[Election-Methods] [EM] RV comments

[Abd ul-Rahman Lomax]

At 04:58 PM 8/1/2007, Juho wrote:
>[I wrote:]
>
> > Please describe a bad problem with Range. Specifically, and show
> > examples. Hopefully, they will be realistic.
>
>I did but I assume you didn't accept the example.

Now comes the alleged "bad problem." It is a good example, actually, 
it shows how assumptions largely inherited from thinking about ranked 
methods infect how we look at Range.

>  I'll use just
>slightly different words this time. The sincere opinions of Democrats
>are D=100, R=80, and for the Republicans R=90, D=80.

"Sincere" is not defined. By many definitions, these "sincere 
opinions" would be translated to Approval style votes. And in any 
ranked method, that is forced. In Range, voters do have an option. 
They *could* vote this way, i.e., the opinions as stated become Range 
votes with the same numbers.

Now, at the outset, let me say that I've never seen an election that 
looked like this. If there are no other voters, and if these are 
"sincere opinions," -- which still needs precise definition, but 
we'll let that go for the moment -- the electorate is going to be 
quite happy no matter which candidate wins. A ranked method would 
choose which candidate? Depends totally on how many Democrats there 
are vs Republicans. It looks like the Democrats have a stronger 
preference for their candidate than the Republicans have for theirs. 
(10/8 vs 9/8). If the numbers of Dems and Reps are equal, it looks 
like the best winner is the Dem.

An 80% rating, which the Republicans give to the Dem, is quite good! 
Let's see what Juho does with this:

>  If Range in used
>in a way that assumes all opinion values to be used extensively, not
>only min and max, then the one that votes more strategically (min and
>max only) is likely to win (assuming that the support of the parties
>is roughly 50%-50%).

Sure. And we presume they will vote that way if they want to win. 
*How much do they want to win?* If their sincere opinions are as 
stated, not very much. But it is being assumed that they want to win 
enough that they will rate an excellent candidate, according to their 
sincere opinions, at zero. I'd say there is a contradiction here. 
However, any ranked method will *force* them to do this.

As to the Dems, if the Rep wins because those evil Reps vote a 
normalized vote -- quite legitimate, not insincere at all -- they 
*also* get a candidate they considered excellent. Where is the "bad problem?"

It was *assumed*. It was assumed that people with no strong 
preference will vote a strong preference, and for what reason? 
Presumably, because they are Republicans. Isn't that how Republicans 
vote, like fanatics, whereas Democrats are reasonable, thoughtful 
people, who are completely "sincere" and wouldn't exaggerate a thing 
if it killed them?

(Not.)

Range Voting is quite difficult to analyze with simple examples. In a 
real election, votes would be spread all over the spectrum. With 
Range 100, there might only be one ballot in a thousand that matches 
another exactly, unless Approval style voting is prevalent. That all 
voters from one party would vote "sincerely" and all from another 
party "approval style" is preposterous.

But if we take these preferences and votes at face value, you could 
toss a coin with this election and get a good result. If this were a 
runoff, lots of voters would stay home, since they already "won." Either way.

Yet this is presented with a straight face as a "bad problem."

Juho is in plenty of company. We have seen many examples like this, 
contrived to make Range look bad unless you look closely.

Underlying this is an assumption that it is "bad" to gain something 
by "exaggerating." And the answer that is proposed: Force everyone to 
exaggerate. That way, the people who would exaggerate would not gain 
some "advantage."

How about this: we want people to vote in the way that they think 
best *for them*! That will include, quite possibility, some 
consideration that it *may* be better for society as a whole if they 
vote "accurately." Or it may not. *It depends on circumstances.*

Typically, the critics asserting that Range has "problems" with 
strategy don't look at the simulations.

What problems?

Warren's simulations were not designed to make Range look good. They 
were designed to study how election methods perform, by the measure 
of overall social utility. They assume that each voter has utilities 
for candidates that are already "normalized" by the "first 
normalization," as I have described it. Various methods, if I am 
correct, have been used to distribute the candidate utilities, I 
think that Warren settled on an issue space calculation.

In any case, the utilities used are *reasonable,* but I'm sure that 
Warren would agree that this needs more work to make the simulations 
even more closely resemble actual voter behavior.

With the postulated internal utilities, we have, essentially, the 
opportunity to "mind read" the voters. We then predict the voter 
behavior based on various strategies that voters may use to translate 
their personal preferences into votes. So Warren has compared Range 
with "sincere voting," "normalized sincere voting," and "Approval 
style voting," plus mixtures. If you want to assert that Approval 
style voters harm the sincere ones, you really should look at the 
simulations in detail. If I'm correct, the results don't support that.

But you could imagine, as you did above, that we have one party 
voting non-normalized sincere, thus diluting their vote by a factor 
of 5, as you did. And then the others take similar utilities in the 
other direction and simply normalize them. So of course the latter 
get what they prefer, it really didn't matter now much they preferred 
it, it could have been 100 to 99. The postulate is that this whole 
group of people, half the electorate, is so greedy that it would go 
for a tiny improvement in outcome, truly below any meaningful 
difference, at the expense of everyone else.

That is, quite simply, an extremely unhealthy society, it needs far 
more than better election methods!

>  Individual voters are thus tempted to
>exaggerate. The votes of those voters that will not exaggerate will
>have smaller weight than the votes of the strategic voters.

They are "tempted" to exaggerate if their preferences are stronger than stated.

Look, nobody is recommending that Range Voters vote as described. The 
standard advice is "vote 100% for your favorite, vote 0% for the 
worst." And most would add, under current conditions, "start with the 
frontrunners, vote for your favorite among them, and 0% for the worst of them."

What people need to know is that a vote of 100% is a vote *for* the 
candidate, purely. A vote of 0% is a pure vote *against* the 
candidate. And everything else is, by definition, a weaker vote.

Something from my work with an exact utility study has largely been 
overlooked. It does need further study to rule out certain 
possibilities, but it looks like even a very few voters voting 
intermediate votes improves the expected satisfaction for *everyone*. 
That is, if you make the *method* Approval, instead of Range, the 
expected satisfaction for the Approval style voter goes down. And, of 
course, everyone is now an Approval Voter.

What method is best for society? It's pretty clear: Range. To prevent 
some alleged small injury to "sincere voters," we simply injure 
everyone. So that way it's fair!

Brilliant! -- that's what I've got to say about this plan!

>One can fix this by letting the voters understand that in order to be
>fully efficient, an approval style vote is in most cases the
>strongest strategy for them. Letting some voters cast sincere opinion
>based votes e.g. for 50 years before they learn that their votes have
>had less weight than the votes of some other voters doesn't sound
>nice to me.

You have 100 votes. You only cast 50 of them. Somebody has to tell 
you that you have been casting weak votes?

Sure, it's possible for someone who doesn't pay attention to the 
ballot instructions, doesn't pay attention to what would certainly be 
discussion in the media, to vote in a weak way.

>Range is likely to become Approval like if used in a competitive
>environment.

Actually, this is highly *unlikely.* The assumption being made is 
that all voters will vote Approval style. But ever hear of 
"independent voters"? You should pay attention to them. In a 2-party 
system, they decide elections. Will they vote as alleged?

Some of them. Some of them won't. And even a few not voting Approval 
style helps *everyone*.

>  Range may however provide worse results than Approval if
>there is a mixture of Approval like and sincere opinion like votes
>(and those votes are not evenly spread among the candidates).

Asserted, over and over, without any proof at all, or even reasonable 
evidence. Apply the statement just made to the above example. And 
define "worse" without using utility analysis. If you can.

>An (exaggerated) example on how Range could elect a "no-good"
>candidate:

Good. Let's look at it.

>  50% D=100, R1=80, R2=70,  30% R1=100, R2=90, D=70,  20%
>R1=100, R2=0, D=0. The "bad" Republican wins. In real life this is
>however not likely to happen since probably the D and R1 supporters
>will understand what's going on and will exaggerate too. Many R1
>supporters might take one step back and give more points (maybe max)
>to R2 too.

For starters, any method can elect a "bad" candidate, if voters don't 
use the method intelligently! The above example was, I think, 
misstated, I'm modifying it here so that it makes sense.

         D       R1      R2
50:     100     80      70
30:     70      100     90
20:     0       0       100
         ---------------------
         7100    7000    8200

What is going on here? 80% of the voters don't care much about who 
wins the election! And they vote that way. So the 20% who care -- Ron 
Paul supporters, of course -- vote as if they care, and they win.

Where is the "bad problem"? What is wrong with the above outcome?

Okay, preference analysis of the votes:

50: D>R1>R2
30: R1>R2>D
20: R2>D=R1

Let me point out, first of all, that the R2 supporters are clearly 
not Republicans, period. They are something different that might be 
operating within the Republican party in some way....

The vote pattern is not believable. However, taking it as written, we 
have three ways of looking at this:

Range: R2 82%, D 71%, R1 70%.
IRV: first round, R2 dropped, second round, D wins 50:30.
Condorcet:      D/R1    50:30 D wins, beats R1
                 D/R2    50:50 tie
                 R1/R2   80:20 R1 wins, beats R2
                 unbeaten: D, D wins.
Approval:       D:      50
                 R1:     30
                 R2:     50
                 tie D and R2.

(The approval vote assumes a common approval strategy (the one which 
generally maximizes, in large elections, the expected outcome for the 
voter: mean-based approval. Thus the ratings are normalized, first, to

         D       R1      R2
50:     100     33      0
30:     0       100     66
20:     0       0       100

Then the Approvals fall out easily. You Approve any candidate higher 
than the mean rating (50%). Approval is a Range method, the 
"strategic" motivations are the same.

Now, is R2 a "no-good" outcome? Why would Juho claim so? Everyone 
agrees that this is a decent candidate! You only see low ratings with 
normalization, which would make anybody look bad if the best possible 
candidate is on the ballot!

> > I find it odd that some will argue against the mild alleged
> > vulnerability of Range Voting to "strategy," which merely means
> > voting range as a pure ranked method with two ranks, and then
> > swallow the much more insincere votes coming from strategic
> > vulnerabilities of Condorcet methods, perhaps claiming that the
> > latter are "rare," perhaps because it's too complicated for people
> > to figure out, so they won't do it.
> >
> > But with Range, these same people will claim that the sincere
> > voters are "suckers." That they are going to be taken advantage of
> > by conniving Approval voters.
> >
> > It's a double standard.
>
>I don't think so. The main difference is that in (sincere opinion
>based) Range the (Approval style) strategies typically work in all
>elections

What is "sincere opinion based Range"? How are votes defined in it? 
Apparently, they are not normalized (second normalization). Yet when 
I'm handed a ballot and it is suggested that I vote, with any method, 
I am being asked to make a choice. Between the candidates on the 
ballot. In that context, with *all* methods, we normalize. For 
example, a case can be made that if the ratings shown above for R1 
and R2 are sincere, and the method were Approval, a non-normalized 
Approval vote would be for the D and R1 voters to approve all three 
candidates! Leaving, of course, the election in the hands of the R2 supporters.

Only by assuming that the R2 utilities are not sincere can we come up 
with the idea that the outcome of R2 is a poor one. I *wish* I could 
see such good election outcomes! (i.e., that the D and R1 supporters 
get with the Range election). It has been rare.

Approval style strategies work *if* you make the correct choice of 
your approval cutoff. It's easy to get it wrong. In my opinion, this 
is the best strategy for Range, short of a full-blown game theory calculation:

Determine the frontrunners. In the election above, there are three, 
none of these candidates is clearly beating the others, in Range. 
However, if the "strategy" of the R2 voters is not known, it would 
appear that D and R1 were the frontrunners.

Rate your favorite frontrunner max and your least favorite min.

I'm going to assume equal probabilities for all the frontrunners, first.

Consider the preference strengths of the middle frontrunner(s), 
compared to the others. Place them on a scale from 0 (the rating of 
the worst frontrunner) to 100 (the rating of the best). Pick a number 
that seems to express the relative preference strengths. (Can I say 
that I prefer A to B about the same as I prefer B to C. If I could 
buy the election outcome for each of those pairs, one at a time, 
knowing that then the one I paid for would win, how much would I pay? 
That's one possible way to look at it. Compare this to the possible 
range votes. How accurately can it be expressed? Round it off in the 
direction of the approval vote.

In Range 2, note, this would mean that if your sincere utility is in 
the range of 40% to 60%, you would vote midrange. Otherwise you'd 
vote Approval style.

What about other candidates? Rate them on the same scale and vote 
rounding off as described.

Voting sincerely, if it involves an error in the expression of 
utility, has a corresponding lower expected return. However, you get 
a *worse* expected return if you err in the determination of frontrunner.

In the above election, you decide that there are three frontrunners. 
Again, the normalized utilities:

         D       R1      R2
50:     100     33      0
30:     0       100     66
20:     0       0       100
         ---------------------
         5000    4650    3980

The assumption was made by Juho that there is only one way to vote 
"sincerely." If the voters vote those utilities, and we assumed that 
the D and R1 voters were sincere, the votes would be sincere. What 
Juho is doing is to assume that non-normalized utilities would be 
used, a preposterous assumption under conditions of competition. You 
will see non-normalized utilities only in elections where everyone 
expects most people to be sincere and desiring to maximize overall 
outcome. The pizza elections, generally.

What Juho is postulating is a competitive election (20% cutthroat Ron 
Paul supporters -- I'm, by the way, a Ron Paul supporter, though I'm 
a Democrat, I might actually vote that high rating for Ron Paul. But 
not for R1. Unless it was R1 who was Ron Paul), but 80% of the voters 
are voting non-normalized "sincere" ratings. I.e., stupidly. Get 80% 
of voters to vote stupidly, you can do what you like!

If voters vote as if they were answering the question "Which one of 
these candidates should be elected?" Instead of the question "On a 
scale from Genghis Khan to the Messiah, what is your rating for each 
candidate?"

Do you really think that voters would answer the second question, 
presented with a Range ballot that describes what you are doing as 
casting 0-100 votes for each candidate, as many candidates as you 
like, the candidate with the most votes wins? No, the vast majority 
of them would answer the first question, unless they really want to 
register a protest at the limited field. In which case they really 
should write someone in!

The D wins the Range election, if everyone normalizes, *with* sincere 
votes from everyone except the evil R2 supporters. And what happens 
to the evil R2 supporters, if they were distorting their preferences?

They lost. Had they voted sincerely, say to rate R1 at 50%, R1 would 
have gotten 5650 votes, and would have won.

Can you imagine what they would be thinking? "If only I hadn't 
listened to R2 and voted my sincere preferences, I'd have elected a 
Republican, whom I prefer to the Democrat by a good margin, R1 is 
much closer to R2 than to the D.

And so next election, they will vote sincerely, no matter what their 
candidate says they should do. And, indeed, they will not trust a 
candidate who tells them to conceal their preferences.

But the critics of Range claim that voters will be so badly burned by 
voting sincerely that they will, instead, move to voting Approval. 
No, they will move toward what they should have been doing in the 
first place, normalizing. Vote max and min for at least one 
candidate, a frontrunner. (In the above election, we assumed all were 
frontrunners.)

Voting sincerely leads to reduced regret, in real terms. It is not 
likely to seriously backfire.

>  and for all voters while in Condorcet the strategies work
>only in some scenarios and are often hard to implement.

I just pointed out, with the example Juho gave, how voting Approval 
style could backfire. Seriously. It only works if you can accurately 
predict how others will vote. But can they predict how *you* will 
vote? If not, why not? Are you smarter than them? Better informed? If 
so, be my guest. If you are right, I *want* you to vote Approval style!

And if you are wrong, the one harmed is you, not the rest of us. I'd 
only be harmed if I voted stupidly, by not normalizing. In Range 2, 
the resolution is so low that the expression error becomes 
significant, so in Range 2, voting Approval style is possibly a 
little safer. Not a lot safer. In Range 10, I think this could be 
neglected, it is not even an issue in Range 99 or 100, in which case 
a normalized and otherwise "sincere" vote is easier than an Approval 
Vote. With the Approval vote, one must make accurate predictions of 
who the frontrunner is. With the sincere vote, it isn't so important 
who the frontrunners are: if you think a candidate might actually 
win, if you think it possible, simply include that candidate in 
frontrunner status.

>  The
>vulnerability of Condorcet methods thus depends very much on how one
>estimates the various factors that influence the probability of
>"failure" due to strategic voting.

The problem is that Condorcet methods *inherently* choose bad winners 
under some conditions. This has nothing to do with "strategy." If you 
neglect preference strength, and only look at rank, you are equating 
a major, life or death preference, you will take up arms if a certain 
candidate wins, with a "toss-a-coin" trivial preference. With a fully 
informed electorate, that already knows how people would vote in a 
Range election -- maybe there have been some trustworthy polls -- 
then, absolutely, a ranked method can do very well. People will 
factor in what they know about the strong preferences of others, and 
some supporters of A will not vote for A if they know that the result 
is a violent revolution, even if their personal preference is A.

Consider the disaster that was Ruanda, where a majority elected their 
preference.... not always a good thing, sometimes very bad. Depends 
on preference strength.

Any method that collects and uses preference strength is going to 
fail the Majority Criterion (as a single-stage method). But we can 
actually fix this, have our maximized voter satisfaction *and* 
majority rule. It's pretty simple, and really corresponds to existing 
practice. A runoff when the consent of a majority is not apparent 
from the results!

So there would have been, had the election in Ruanda been held with 
Range, a runoff, I'd expect, between the Hute and Tutsi candidate. 
And the electorate would understand, much better, the consequences of 
their votes. Indeed, had it been Range, it's probable that the ballot 
composition would have been different.... It becomes possible to run 
multiple candidates for the same party, so less polarized Hutu 
candidates might have been there. Instead, we got the rabble-rousers, 
the ones appealing to the basest instincts, firing up the base.... 
Milosevic did this in Serbia, with similar results, a disaster for 
nearly everyone.

>  In some calculations Condorcet
>methods can be considered fully safe while others may consider the
>threats more probable. (Note also again that Approval is also not
>without strategy problems, and plurality etc.)

It's nuts. Avoiding strategic voting, which in Range only means 
"exaggerating," is being compared with preference *reversal*. I 
agree, preference reversal is not terribly likely. But it is not 
really the issue. The issue is that ranked methods do not collect and 
use the preference strength information that is essential to making 
intelligent choices.

The human brain doesn't ordinarily use ranked methods to make 
decisions. Why not?

It would be *stupid*!

Artificially, sometimes, we do use ranked methods, we may take 
options and put them in pairs and run a round-robin. And then we 
discover that a choice we discarded, really seems better to use than 
one who beat every one *in the contests we ran*. But normally, we 
don't even use roundrobin, it takes too much time. Instead we allow 
ourselves to sense a kind of weight for each choice; each choice 
stimulates a kind of good/bad reaction, and we compare that reaction, 
very rapidly. The choice with the highest positive reaction, we 
normally will make; certainly this is the one we will investigate 
most carefully if we have time. If we don't have time, we just go 
with it. Range works in emergencies, based on accumulated instinctive 
and learned responses.

> > I am *not* saying that voting sincerely in zero knowledge is being
> > a sucker. But voting so, ignoring the identify of the frontrunners,
> > is, quite simply, foolish. There is *strategy* for voting Range.
> >
> > If people don't use it but do normalize, they will not be harmed
> > seriously.
>
>I think you should refer to such normalization where at least one
>frontrunner gets min and one gets max (or something close to that).

This is how most advice on Range Voting does it. Have you seen 
anything different from a Range supporter?

The implication that people won't normalize comes from critics of 
Range. And it isn't based on poll behavior, it is just an assertion, 
a speculation. I think it's quite likely that *some* people won't 
normalize. But some people will vote, in a large election, any way 
you can imagine. Ballots are received, in Plurality, with every 
candidate marked, or none. The totals aren't normally reported, they 
really should be.

A major initiative of mine is Public Ballot Imaging, which would make 
possible detailed ballot analysis, we would start to know much more 
about how people actually vote.

>(Note btw that normalization also destroys the otherwise nice
>behaviour of Range in the pizza example. If the sincere opinions of
>three pizza lovers are [A=100,B=99], [A=100,B=99] and [B=100,A=0]
>(the third voter is allergic to pizza A) the normalization changes
>the selection to pizza A.)

That's right. Which is why I've written, many times, that 
non-normalized voting behavior is only to be expected where the 
context is non-competitive.

But this avoids the issue. It seems clear to me that most people will 
normalize, they will vote max for one and min for another. As long as 
they don't reverse preferences, this almost automatically guarantees 
that they will cast a reasonably effective vote (not necessarily 
perfect, but reasonably close).

What if voters normalize? Is it still harmful if some voters vote 
Approval style and some vote a spread?

What is the alleged "bad" outcome? None, so far, has been alleged, a 
*good* outcome was labelled bad, that's all.

Note, also, that it is possible that, in a particular election, 
voting Approval style would produce a benefit for the Approval 
voters. But this is balanced by the risk, and it will come to pass in 
other elections, that Approval style voting will cause harm *to the 
Approval voters.* Critics typically show us an election where the 
Approval Voters benefit, making it look like they would *always* benefit.

No. Voting Approval and Voting sincerely -- if the Range resolution 
is sufficient -- have very close expected utilities for the voter. 
What this means is that if the Approval voter benefits in some 
elections, the Approval voter loses in others. And from what I've 
seen -- Juho really should look at the work, if he hasn't, or pay 
more attention to it if he has -- the extremes are larger with the 
Approval Voting strategy.

(*Both* are strategies! -- that is, methods for converting 
preferences to votes for maximized results, according to some 
standard of the voter.)