[EM] replies to Lomax re voting strategically and DH3 pathology that results

[Abd ulRahman Lomax]

At 03:13 PM 10/23/2005, Warren Smith wrote:
>Here is the Lomax quote:
>
>By the way, wouldn't Range have produced similar results with similar
>selfish exaggeration?

Conscious strategic voting with ranked Condorcet ballots depends on a 
belief that Condorcet cycles can be created or broken through 
insincere voting. I find it unlikely that such a belief would be 
common enough to seriously affect elections. Without that belief, 
there would be no motive to insincerely rank an undesired candidate 
above an acceptable one.

DH3 is a fantasy that Mr. Smith believes is a proven fact, based on a 
single personal experience with a Borda election under bizarre 
circumstances (as he relates on one of his web pages), and another 
Borda situation where a dark horse was "almost elected."

If a method requires ranking of all candidates, however, DH3 is a 
real possibility, I would think, particularly where there are only a 
few significant candidates, if voters are required to (or, perhaps, 
are given an opportunity to) rank all candidates. This is because 
supporters of one major candidate may artificially reduce the ranking 
of another major candidate out of partisan fervor, which is quite a 
distinct phenomenon from what we normally think of as strategic voting.

The more I think about it, the more I'm convinced that Range is 
vulnerable to this second kind of "insincere voting." The word 
"insincere" is problematic, because such voters might be "sincere" in 
their rankings, but what I mean by it is that, if faced with real 
pairwise elections, they would vote differently than their rankings 
in the full election would indicate.

The Range equivalent of this would be for a leading candidate voter 
to vote 0 for another leading candidate, and then a more realistic 
rating for a dark horse. If enough major candidate voters do that, 
the dark horse could win.


> >  also point out that another example was the world's only Borda
> > government (Kiribati)
> >where again such phenomena were immediately observed.
>
>Borda is particularly vulnerable to this problem, but I would think
>Range would be as well. But what do I know? Not much....
>
> >--As far as "horribly common" by that I meant (as I described on 
> the DH3 page
> >    http://math.temple.edu/~wds/crv/DH3.html )
> >that DH3 occurs whenever there are 3 comparable rival good
> >candidates and a bad one.
>
>The theory here is that voters will rank the bad candidate higher
>than the rival good candidates. And the bad outcomes seen are proof
>that the strategy sucks.
>
>What is needed in a democracy is for voters to *trust* democratic
>process by voting sincerely. If enough voters try to distort the
>system by strategic voting, in order to gain a very short-sighted,
>narrow, and immediate purpose, any system which depends on sincere
>ratings or rankings is going to be in trouble.
>
>[end of Lomax quote]
>
>OK, first of all, NO, range would NOT
>have produced similar results with similar
>selfish exaggeration, and is immune to DH3.

Where is the proof of this?

Consider this election, classic DH3:

fully considered and sincere votes:
30: A>B>C>D
33: B>A>C>D
37: C>A>B>D

pairwise:
A:B 67:33
A:C 63:37
A:D 100:0
A is the Condorcet winner.

However, because of the kind of strategic thinking that Warren 
describes, they actually vote:

30: A>D>B>C
33: B>D>A>C
37: C>D>A>B

pairwise:
A:B 67:33
A:C 63:37
A:D 30:67
B:C 63:37
B:D 33:67
C:D 37:63

D is the Condorcet winner.

Now, is Range subject to this effect? Let's suppose that the same 
groups of voters are faced with a Range election. Sincere votes 
(rankings followed by range numbers chosen to produce those rankings):
                 A       B       C       D
30: A>B>C>D     9       7       5       ?
33: B>A>C>D     7       9       5       ?
37: C>A>B>D     7       5       9       ?
totals          23      21      19      0
Range winner: A

(I'm assuming that none of these voters have even heard of D, which 
is, of course, unrealistic, but the phenomenon is demonstrated. This 
does raise the question of how blanks should be counted.... here, I 
assume that D was left blank and that this was counted as zero. Any 
better ideas?)

But because each set of voters thinks that the other major candidate 
voters will vote insincerely and so votes insincerely themselves, or 
simply because of strong rivalry between the major candidates, whose 
devoted adherents tend to think that a major opponent is the devil 
incarnate, and we get this:

                 A       B       C       D
30: A>B>C>D     9       0       0       4
33: B>A>C>D     0       9       0       4
37: C>A>B>D     0       0       9       4
totals          9       9       9       12
Range winner: D

>YES, you do not know much.

True. Difference between me and Warren: I know that I don't know much.

This allows me to ask stupid questions, which, occasionally, turn out 
to not be stupid. Everyone benefits from such....

This reminds me of a conversation I once had with a certain adherent 
of an obscure 
sect-that-thinks-of-itself-as-not-a-sect-but-as-the-repository-of-truth. 
The man was a successful businessman and quite bright. I said 
something to him which he was quite certain was wrong (about 
variations in the text of the Qur'an, he thought there were none, 
which is common wisdom, and incorrect). He said "I do not put up with 
fools." I said, "That's the difference between you and me."

It speaks well for this man that he laughed, and then he was actually 
able to listen and learn.

>Actually, even thinking 1 minute would not be required,
>since it already explained exactly why range is immune to DH3, right 
>on the DH3
>web page that you were responding to in  this webpost.

Actually, I was not responding to that page in that post. I couldn't 
find the URL. Which is why I put my thoughts about Range in the form 
of a question.

However, had I actually looked at the page, as I did do now, I would 
have been much more certain about the vulnerability of Range to this 
kind of voting.

The fallacy in Warren's theoretical situation is that the A, B, and C 
voters would downrate D as well. But they don't know D, so they give 
him a low grade. Not a zero.

None of this is terribly likely. Warren's claim that DH3 is common 
seems to be singularly devoid of evidence, as mentioned above. *No* 
examples of a dark horse winner created by DH3 in a public election 
has been shown, and as to other elections, only one idiosyncratic 
private poll demonstrated the phenomenon. Warren thinks. Actually, I 
would wonder that he knew the inner thinking of so many of his 
coworkers. But even if he did, that's one example out of the very 
large number of elections which take place in the world.

>Second of all, your final paragraph is rather reminsiscent of Borda's remark
>sometime around 1790.  Borda was being attacked by those who
>were pointing out the bad reaction of Borda Voting to strategy.  He responded,
>presumably with a similar air of autraged contempt:
>"My system is designed for _honest_ men."

As is Range.

Once again, we see Mr. Smith as the mindreader: so good is he at 
reading minds, that he can derive an "air of outraged contempt" from 
those few and fairly accurate words. Borda is designed for sincere voting.

>However, the subsequent 215 years have indicated that Borda was wrongheaded
>and strategic voting is common.

Actually, what has been demonstrated is that dishonesty is common. 
People will lie in order to get what they want. And insincere 
rankings in elections are a kind of lie. So, as I said, if enough 
people lie, they get what they deserve. The sad thing is that they 
can drag everyone else along with them.

>   For example, studies indicated that of those who
>felt Nader was best in 2000, something like 1 in 10 or fewer voted for him,
>as opposed to somebody else.  Similarly for Buchanan.  So, amazingly enough,
>it appears that 90% of voters still have not yet reached Lomax's 
>high state of wisdom
>that they should be sincere instead of shortsighted and strategic.

Ah! Got me with that one!

Plurality is not ranking or rating, it is purely a political act. The 
ballot does not ask "Vote for your Favorite." It simply says, "Vote 
for one." And such a vote has consequences, and voters are 
responsible for understanding the consequences of their votes.

>   They all
>seem to want to greedily advance their own agenda's chances

"Greedily" would not be my word. "Shortsighted" would be more like 
what I would say, except that it is quite incorrect to ascribe this 
to "all." What percentage would see beyond personal desire? I'm not 
sure. But the present system is not conducive to sincere voting, that 
is clear. Asset Voting would be a very quick and simple fix. 
(Politically very difficult at this time, so it is only "simple" conceptually.)

>instead of recognizing that if everybody just
>voted sincerely that'd be better for all society (which it would).

In other words, Warren knows that sincere voting is better for 
society, but he expects voters to be massively insincere in a DH3 
Condorcet election. Obviously, they have not reached his state of 
enlightenment.

>And gee, this has just kept happening for 200 years.

 From my point of view, we have only the most primitive form of 
democracy. In the U.S., we still vote in pretty much the same way as 
we voted 200 years ago.

>So sooner or later, I am hoping that Lomax's understanding of democracy
>will advance to the year 1790 and he will recognize that voting systems
>should be designed not to degrade dramatically
>when confronted by strategic voters.

Asset systems and proxy systems do not reward strategic voting. Range 
does. Smoke that, Mr. Smith!

>   (DH3 being an example
>of dramatic degradation:  the DH3 web page is
>http://math.temple.edu/~wds/crv/DH3.html .)
>
>Fortunately, range voting may be regarded as having been designed 
>with that in mind.

Dream on. Regarded by whom?

>In fact, there is a theorem, which admittedly I wrote up somewhat 
>clumsily (but it
>is valid) in my 2000 RV paper, which basically characterizes range voting as
>the unique "compact additive fair" voting system in which voters can be
>maximally expressive without being strategically stupid.

But if they exaggerate? We can assume that voters would rank their 
favorite with the top rating. This is actually the correct sincere 
vote in Range, since ratings are relative in effect, not absolute. 
But if they rate others lower than their sincere rating, in order to 
increase the possibility of their favorite winning, they risk exactly 
what sincere voters voting for a third party candidate currently risk.

The DH3 scenario example Warren proposes is nothing but a plurality 
contest. He has all voters rank their favorite as 99 and everyone 
else as 0. (This is the same election as I showed above, but he makes 
different assumptions about how the voters would vote). Thus C wins.

*Because C is the plurality winner.* Warren has just reproduced, in 
Range, exactly the result that plurality would produce. Each 
candidate would be rated, relatively, with the percentage of their 
vote. Yet most of us have come to think that, in such an election, A 
should be the winner, because A will win in a pairwise contest with C 
(and with the other candidates also). Please, Mr. Smith, tell me why 
C is the best winner of that election? To quote Warren's comment 
about this election, from the web page:

>In contrast, with range voting the A voters will exaggerate thus: 
>A=99, B=C=D=0, and if everybody acts that way, then C will 
>(deservedly) be elected. C also wins with IRV and plurality. This is 
>an example of the fact that range voting is designed to exhibit only 
>a mild degradation in reaction to dishonestly-exaggerated "strategic 
>voting." With Condorcet and Borda, the allergic reaction is not 
>mild: it is "anaphylactic shock."

The shock condition occurs if everyone votes insincerely. One thing 
that Mr. Smith has overlooked is that many voters (perhaps most) are 
not seriously dedicated to a party or candidate. These voters will 
vote sincerely, probably. They think of themselves as "independent," 
even if, sometimes, they are registered in a party. And getting even 
the adherents of a major party to vote insincerely in large numbers 
as Mr. Smith describes would be a major undertaking, probably quite impossible.

I don't think strategic voting is nearly as large a problem as it is 
often made to be by election methods fans, beyond the obvious 
strategy in plurality of voting for your favorite among the 
front-runners. The problem with plurality, that a sincere vote is 
essentially punished by depriving the voter of a say in the election 
of the winner (with respect to the top two), is much more severe.

The claim that voters would massively be *forced* to betray their 
favorites in Condorcet elections is probably false. It takes special 
conditions to even make it possible for Favorite Betrayal to have a 
positive effect from the point of view of the voter. And the risks 
are substantial (such as DH3, though I think that scenario is 
unlikely as described). I don't think voters would go for it, even in 
the rare situations where it might be possible.