[Election-Methods] Two replies

[Abd ul-Rahman Lomax]

At 03:41 AM 8/12/2007, Juho wrote:
>On Aug 12, 2007, at 6:40 , Abd ul-Rahman Lomax wrote:
> > 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.
>
>I'm ok with any stable definition.

The standard definition seems to be [wikipedia]:
>In <http://en.wikipedia.org/wiki/Voting_system>voting systems, 
>tactical voting (or strategic voting) occurs when a voter supports a 
>candidate other than his or her sincere preference in order to 
>prevent an undesirable outcome.

However, "strategic voting" was used prior to the consideration of 
Range methods. In the context of ranked methods, from Plurality on 
up, "strategic voting" involves a preference reversal. The literal 
meaning of the above definition would actually require calling an IRV 
vote of A>B>C "strategic voting" because expressing the B>C 
preference "supports" candidate B -- only partially. The article goes on:

>It has been shown by the 
><http://en.wikipedia.org/wiki/Gibbard-Satterthwaite_theorem>Gibbard-Satterthwaite 
>theorem that any voting method which is completely strategy-free 
>must be either dictatorial or nondeterministic (that is, might not 
>select the same outcome every time it is applied to the same set of 
>voter preferences).

The theorem mentioned appears to study only ranked methods.

If we assume that we have "strategic voting" whenever a voter votes 
equality for two or more candidates, no matter how small the 
preference, we end up with a totally useless term, because the most 
trivial preference, transient, below the level of preference noise, 
would be called a "strategic vote." Rather, for the term to be 
useful, there must be some threshhold of preference, below which 
voting equality is simply "sincere," not "strategic."

We get some help from the common opposition: sincere and strategic. 
If the opposite of sincere is strategic, i.e., strategic means 
"non-sincere" (with the additional condition that it is done to gain 
some tactical advantage), then we know that any vote that is not 
sincer, done for the purpose of improving election outcome, is "strategic."

Is it "sincere" vote equality when you have some preference? Well, it 
could be. But first, note something. Suppose we are voting Approval. 
I approve my favorite only. Am I voting "strategically?" Indeed, with 
any ranked method, suppose I rank all candidates but two, with 
sincere rankings. Is this a "strategic vote" if I do, in fact have 
some preference among those I did not approve or rank?

Most would not consider it that. I conclude that the best definition 
of "strategic voting," one that does not lead to uselessness of the 
term, is that it involves expressing a preference reversal. In 
Approval, for example, if one prefers one candidate to another, but 
Approves the other and not the preferred, and this were done for 
strategic purpose, it could be called "strategic voting." But 
Approval does not reward that behavior, the "strategic purpose" must 
be other than determining the winner.

In Range Voting -- and Approval is really the same -- we can assume 
that the voter has an internal ranking. Equal ranking is possible in 
this internal ranking, but would be relatively rare. However, the 
voter uses some algorithm to translate internal rankings to votes. In 
doing so, the voter, we can normally expect, will preserve rank 
order; however, the translation need not be linear, it need not 
preserve preference strengths.

Range N is equivalent to casting N votes in an Approval election. One 
may quite sincerely decide that it is offensive to cast *any* votes 
for Bush, for example. Even if Adolf Hitler is on the ballot. A 
Republican might think that way about Hillary Clinton, perhaps. Is 
this "strategic voting" if, forced to make a choice, the voter 
actually does have a preference? I don't think so. Yet it is equal 
ranking, at the bottom.

Similar arguments may apply to the top as well. I might think it 
offensive to insist on a preference when two candidates are really, 
in my view, both suitable for the office, and I know that others may 
not feel that way. Thus, with respect to all candidates other than 
these two, I express a full pairwise vote, and between the two, I 
abstain. This can be fully sincere.

Now, in the example Juho gave, we had some Republican voters who 
voted R2 100, R1 0, D 0, when they allegedly had sincere preferences 
of 100, 90, 70. Is this "strategic voting"?

What the voter has done would be considered a "sincere vote" in 
Plurality. In Approval, *it depends on the Approval cutoff*. But for 
a vote to be strategic, there are two aspects: preference reversal 
(or some obviously include preference equality), *and* strategic gain.

We assume, and indeed we encourage, voters to vote in order to 
influence the outcome toward what they want. Is an Approval vote by 
an R2 voter, as described, however, a 'preference reversal or 
equality,' for strategic gain. The voter voted sincere first 
preference. The alleged insincerity would be at the other end. On 
what basis is it considered "strategic"?

If we required mean-based Approval as the only sincere form, we could 
indeed claim the R2 vote is strategic. However, that's preposterous. 
The sincere utilities we were given of 100, 90, and 70, are 
half-normalized. What if non-normalized utilities (full scale) were 
50, 45, 35, and "50" in this internal scale means "barely 
acceptable." This would explain the Approval Vote, and it would be 
totally sincere.

(The voter normalized by multiplying all utilities by two to get the 
Range Vote. This is a normalization which ties the top vote to the 
max rating and leaves zero untouched. That's why it is called 
"half-normalization.")

A voter who votes as the R2 voters voted is using a certain kind of 
transformation to convert internal utilities to Range Votes. The 
error typically made by Range critics is to assume that the voter 
distorts their vote, for strategic purpose, when, suppposedly, they 
don't have a preference as strong as what they expressed.

But there must be a motive for them to do this. Why is this motive 
not *included* in the "sincere preferences?" For example, a voter, in 
some abstract sense, might rate D, R1, and R2, as 70, 90, 100, what 
was given as the "sincere" ratings for the R2 voters. However, the 
voter is married to R2, and *really* wants R2 to win, very strongly. 
Wait a minute! Wouldn't this be included in the ratings?

What is assumed is behavior unmotivated by preference, gaining some 
presumed advantage for the "strategic" voter. But if it is an 
"advantage," it *is* a preference.

I'm pointing out, as I have many times, that assuming low preference 
voted as strong preference is a contradiction. It's a defect in the 
preference model, not in the election method.

>Yes, the voting pattern in the example is exaggerated. Casting "weak"
>votes is possible in practically any set-up and they may influence
>the outcome in many.

Indeed it can.


> > Juho has asserted that these are sincere utilities, but he has
> > totally avoided the question of what they mean. What *kind* of
> > sincere utilities?
>
>I'm ok with any kind.

Apparently true. Juho is content with "sincere utilities" that make 
no sense at all, given the voter's behavior!

I've pointed out how the "sincere utilities" he posited could be such 
that the vote is entirely sincere. Yet he thinks he can judge whether 
or not a particular vote is "strategic" by looking only at the vote.

It's preposterous. It would be better for Juho if he simply admitted 
he backed himself into a corner. Nobody will hold it against him!


> > He is not explicit about what he is comparing the method with. Bad
> > compared to what? Or just *absolutely* bad?
>
>I compared use of weak and strong votes within Range.

No, why is the *result* bad? Who thinks it is bad? The D or R1 voters?

But, wait a minute! It's been acknowledged that R2 is considered a 
decent winner by the Ds, and the R1 voters presumably have an even 
higher opinion of R2.

> > 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.
>
>Your scenarios are ok to me. I accept any way of determining utilities.

But not any way of determining *votes* from utilities, apparently. By 
allowing himself to posit one set of utilities for the voters, and a 
radically different set of Range Votes, he can obviously manipulate 
the scenario so that it does not elect the "true" SU winner. However, 
it fails to do so for two combined reasons:

The R2 voters set an Approval cutoff above R1. And: The D and R1 
voters voted Range, which is not explicit as to Approval cutoff, but 
we might normally assume an Approval cutoff of 50%. Their votes were 
telling the method, "we accept any of these candidates, though we 
prefer them in this order."

So the method maximizes the expressed approval of the voters. The D 
and R1 voters, by their votes, partially abstained, which is their 
right. However, they are thereby telling the method that they don't 
care so much about who wins, thus deferring to those who *do* care.

Clearly, the R2 voters care! Their supposed "sincere" ratings are 
inconsistent with their votes.

By assuming something false, you can prove anything....

The point about so-called 'strategic voting' in Range is a very 
important one. This argument that Juho presented is quite common 
among Range critics. Quite a similar example is presented by Rob 
Richie of FairVote. It's an example where the supposed bad outcome is 
one where all voters, in fact, see a winner whom they rated as very, 
very good. What is supposedly bad is that a majority had a preference 
for someone else, and, allegedly, the strong vote of the minority was 
"insincere."

It is not only a contradiction, it further rests on the presumption 
that the Majority Criterion is pre-eminent.

But we know that majority preference, if it is weak, in ordinary 
human social interactions, is a poor standard for making decisions. 
Force simple majority preference, you can get armed insurrections. Or 
some friends who go hungry because they can't eat, at all, the pizza 
that the majority had a small preference for, when another choice was 
*quite* acceptable to every friend.

The *foundation* of the majority criterion is majority rule, which is 
quite another matter -- Richie conflates them explicitly, calling the 
Majority Criterion, "Majority Rule." But majority rule refers to the 
right of the majority to make a decision. It's well known that this 
decision is not clear when made as a multiple-choice question, so we 
only know "majority rule" when the majority explicitly votes for an outcome.

(If you say to the voters, Do you want A or B, and a majority of 
voters select B, is this "majority rule"? Maybe, but it has not been 
shown. What if the majority preferred "Neither"? You know you have 
majority consent if they express it explicitly, either by voting Yes 
or No to the question, "Shall A be elected," or, possibly, by 
expressing explicit Approval on a multiple-choice ballot. (Simple 
Approval, unless the instructions make it explicit, and there is no 
forcing of equal rating from election context, doesn't do this, but 
it could be made explicit, by any of various methods.)

> > 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.
>
>Yes, and R2 had the worst in S.U. in this example.

I'm suggesting that this is because the true utilities of the R2 
voters were not as stated. Juho avoided considering what kind of 
utilities these were, but it matters. The utilities of all voters 
were "half-normalized." Normalization loses utility information. If 
you want to know the true SU, you must know non-normalized utilities. 
Warren's simulations start by simulating utilities on a common scale, 
so the utilities can then be added to determine true SU. Juho avoided 
the whole issue, leaving him with no way of determining that his 
statement is true.

We know that Range Voting does not always optimize SU. But it does a 
better job than any other method, short of bybrids (which I propose 
as much better election methods than Range alone) and, I think, 
random voter, which is politically unacceptable; it produces the best 
*average* outcome, but has too wide a variation.

So a finding that in some situation Range Voting does not choose the 
SU winner is unsurprising. It can fail to do that; however, the 
conditions under which it fails are such, typically, that very little 
harm is done. The allegedly "bad outcome" for the Range election 
posited by Juho was actually, as he has acknowledged, a good outcome, 
just not "the best."

But even that conclusion is far from clear. It is quite true: if 
voters know how the other voters will vote, then the voter may, given 
the opportunity, vote to maximize personal utility. Range does not 
create this situation, it is true for ranked methods as well. The R2 
voters would be insane to vote as they voted, if the sincere 
utilities were actually as stated (according to certain assumptions 
about what they mean, which Juho never stated). The reason is that 
for their votes to be optimal, they would have to know that the other 
voters were going to vote weakly. And that situation, that most 
voters would vote weakly, is entirely out of what we expect in the 
near future. Or ever.