[EM] Intermediate RV rating is never optimal

[Abd ul-Rahman Lomax]

bits and pieces

At 05:33 AM 7/21/2007, Michael Ossipoff wrote:
>That's incorrect. It's exactly the same in RV as in Approval. In 
>your example, with B at your Approval cutoff, it doesn't matter how you rate B.

In what I wrote, B was not at the voters "approval cutoff." I didn't 
give an approval cutoff. Approval cutoff is an artificial insertion; 
it's a device for converting range ratings to approval votes.

This is the situation described:

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.

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." 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.

But what if we have, instead, some spread of probabilities of 
election of the various candidates? What if all three candidates are 
equally likely? I've proposed, in another thread, a test of this 
latter scenario.

This has practically nothing to do with "approval cutoff."

In the end, the voter casts a vote. The vote is counted in a certain 
way. It's an action, it has an effect. If a voter casts a 
full-strength vote for a candidate, we could term that Approval, 
though it may not be anything more than a lesser of two evils choice, 
and it's quite possible that the voter would prefer the office be left vacant.

If the voter casts no vote for a candidate, it may actually be true 
that the voter "approves" of the candidate, i.e., the candidate is 
above some "approval cutoff," but in the context -- say there are 
only two candidates in the election and this one is not the favorite 
-- it would not be optimal to vote for the candidate.

For "Approval cutoff" to make any sense, in what Ossipoff wrote, we 
have to define Approval cutoff in quite a complex way, which 
integrates both the utilities of the candidates and the election probabilities.

And if this is a Range election, whether or not the candidate is at 
the approval cutoff or above it or below it, by itself, tells us 
nothing about the optimum vote.

"Approval cutoff" is usually used to imply some kind of rating level, 
above which we will Approve the candidate. Yet it is quite clear that 
the optimal rating for a candidate is not dependent upon being above 
or below a certain specific rating level, but depends not only on 
rating but on election probability as well. Our optimal vote is not 
just a matter of fixing an approval level and determining if the 
candidate is above that or below it.

The reason "approval cutoff" seems to make some sense is that if we 
rate one candidate higher than another whom we have decided to 
approve, we should likewise approve of the higher one. So it is as if 
there is an approval rating level somewhere between the ratings of 
the candidates we are approving and those we are not, and, we *could* 
use some device to indicate approval on a Range ballot. For example, 
a dummy candidate, the rating for which sets an approval cutoff.

How would this be used? Well, it would be used to determine if a 
majority "approved" of the Range winner. If not, then we would not 
have in indication of majority support for that winner, and the 
election would require a runoff or would simply fail. Basically, a 
majority of voters would have voted No on the election of the Range winner.

If you want to avoid having to come in and vote again, then set your 
approval cutoff in a sincere way! Consider how you would vote if the 
only question were "Shall this candidate be elected?" If you'd vote 
Yes, then approve the candidate -- with the cutoff. That isn't going 
to determine the winner, in itself. It's just going to decide whether 
or not there needs to be some further process.

It's my strong opinion that, like any democratic decision, the 
majority should explicitly accept the winner of an election. This is 
actually standard process in many small organizations, it takes a 
majority vote to finalize an election. (And, even where it is routine 
to simply announce the election result, officers can be removed by 
majority vote at any time, so that the majority allows an officer to 
continue is tacit approval. When there is a fixed term, it's more complicated.)