[Election-Methods] Two replies

[Abd ul-Rahman Lomax]

At 12:58 AM 8/11/2007, Juho wrote:
>I don't want to define/redefine "strategic". The technical properties
>of the votes are enough.

Two opposite statements made in the same two-sentence paragraph. Juho 
has redefined "strategic." Strategic votes have never been defined 
from the vote alone. Rather, a "strategic vote" has referred, in 
ranked methods, to a vote where the voter reverses a preference in 
order to gain some advantage. Another term used is "forced 
strategic," where the voter, again, reverses a preference because to 
express the true preference would cause a poor outcome, sometimes 
even worse than not voting at all.

The extension of "strategic" to include votes which involve 
expressing an equal rating for candidates when the voter actually has 
a preference is, in my view, properly controversial. Few have called 
equal voting in Approval "strategic," nor does anyone call the 
bottom-equal voting for all candidates but one in Plurality 
"strategic." (But top rating other than the favorite in Plurality is 
a preference reversal, and certainly is strategic.)

However, until now, *nobody* has claimed that a vote is "strategic" 
because of its form, regardless of intention or the true preferences 
of the voter. Juho is claiming that voting max and min in Range is, 
ipso facto, "strategic." He has not even qualified the statement to 
make it clear if this covers *any* use of min and max, though I think 
he did say that a strategic vote was one which did not use 
intermediate ratings.

So, suppose a voter, in a three candidate election, votes A max, B 
min, and leaves C blank. Is this "strategic?" What if the election is 
default zero (i.e., it is sum of votes Range) and the voter only 
marks A max? Is this "strategic."

Note that if a voter does not vote min and max for at least one 
candidate each, in Range, the voter is weakening the vote. Juho's 
arguments about the alleged harm of "strategic voting" all included a 
so-called "sincere" voter who did not vote the extremes, and then, 
because the outcome went as voted by those who *did* use the extremes 
-- something we expect to be the norm, particularly for frontrunners 
in a 2-party system, allegedly there was a "bad" outcome.

>I wrote:
> >> Range could ignore also a clear majority
> >> opinion.
>
>I should have written "a clear majority and utility opinion as a
>result of strategic voting".

There is no meaning to "a clear utility opinion," that I know of. We 
only know opinions two ways: expressed and simulated. Expressed 
opinions are how people actually vote. In simulations, we assume some 
internal preference rating scale, but this has never been called a 
"utility opinion."

No election method can use data which is not expressed on the 
ballots. Range *allows* voters to express finer gradations of 
preference. If voters don't use them, the method cannot satisfy the 
voters as efficiently. Further, if voters translate their preferences 
to Range votes in a totally silly way, which is what Juho proposes 
some will do, a way that conceals the true strength of their 
preferences in context, the method likewise cannot fully take them 
into account.

Juho proposes one set of voters who, quite intelligently, translate 
their internal preferences to Range Votes that include the endpoints; 
another translates them in a way that doesn't use the full Range. 
Range, of course, gives more weight to those who express the full range.

Range N is quite like having N votes to cast, in an Approval 
election. If you don't cast N votes, but, say, N/2 votes, it is quite 
like a half-abstention. And if you and those like you abstain, how 
can we call a result which does not fully consider your defectively 
expressed opinion "bad."

When I first started working with Range, I suggested that votes might 
be normalized. That is, one would take the range of values used by 
the voter and expand them, if necessary, so that the voter was 
casting one vote.

However, deeper reflection led me to the conclusion that this was a 
complication of counting that was unnecessary. It's highly unlikely 
that significant numbers of voters would fail to use the full range, 
except as a protest. And if voters want to protest, why not let them! 
Why modify their votes to what *we* think they should be!

Juho *could* have focused on the use of intermediate votes *in 
addition* to the use of extreme votes. But he did not. His examples 
of "bad" outcomes involved an election, for example, where the Dems 
voted 100 for the D, 80 for R1, and 70 for R2. What we have is all 
the Ds casting 0.3 vote each! Then come the Republicans supporting 
R1, and 30% of them also vote in this crazy way, 100 for R1, 90 for 
R2, and 70 for D.

Finally, the supporters of R2 vote Approval style, 100 for R2 and 0 
for R1 and D.

Now, in a real election, this voting pattern is extremely unlikely. 
Because 50% of the electorate, it was proposed, is D, the Republicans 
would know that if they split their vote, the D is likely to win. 
Only the utter insanity of the way in which all the Ds are supposed 
to have voted is what makes a Republican win.

We have noted that if all voters vote sincere absolute utilities, 
Range maximizes social utility. *However*, it is rare that voters 
would even know what their "sincere absolute utilities" were. 
*Nobody* is recommending that voters vote other than the full Range.

And what we expect to see, in the implementation of Range, is quite 
possibly gradual. That is, we start with Approval.

Now, if Approval voters voted the crazy way that Juho is proposing 
Range voters may vote, The Ds might approve all candidates. Thus 
totally abstaining from the election....

No, one might say, they would set an approval cutoff above R2, at 
least, maybe above R1. Mean-based approval would suggest that they 
Approve only D. (And, by the way, that the Rs vote to approve both 
Rs, and in this context, the danger to the R2 supporters of voting 
the strategy they voted, if it was a strategy and not sincere, would 
be apparent. They would throw the election to the Ds by refusing to 
also approve the other Republican. The same thing would happen in 
Range, quite likely.

> > >  One could e.g. translate utility values 1
> > >A=90, B=80 and 1 B=90, A=70 to actual votes 1 A=100, B=0 and 1 B=90,
> > >A=70.
> >
> > So this is two voters. Thus it is 50-50 as far as first preference
> > is concerned. (And we can imagine that this is two whole sets of
> > voters voting identically.) Fine. If I'm correct, Juho is asserting
> > that, if the votes are translated as stated, the outcome is "bad."
> >
> > Yet what method is going to do better than Range in this example?
>
>Range changes the winner depending on the level of strategic voting.
>Most other methods would give a tie.

Juho is inventing new language, and quite misleading language. The 
true statement is that Range can change the winner according to the 
expression of preference strength. Juho calls the expression of 
strong preference "strategic," though this is totally outside normal 
usage of the term.

If we are talking about what to do, and you say that you *strongly* 
prefer A over B, and I say that I have only a small preference for B 
over A, what is our likely conclusion, assuming that there is no 
third choice C?

Most people would have no trouble with considering A the better 
choice. Only if time after time, a person expressed strong 
preference, and the other began to suspect that it was exaggerated, 
or simply got tired of never getting his or her first preference ... 
what would happen?

Naturally, the preference of the second person would increase. This 
is not "strategic voting" in response, it is a natural reaction to 
balance out a series of small losses. (or, more accurately, smaller 
gains than preferred).

But if I knew that the strong preference of a person was soundly 
based, I would not start to discount it simply because I was 
continually not getting my first choice. However, I'd presumably be 
careful to fully and accurately express my own preferences in such a 
way that the comparison of mine with the other person was fair.

We expect most people to start out voting Range quite as if it were 
Approval. It's what they are accustomed to. But there are two very 
important exceptions, and Juho seems strangely uninterested in them.

Supporters of third parties would have a choice. Let's assume that 
it's Range 2, the lowest resolution Range that isn't Approval. They 
could equal-rate their favorite and the preferred frontrunner, quite 
as they would probably do in Approval, or they could give the 
frontrunner a half-vote. If they do the latter, they are possibly 
wasting a half-vote. However, there could be reasons they would want 
to do this. Perhaps the frontrunner they prefer snubbed them, so this 
is a protest, but not as drastic as not voting for this person at all.

On the other hand, suppose that the preferred frontrunner is truly, 
to them, almost as bad as the other one. The half-vote is actually 
quite a good vote, in some ways better than the Approval style vote 
of 110. If there is *any* chance that the third party candidate might win.

>-------------------------
>
>On Aug 11, 2007, at 5:50 , Abd ul-Rahman Lomax wrote:
>
> >> >         D       R1      R2
> >> > 50:     100     80      70
> >> > 30:     70      100     90
> >> > 20:     0       0       100
> >> >         ---------------------
> >> >         7100    7000    8200
>
> > In any case, what is "bad" about this scenario?
>
>The success of the strategic voters.

Why is it bad for someone to be successful?

These voters are voting as they are allowed, and to some degree 
encouraged, by the system. If the other voters had voted in a sane 
way, the R2 vote actually would have been a serious loss for them; 
but they lucked out.

The D and R1 voters indicated strong support for R2! So why should 
the method not choose R2?

Now, the way the R2 voters voted was not merely "Approval style." 
Approval style voting would have had them vote  D:0, R1:100, R2:100. 
That's mean-based approval. Now, suppose that this is an Approval 
election. If the Ds and the R1 supporters vote mean-based Approval, 
and we assume that the D and R1 votes above were "sincere, but not 
fully normalized, utilities," we get 50 votes for D, and then, if the 
R2s vote "sincere, mean-based Approval, 30 + 20 votes for R1 and R2. 
A three-way tie.

However, we have postulated that the R2s are betraying their second 
favorite. So they vote as described before, and it is a two-way tie 
between D and R2. And the R1 supporters are quite upset with them.... 
As they would be in the Range election described.

This has little to do with election method. In Approval, the R2 
strategy defeats R1 without defeating the D. In Range, the Ds voting 
sensibly -- even a relative few of them, which I mentioned and Juho 
dismissed -- would have cause the D to win, and the betrayal vote of 
the R2 supporters would have been the cause.

This scenario does not show bad behavior of Range.

> >> They were intended to be strategic/exaggerating republicans whose
> >> sincere opinion could have been e.g. R2=100, R1=90, D=70.

> > These are not normalized utilities, on what basis are they made
> > commensurable?
>
>The problems rose from some voters normalizing or exaggerating and
>some not.

Of course. What would you think if voters voted A=2, B=1, C=0. In Range 100?

Range allows you to vote fractional votes. If you decide to only cast 
a fractional vote, can you blame the system for only giving you 
fractional power?

Different issues get mixed. It is conceivable that some voter could 
be confused by the system, especially if high resulution Range were 
implemented and poorly explained. As I've noted, if the ballot asks 
you to "rate" candidates, it might encourage a misunderstanding, 
unless it is made clear that if one does not use the full range in 
the election, at least one candidate max and one min, the vote is 
weakened. And that is probably a more complicated explanation than 
should be on the ballot, so I would simply describe Range N as 
casting 0-N votes for each candidate, with the election going to the 
candidate with the most votes.

Practically speaking, we should see Approval first, so voters would 
be accustomed to the idea that you can vote full strength for more 
than one candidate.... And intermediate votes would probably be 
introduced gradually, perhaps starting with Range 2 or 3.


> > 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.
>
>Any reasons and votes that give other than min and max values will do.

Do for what? What Juho is saying that if voters vote weak votes, they 
have a weak effect. Yes, they do. Is this a criticism of Range?

If I vote 70 for a candidate, as these Ds did for the *worst* R, R2, 
from their point of view, they are saying that R2 is quite a good 
candidate! If they would be upset that R2 is elected -- isn't that 
what a "bad outcome" would mean? -- then why did they vote such a high vote?

Juho has asserted that these are sincere utilities, but he has 
totally avoided the question of what they mean. What *kind* of 
sincere utilities? How was the scale set? Does 70% mean "acceptably 
good," as I would normally assume in 0-100 Range -- it's been 
proposed, sometimes, that 50% be made explicit as an Approval cutoff, 
and that is what is done in mean-based Approval, essentially. (The 
ratings are normalized to the candidate set, then one approves any 
candidate above 50%.)

> > 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.
>
>I don't want to claim anything about Approval or Approval like
>strategies.

He's made a claim about an "Approval-like strategy." That it leads to 
a "bad" result. He is not explicit about what he is comparing the 
method with. Bad compared to what? Or just *absolutely* bad?


> > If the Ds considered R2 a poor choice, why did they rate him at 70?
> > *That is a high rating.*
>
>They didn't consider R2 to be a poor choice (although R2 was to them
>the worst choice).

That's right. They considered him a good choice, apparently. So, in 
the face of that, why shouldn't R2 be elected? The Ds consider him a 
good choice, the R1s consider him a better choice, and the R2s 
*really* want him.

(That they have "sincere" utilities of 100, 90, 70 is actually 
inconsistent with their vote of 100, 0, 0. Now, if the supporters of 
R2 are going to show "exaggeration," why don't the supporters of R1 
and the Ds? Somehow, this particular kind of "sincerity" -- I'd call 
it pure foolishness, *unless* this really is a consensus election, 
and the Ds and R1s will really be happy with the outcome -- is 
confined to R1 and D supporters.)


> > Who would be a better winner?
>
>R1 and D based on social utilities (and according to the choices of
>many methods).

First of all, election methods don't define what is a good winner. 
There really is only one standard that has been proposed that makes 
any sense, and that is S.U., or perhaps a little more clearly, 
expected voter satisfaction.

Juho did not provide us a basis for concluding that R1 and D are 
better winners. To conclude that, we would have to know how to 
compare the utilities of the D, R1, and R2 winners. The utilities he 
stated are "half-normalized." That's odd. In order to compare and sum 
S.U., the ranges of utilities need to be tied to each other in some 
way, so that they are commensurable, so that summing them has meaning.

I discussed this at some length, but it seems it sailed past Juho.

Then, we know that Range does not always maximize S.U., there are 
better methods than simple Range. For example, Range+2 (Range with 
top-two runoff) does a better job. Why does Range not always maximize 
SU? There are a number of reasons, and one of them is that voters 
won't vote accurate utilities. There are two reasons for this; the 
first is normalization to the candidate set, which causes weak 
preferences to be equated with strong ones, in some cases, and the 
second is inaccurate voting, most particularly, what Juho calls 
"exaggerated voting."

So it is utterly unsurprising that you can construct a scenario where 
some pattern of voting by voters causes Range to not elect the SU 
winner; in this case, the R2 supporters, by understating their "real 
feelings" about D and R1, elect R2. However, the way in which they 
are shown as having voted would be highly risky in the real world. It 
is utterly unsurprising that they would vote 0 for the Democrat. This 
is what we would have expected for the R1 supporters, also, and for 
the Ds we'd have expected the reverse. What is unusual -- and quite 
dangerous for them -- is that they voted, in a tight election, 0 for 
R1. They violated standard Approval strategy to do this. There is a 
reason for that strategy! Only bizarre behavior on the part of the D 
and R1 supporters caused them to prevail.

No method can maximize SU if the voters conceal it! However, the 
question is really, "Who is harmed by concealing it?" In this case, 
in a normal election, it would have been the R2 voters who would have 
been most harmed by concealing their support for R1. And, as it was, 
the Ds and R1s -- if we accept Juho's assertion that the outcome was 
"bad," *also* concealed their preferences.

No election has had a "bad" outcome if all the voters consider it a 
good one! And Juho ackowledged above that the Ds considered R2 "not a 
poor choice."

Not a poor choice is, quite simply, not a "bad" choice. Juho has 
contradicted himself, in more than one way.