, so, since no voting system meets all criteria proposed, 
which ones are important? How could we answer this question?

In order to do it, we need a method of *measurement* of election 
performance. Enter, stage right, Bayesian regret. Got any other 
alternative? Has any other alternative been seriously proposed?

Then comes the study of this using simulations. The old problem with 
the utility approach, we find it in papers essentially pooh-pooing 
the idea, is that utilities are incommensurable, allegedly. However, 
simulation avoids the problem by starting with absolute utilities 
which are *defined* as commensurable. It's true we don't actually 
know these utilities except in certain situations. What may be noted 
is that, in those situations, we use the equivalent of Range voting, 
we sum the absolute utilities to make the optimal choice -- and where 
this is inequitable, we may provide compensation, where some of the 
*winners* give up some of their winnings to *losers.* Since 
optimization raises all boats (on average), then, all benefit. 
Collective decision-making is generally not a zero-sum game; what 
Range voting does is to seek maximum *overall* benefit, choosing the 
choice most satisfactory on the average.

With distorted information, its ability to do that is impaired, but 
the nature of the system and averaging over many voters greatly 
reduces the damage. It still works better than alternatives.

The systems that can beat it are hybrids that include it. And that 
ought to be obvious! The necessary information is simply missing from 
ranked systems. Somewhat distorted information, as long as all 
expressed preferences are real preferences -- which is what Range 
encourages -- is better than only ranked information, which is 
*maximally* distorted, even if sincere, compared to Range votes. Some 
voters will provide exaggerated -- or minimized -- information, 
others will provide more accurate information. The average of this 
will be better than all exaggerated information, i.e., Range will be 
better than Approval, and Approval is better than Plurality, rather 
obviously. Unless you really want to suppress third parties through 
an idea that they are dangerous.

In fact, though, moderate advances in voting systems make third 
parties *less* harmful.

Runoff voting is not a moderate advance, it is a major one. Want to 
damage the prospects of third parties? Replace real runoff voting 
with "instant runoff," an ersatz version. Cheaper? It claims to be. 
Probably not. Probably significantly increases costs, or doesn't 
reduce them significantly. Given that there are reforms that 
accomplish the good things that IRV can do, with much less cost, the 
top-two runoff to IRV convension is a very bad idea. Instead, fix the 
problems with top two runoff. Make runoffs less likely by using a 
better form of preferential voting. Condorcet if you must, but you'll 
find it easier to sell Approval or Bucklin (probably the latter, it 
answers the most common objection to Approval). Condorcet methods 
don't require voters to compromise; if one must use Condorcet, make 
sure that an approval cutoff is expressible, otherwise one will not 
be able to determine majority acceptance of a result, that can be a 
severe limitation of Condorcet. In Optional Preferential Voting, we 
can assume that a voter accepts a result if they voted for the 
candidate, but this form of IRV -- it's what we have used in the 
U.S., unfortunately, even with only a few viable candidates, when an 
instant runoff is needed, usually fails to find a majority because of 
ballot exhaustion. Bucklin is a little more efficient, because it 
does count all the votes.

Did I mention that we should Count All the Votes? There are some 
cogent constitutional arguments raised against IRV because it does 
not count all the votes. Whether a vote gets counted depends on the 
sequence of eliminations. In Bucklin, second rank votes are either 
all counted, or none are. (And I'd suggest that all votes be counted 
regardless. We need the information for more purposes than 
determining the winner.)

> > And, of course, we'd compare these results with
> > simulation predictions and eventually we might build up
> > enough data to confirm or improve the models. The problem
> > with this approach for the short term is that the
> > simulations can study thousands of elections and thus see
> > the behavior of a voting system under many different
> > conditions, whereas the actual experimental approach, with a
> > lot of effort, only shows one instance. Useful, still, but
> > probably best used to improve the models used in
> > simulations.
>
>I strongly agree with improving the models used in simulations.

Everyone who understands the issues, I think, would agree, including 
Warren. He's done quite a bit of work to make them as good as he can, 
and he did not design them to produce some outcome, I'm sure, but 
he's only one person. To some extent, the models, though, don't need 
to be accurate, they just need to be reasonable. A voting system 
should be able to handle the kinds of preference distributions that 
are generated in the simulations. Real voting will have different 
kinds of preference distributions in different contexts. Still, its 
more satisfying, and more convincing, if there is real-world 
confirmation of the simulation predictions, or real-world 
confirmation of the preference distributions (the former is actually 
better, because it would validate the overall process, not just the 
underlying utility assumptions.)


>(It works when we
> > can see it and test it, why would it stop working when we
> > can't?)
>
>Because real people will be involved

That doesn't actually answer the question. Real people are 
complicated, that's true, but they still behave, more or less, in 
roughly predictable ways, especially when we are looking at average behavior.

Obviously, there can be differences between behavior assumed to 
continue "in the dark," so to speak and what in reality does not. 
However, children learn at an early age that when they see an object 
moving and it disappears behind an obstacle, they can predict, more 
or less, where it will reappear. And you can play games with them by 
violating the assumption of continuation, they will find it funny. 
"Funny" means "unexpected."

So unless the fact that the roots of the behavior are hidden itself 
causes change (and I don't see evidence for that in this case), it is 
a reasonable starting assumption that the behavior will be similar 
whether the roots are hidden or not.

The "roots" are the absolute utilities that voters assign or sense or 
have with respect to each option possible in an election. It might be 
possible, in some way, to measure these directly, through studies of 
brain responses and activity. But I'm certainly not going there. I'm 
only suggesting that we have internal mechanisms for making 
decisions, natural ones, evolved over a long time. It is highly 
likely that they use something like Rational Utilitarianism. We don't 
run an internal Condorcet matrix; rather, we use a preponderance of 
impulses system. We do it quickly or slowly. When needed, we do it 
very quickly, instinctively, to avoid danger and seek immediate 
benefit, when there is a sense of urgency (which means high immediate 
preference) but when preference strengths are low, we decide slowly 
-- when we are healthy -- allowing the impulses to integrate over a 
longer time, thus considering more inputs, such as rational 
consideration, and we do so iteratively, going back and forth between 
reason and emotion. Emotion is, itself, deeply rooted and of a Range 
Voting nature, coupled with chemical messenger responses, which are range-like.

Regardless, it's obvious that in natural human decision-making, 
preference strength counts, and also success probabilities. We may 
prefer to catch a certain fish, but if that fish is not common, we 
will not design our entire food-gathering strategies around that 
fish. We will put our effort where it is likely to produce a reward. 
We will vote for a frontrunner! Because every other vote is likely to 
be moot. It only gets tricky when there are more than two 
frontrunners, but we are still well-equipped to make this kind of 
decision, particularly when the investment is low. One vote is not a 
high investment....

> > There is no usable definition of "a sincere set of
> > ratings irrespective of context," because there is no
> > way for voters to even determine such in a manner that they
> > could vote them.
>
>Ok, I will concede again that there is no way for voters to determine
>their sincere set of ratings in a votable way.

No single way such that we have the right to say to them that their 
way is the wrong way. It's simply part of the prerogative of the 
voter, always has been and so it should remain.

I was pleased to see that the ballot instructions for RCV did not 
say, Rank the candidates in order of preference.

Rather, they simply said to indicate your First Choice in one column, 
your Second Choice in the second, etc.

Choice. That's a vote. It is not necessarily a preference indication, 
it's a decision which may include strategic considerations. For 
example, RCV only has three ranks. Want to cast an effective vote? 
Makes sure that one of your votes is for a frontrunner. Want to avoid 
center squeeze, think it might be possible. Rank a compromise 
candidate in first rank! I.e., reverse preference. A choice. Not a preference.


> > The ratings that we can determine, in
> > practice, are not absolute, independent ratings.
>
>Yes, I thought this was the sincere/strategic vs. accurate concept.
>
> > We can approach, this, though, in certain respects, through
> > runoff elections, and we can approach it through binary
> > choices in sequence.
>
>I don't really mind if it's theoretically possible.

It's standard democratic practice, proven to work quite well for 
centuries. The problems we see come when we don't do this and when we 
use representational methods that exclude large numbers of voters 
from exercising any effective power. Often the majority is just plain shut out.

> > > I also wonder, what, theoretically, does it look like
> > when Range fails
> > > and gives a poor result. Is such a thing allowed?
> >
> > Well, what's a "poor result"? My claim is
> > that the only way to objectively study this is to see how
> > the method performs when absolute utilities are known.
>
>Well, if we know the absolute utilities, then we can definitely call
>certain votes inaccurate.

That's right. And a particular kind of "distortion" away from the 
accurate votes is voting von-Neumann-Morganstern utilities, which are 
modified from accurate relative utilities by probabilities of 
relevance. An irrelevant alternative receives no vote strength. That, 
by the way, leads to the satisfaction, by a method of amalgamation 
that uses these utilities, of IIA, Independence from Irrelevant 
Alternatives, a crucial stumbling block for some methods.

Remember, Arrow's theorem was not about voting systems. It was about 
determining a social preference order from the collection of 
preferences of individuals. He assumed a ranked preference list, and 
this assumption, essentially, led to his impossibility theorem, that 
no method for amalgamation existed that satisfied a short list of 
what he considered reasonable assumptions and voting systems 
criteria. IIA was one of them.

In order to apply IIA to cardinal ratings systems, some shifts of 
definitions are needed, and what Dhillon and Mertens purport to show 
-- and there is some literature which seems to confirm their result, 
and none that I've seen contradicting it -- is that with a reasonable 
application of the Arrovian criteria to rating systems, there is a 
unique solution for the amalgamation. Starting with, instead of a 
ranked preference list, include preference strength information and 
modify it by probabilities, using von Neumann-Morganstern utilities 
instead of absolute ones, and it is a unique solution. No other 
method that is not equivalent to it can satisfy all the neo-Arrovian 
criteria. Now, exactly how they pull this off isn't clear to me. 
Intuitively, I imagine I understand it. But I cannot confirm the 
proof, not today anyway! I'd have to learn what Warren calls 
"notation from hell." And he's a mathematician, quite familiar with 
ordinary notation in this field.

This is a theoretical approach. It doesn't trump the simulations, 
which are closer to real-world experiment, which always trumps 
theory. The reason for using simulations is that when we are 
considering election system behavior, the pathologies tend to be 
relatively rare, and, as well, the system may not collect or make 
known the data necessary to determine if a pathology exists. We think 
that, with nonpartisan elections, which is what's been the situation 
with almost all IRV elections in the U.S., we only had, before 
November, about 33 elections, with something on the order of, my 
rough recollection, ten instant runoffs. From comparison with real 
runoff elections, I'm *guessing* that we might have roughly three 
problem situations in there, and if we exclude the runoff elections 
where the improvement from them was due to shifts in voter 
preference, from whatever cause, we might be left with only one or 
so. Very rough estimate.

And we don't have full data on many of these elections. We do have 
RCV data from San Francisco, the most recent elections, so there are 
a few elections to work with there. When we use simulations, we have 
thousands of simulated elections, so we can get a statistically much 
more solid result, and we can compare various election methods using 
the same starting utility sets. And it's reproducible.

> > That's what the simulations do, the "know" the
> > absolute utilities by assuming them, in some hopefully
> > reasonable way. (Don't think it's reasonable? The
> > simulators are configurable. Use a better simulation of
> > underlying utilities! Until then, Warren's work is the
> > best we've got!)
>
>I have no problem with the representation of utilities.

Good. Some do. I should have written "they know."


> > Now, following Warren's work, Range would very rarely
> > give a truly "poor result." It would take some
> > very bizarre preference profiles. You can construct them
> > .... but for them to occur in real life would be practically
> > impossible. What it can do, and the simulations show it, is
> > to miss the true ideal winner according to the normalization
> > of absolute utilities, and, as well, due to the non-linear
> > expression of utilities (but still monotonic) by voters
> > seeking to maximize the effect of their vote. However, when
> > it does this, it would not then flip to a much worse
> > candidate, unless, again, the conditions were truly bizarre.
> > It would simply choose, in almost every simulation (quite
> > likely all or nearly all), the next best winner, and the
> > best would be in second place.
>
>Actually a lot of methods fail in this way: The best candidate actually
>places second.

Yes. However, the difference with Range is that this can only 
reasonably happen when the preference strength -- overall --  for the 
better winner over the actual winner, first place, is weak. With 
other methods, it can be quite strong. (This, in fact, is strong, 
because the other methods don't consider preference strength at all, 
and can thus make a huge error.)

> > In real life, though, the majority will surprise us. The
> > runoff will have different turnout than the original
> > election, and some voters will change their votes, and both
> > of these effects will favor the *fully sincere, absolute*
> > Range winner over the majority preference, because, in this
> > situation the majority preference must be weak. So only if
> > the normalization or strategic voting have sufficiently
> > distorted the Range results, I'd predict, would the
> > apparent Range winner fail to win the runoff. You hold the
> > runoff, indeed, because of this possibility, the possibility
> > of distortion.
> >
> > Are you starting to see this, Kevin? I'm not writing
> > just for you, as I assume you know, and much of this,
> > I'd think, you already understand. Or did you? Or do
> > you?
>
>Which part are you asking about, the runoff part? I'm well aware of
>the fact that you prefer a runoff, and I don't disagree with the idea
>that the result of the runoff could be different.

It's not debatable, actually. Several aspects of this are well-known, 
what's new is my observation that preference strength affects turnout 
and that this means that runoffs shift results toward a sincere 
utility winner, among whoever is included in the runoff. In fact, 
given sufficient preference strength and a runoff that allows 
write-in votes, an error in the selection of the top two can be corrected.

>Actually the fact that you are not writing just for me, makes it hard for
>me to find the answers to my questions, or even determine whether you
>are specifically trying to answer them, at any point in time.

I am trying to answer your questions. If I have not answered them so 
far, either I haven't understood them, or I answered them and you did 
not recognize it, perhaps I buried it in too much dicta, or I simply 
got diverted. It happens.

What questions remain? I see substantial agreement in certain areas. 
What do you think?