[Election-Methods] [EM] RV comments

[Abd ul-Rahman Lomax]

At 05:05 PM 8/10/2007, Juho wrote:
>I think we have by now covered most of the stuff and are now to some
>extent repeating things. Let's try to cut that out.

Certainly. It would help if Juho would supply an actual example of 
harm instead of proposing an example that shows no harm, but simply 
asserting that it was harmful.

>On Aug 10, 2007, at 1:22 , Abd ul-Rahman Lomax wrote:
>
> > That all voters from one party would vote "sincerely" and all from
> > another party "approval style" is preposterous.
>
>It is not a requirement that all would be "sincere" or "approval style".

Requirement for what? Presumably for "harm." The example showed what 
I called "preposterous," and a significant dilution of the votes 
shown by mixed voting would alter the significance of the example.

What is behind the usual assertions of harm from "strategic" voting 
in Range (it is not what is considered "strategic" in ranked methods) 
is an assumption: the voters don't have a strong preference but that 
is what they vote. Why would they vote a strong preference if they 
don't have one?

It seems to be assumed that it is some kind of plan. Plan to what? 
Plan to win the election! Why do they want to "win the election? 
Well, because they care about winning.

Isn't that a strong preference?

Now, the trick with Range is that it does not allow, with three 
candidates, simultaneously, maximim preference between A and B *and* 
between B anc C. If you vote full strength in the AB pair, you vote 
minimal strength -- you abstain -- from the BC pair. And vice versa.

This is actually a bound that encourages relatively sincere voting! 
Basically, Range equates, between voters, the strength of their 
entire vote. Every voter's full vote is equivalent to every other 
voter's full vote.

> >>  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.

And Juho will continue to simply assert it again:

>In any election/example, if your competitors use non-exaggerated
>votes and you use fully exaggerated votes, you have higher chances of
>winning.

This is not necessarily true. What I've seen is that if you vote 
*accurately*, which can involve intermediate preferences, you may 
have the same expected outcome as the Approval style voter. 
Basically, the Approval style voter increases the power applied in 
one or more pairwise elections, but abstains fully from others. 
Depending on the probabilities of election, Approval style voting may 
*increase* expected utility, or decrease it.

In any case, Juho hasn't presented a *shred* of evidence to support 
the claim. I have to conclude that he doesn't have any evidence. 
Perhaps he can remedy this.

What critics do is to take a particular election scenario where an 
Approval style voter gets a better outcome, from his point of view, 
by voting Approval, and then claim that this is typical. It isn't. 
You can get burned by voting Approval style, if it distorts your 
utilities. If you really want A to win and you don't care about B and 
C, they are both pretty much the same to you, then, *of course*, you 
will vote A 100 and B and C zero. But what if you have these 
normalized utilities: A 10, B 6, C 0. How should you vote for maximized effect?

Mean-based Approval suggests voting 100 for A and B and zero for C. I 
have not studied the exact performance of Approval vs. Range in this 
scenario, what I studied was Range 2, with utilities of 2, 1, 0. In 
this situation, the accurate vote and the Approval vote (both of 
them, in large elections) had *exactly* the same expected return.

There is no substance to what Juho is claiming. (The question of 
optimal voting strategy in Range is a complex one. Mean-based 
Approval is a good strategy, but so is accurate expression of 
utilities, and, based on what I've seen, is less likely to result in 
voter remorse. Vote zero for Gore because you love Nader, and you 
might later be kicking yourself. Unless you *really* did believe that 
Gore was worthless, just the same as Bush.

>Term "worse" refers to the Range promoters' use of the term when
>explaining why Range is better than other methods.

What is rather offensive about this is that "Range promoters," most 
notably Warren Smith, *became* Range promoters because they did the 
studies of utility.

What has been studied is average outcome, generally. We know that if 
all voters vote absolute utilities -- something that is theoretically 
possible under some circumstances -- Range does indeed *perfectly* 
optimize social utility. But nobody expects to see absolute utilities 
voted in public elections. Instead, we have an all-voters-are-equal 
assumption, and we expect voters to normally behave that way, they 
will behave as if they have *one* full vote and they will exercise 
it. They will not say, effectively, "Well, I'm here voting, but I 
really don't care that much, don't pay much attention to my vote."

Range *allows* them to do this, but it certainly does not encourage 
it. However, if voters did this when they sincerely believed it, it 
would actually improve outcomes.

What Juho and others like him are doing, though, is proposing a set 
of voters who vote weak votes, but then -- quite in contradiction -- 
they will be upset when their favorite doesn't win! Who is the 
"insincere" voter if they get upset when the system treats their votes as writ?

And if they don't get upset, then why is the outcome termed "a mess," or "bad"?

Absolutely, Range doesn't fully optimize social utility. There are a 
number of reasons, and in any given election, Range can fail to 
choose the true SU maximizer. This is utterly unsurprising! Range is 
a *voting method,* and its relative success, according to 
simulations, at SU maximizing is why Range promoters consider it a 
better method. It *usually* chooses the SU maximizer, and it does so 
more frequently than other methods. Approval is not quite as good.

And the simulations include mixtures of accurate and Approval-style voting.

Once again, Juho has simply passed over without comment a result from 
the exact study of Range 2 that I did. Changing the method from Range 
2 to Approval (Range 1) lowers the expectation for the Approval 
voter. If voters are allowed to vote 0,1,2, and there are three 
candidates with utilities of 2, 1, 0, to the voter, and the election 
is zero knowledge, the voter's expected outcome with a vote of 210 is 
40% over not voting. (This is a *relative* increase, not an absolute 
one; the absolute increase from voting is very low; but voters can 
assume that if they think a certain way, so will others, so we can 
multiply our own choices by the power of many making the same 
choices.... this is an argument for voting. Pure game theory says it 
is not worth it.). The expected utility increase for voting 220 is 
very slightly below 40%, approaching it as the number of voters 
increases. And the expected utility increase for voting 200 is very 
slightly above 40%, approaching it as the number of voters increases. 
In a large election, there is no practical difference between the 
utilities for the accurate vote and the Approval vote, of either flavor.

However, if we restrict the election to Approval with the same 
initial utilities, the expected utility increase for the voter is 33% 
(with either vote).

Changing the election from Range 2 to Approval lowered the voter's 
expected return from voting. Isn't that interesting?

(This result and its implications have not been confirmed by anyone. 
I must say that I don't understand it myself. But it is clear, the 
math was pretty simple. What has not been studied is the relationship 
between the expected utility of the vote given the assumption that 
the vote is not moot, and the risk that the vote is moot. )

>  Easy to define as
>sum of or average utilities but also other formulations are ok with me.

Haven't seen any, so this is moot.

> >>  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.
>
>I didn't assume anything on how much the voters want to win.

*But this is what drives preference strength*!

>  I
>assumed only that some voted strategically and some gave their
>sincere opinion.

And you assumed that the so-called "strategic" vote was insincere, 
and that the sincere votes were not min/max.

>  It is possible to rate a candidate at 100 but not
>care too much about who wins.

Yes. However, where preference is weak, over large numbers of voters, 
Approval style voting averages out. Where it is strong, it remains expressed.

In any case, what is "bad" about this scenario?


> > Let me point out, first of all, that the R2 supporters are clearly
> > not Republicans, period.
>
>They were intended to be strategic/exaggerating republicans whose
>sincere opinion could have been e.g. R2=100, R1=90, D=70.

Juho continually refuses to face the complications in asserting that 
this is their "sincere opinion." These are not normalized utilities, 
on what basis are they made commensurable?

Suppose that I set 100 at "the best candidate in the election." Fine. 
Where do I set zero? Genghis Khan?

There are several possibilities. Setting the max as I did is 
half-normalization. I can set the min at the absolute worst possible, 
in which case the D=70 might be a poor opinion of D. Or I can set it 
at the worst in the candidate set, in which case the 70 could be a 
fairly good opinion. But what we actually expect is for most people 
to vote as they have been voting for a long time in public elections: 
they neglect candidates that they don't think can win. Range then 
gives them a choice, but they don't set their utility scale 
considering those moot candidates. So on what basis does Juho assume 
utilities as he did. Why is the worst candidate in the set a "70"?

He is postulating circumstances that are unreal.

When the simulations are done, utilities are generated according to 
certain random distributions. You might find a voter with absolute 
utilities that are as stated (100,90,70). However, these are not yet 
Range Votes. And, remember, people don't carry these numbers around 
in their head. Rather, they have preferences. We are *simulating* the 
preferences with utility numbers.

Suppose this is a Plurality election. How would the voter vote? A 
rather dumb simulation would assume that the voter would vote for the 
100. However, voters actually consider the election probabilities. 
Plurality restricts them from expressing simultaneous votes, so they 
will want to know who the frontrunners are, and then vote for their 
favorite from that set.

Why in the world would we suppose that they would do differently with 
Range? And if they do behave as they have been behaving for a long 
time, these supposedly bad scenarios won't happen. If I have 
utilities of 100, 90, 70, for a choice in my life, I make the choice 
quite simply. I give my full vote to the 100. If I'm interacting with 
someone else whom I trust -- or have decided to act as if I trust -- 
I may express absolute utilities. "I really like all three of these, 
though my favorite is the first, the last is about 70% as good, and 
the middle one is almost as good as the first. How do you feel?" And 
we will work it out.

If it is a more distant relationship, and the goal is for each of us 
to consider our full range of preference equal -- which is a basic 
assumption in general public elections -- then I would normalize. And 
I described the normalization. And people would very naturally do this.

A major contradiction in Juho's argument is that he assumes that 
voters would vote a weak vote in Range but that they would accurately 
predict which form of Approval vote would serve them best, and they 
would not vote a weak vote in Approval. But if you have three 
candidates, you *must* vote a maximally weak vote in Approval, for at 
least one pair of candidates.



> > Now, is R2 a "no-good" outcome? Why would Juho claim so?
>
>R2 represented the smaller segment of the Republican party. It won
>because its supporters exaggerated.

How do we know that they "exaggerated." You posited it. But who did this harm?

Why is it "bad" that the smaller segment of the Republican party 
wins? Assuming that it is bad is simply assuming the supremacy of 
"plurality rule." It's circular.

I looked very carefully at the scenario given. It looks to me like 
the outcome was satisfactory to all the voters. Why is this "bad"?

If the Ds considered R2 a poor choice, why did they rate him at 70? 
*That is a high rating.* I have rarely seen such a good candidate win!

And the R1 supporters have an even higher opinion of R2, the rating 
is almost perfect.

Please, explain why this is a "bad" outcome. Who would be a better winner?

> > What is "sincere opinion based Range"? How are votes defined in it?
>
>For the purposes of these examples: "votes that use all values
>instead of focusing in use of min and max".

But there is no assumption that the use of "all values" is superior 
to the use of min and max. What we assert is that it is superior *if 
voters have the choice.* There is no assumption that min and max are 
less sincere. Lots of people get that idea, true, but it is based on 
a shallow understanding of the process by which Range votes would be 
determined from some presumed internal scale.


> >> 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?
>
>Yes, at least "summing up the voter utilities to a society utility"
>and some other normalisation schemes.

You have mistaken a discussion of the social effect of Range for a 
discussion of how to vote. The former is a piece of the latter, in a 
sense. Knowing that outcomes improve *overall* if I vote accurately, 
even though I might be giving up something small, motivates me to 
vote accurately. Further, voting accurately frees me of the burden of 
serious consideration of election probabilities; it's quite enough 
that I have an idea of the two or three frontrunners.

Where there are three frontrunners, it is quite a good strategy to 
vote accurate utilities for the candidates, normalizing to the best 
and worst. However, if the range resolution does not allow good 
accuracy (suppose my utilities were, absolute, 5,4,2, and the method 
was Range 2, my optimal vote would indeed be 220), then it is also 
quite a good strategy to vote Approval style, mean-based Approval.

Elections are a method whereby we entrust social decisions to voters. 
The votes are *actions*, and it is an error to place much emphasis on 
"sincerity." "Sincerity" in voting can be so foolish as to be a 
crime. Our votes have effects, and, as with any action, we must 
consider the effects, and what is good in an action is what is good in effect.

"But I voted for my favorite in 2000, don't blame me for those 
hundreds of thousands of deaths! I voted sincerely, isn't that what I 
was supposed to do?"

No. A vote is an action, it is not a sentiment. If I said to you, "If 
you like ice cream, drop this rock from the rooftop," and you liked 
ice cream, and you dropped the rock, would this excuse you from the 
consequences of dropping the rock, perhaps it fell on someone's head?