[EM] Intermediate RV rating is never optimal

[Abd ul-Rahman Lomax]

At 01:04 PM 7/22/2007, Chris Benham wrote:


>>The voter prefers A>B>C, with the preference strength between A and B
>>being the same as the strength between B and C.
>>
>>There is nothing here about Approval cutoff, there is nothing that
>>says that the voter does or does not "approve" of *any* candidate.
>
>I think we safely say that max-rating a candidate is equivalent to 
>"approving" that candidate.

The term "Approval" causes a great deal of misapprehension or even 
misrepresentation. Max-rating a candidate indicates, clearly, that 
*of the candidate set*, that candidate is most-preferred. It says 
nothing about the opinion of the voter toward the candidate *except* 
in comparison to the others. Yes, we will generally treat such a 
rating as an Approval, but there is a critical point.

If the voter were presented with the opportunity, after the election, 
to ratify the election or not, the voter, it is possible, could vote 
No because, in fact, the voter would prefer to leave the office 
vacant (or to hold another election with a new candidate set).

I put "approval" in quotes to indicate that I was using the word in 
its ordinary usage, as being some kind of positive judgement of the 
candidate, a condoning of the candidate's views and practices, etc.

So, no, we cannot say that safely, except within the technical 
language of election methods discourse, where "Approve" merely 
indicates "votes for." And, I'm claiming, it is better to call it 
that, simply. The voter votes for the candidate, not the voter 
"approves" the candidate. Generally, on ballots, I will argue, the 
word "Approval" should not be used. Unless that is the information 
one wants to collect.

In that case, to Approve a candidate would mean to indicate that the 
voter will, indeed, accept this candidate as suitable for the office, 
and would vote Yes in a ratification.

>>Ossipoff confused the fact that the candidate was intermediate
>>between A and C in sincere rating, i.e., being midrange, with being
>>"at your Approval cutoff."
>If the preference strength between A and B is  weaker than that 
>between B and C then with
>the winning probabilities being equal (or unknown) then the voter's 
>best strategy is to max-rate
>A and B. If instead the preference strength between B and C is 
>weaker, the voter does best to
>min-rate B and C (and of course max-rate A).

This is the assertion. It is apparently not true. A strong clue 
should be that this is a discontinuous function. No matter how small 
the preference disparity, the vote flips from one direction to the 
exact and complete opposite. This kind of output function in 
engineering can cause drastic instability in a control system. 
Elections are used as control systems.

Now, if the outputs are limited to two, then such a maximal 
discontinuity is built into the system. However, here we have a Range 
election, and Benham, Ossipoff, and others are asserting that the 
*optimal* vote suddenly, with an infinitesimal change in preference 
strength, flips from one direction to the other, skipping over the 
midrange vote. This led me to suspect that the analysis was wrong. 
And, from what I've found, it was.

Indeed, I haven't seen an analysis from these people. What I can 
recall having seen is specific examples of votes where the voter 
would regret having cast a midrange vote. But if the voter casts an 
Approval style vote, the voter could also regret that. Which of these 
effects is stronger? Or are the equal?

As I suspected, (and also knew from Warren Smith's reports of 
simulations), the claim that a sincere Range vote is necessarily 
suboptimal, or, at best, no better than an Approval style vote, is 
false. Simply false.

Since Behnham and others have made the claim, they really should 
prove it! But this claim has been made over and over again without proof.

If what I'm writing now is confirmed, it says something about a 
segment of the election methods world.

>Since the situation you describe is at the border of these two 
>(max-rate B or min-rate B), we can
>say that "B is at your approval cutoff".

It's up to the voter to set an approval cutoff. There is no universal 
cutoff, generally. It's possible to define a rating as a cutoff; for 
example, in Range 2, midrange could reasonably be set as an Approval 
cutoff, but strategic considerations would require that voters 
"Approve" a midrange candidate, even though they would vote against 
the candidate in a ratification.

Properly, votes on ballots are actions, and it is dangerous to posit 
a psychological meaning to them. Yes, the term Approve can be used as 
the name of an action; the governor approved the release of the 
prisoner. due to the gun that was being held at his head. However, 
because of its more common meaning as a term for a mental state, a 
benign one, it's misleading to the public to use it for these votes. 
Unless the system is free of strategic imperative, which is possible. 
But probably not in a single-stage election.

>>And, quite clearly, it *does* matter how
>>you rate B in some scenarios; for example, if the real pairwise
>>election is between A and B, then the optimum vote is to rate B at
>>minimum. And if it is between B and C, then the optimum vote is to
>>rate B at maximum.
>
>Of  course it can "matter" after the fact, but with both possible 
>"real pairwise elections" being
>equally likely at the time of voting, in Abd's scenario it 
>probabilistically makes no difference what
>rating the voter gives B.

Can Benham point to a proof of this? He referred to an unpublished 
paper that made the claim, but did not describe any proof. Now the 
author of the claim has posted a note that the claim is based on 
"reasonable assumptions," but the assumptions were not stated.

I have now posted a counterexample. But the author qualified his 
statement as referring to "public elections with more than a few 
voters." Right off, I'm suspicious, because utility analysis of 
public elections is a tricky thing, and it is fairly easy to make 
assumptions that seem reasonable at the outset but which turn out to 
be poor choices, leading to clearly incorrect conclusions. So it 
would be best if we could see the paper, or, at least, if someone 
with access would describe the proof. If nothing else, a list of the 
"reasonable assumptions"!



>Chris Benham