[EM] Re: Approval vs. CR (again)

[Richard Moore]

Bill Lewis Clark wrote:
 >Richard Moore wrote:
 >> Granted it may be possible to have different sets of probabilities in
 >> a CR election than you would have if the same election were held with
 >> Approval -- for instance, you might know that members of party X have
 >> a tendency not to vote all-or-nothing in CR while members of party Y
 >> have a tendency to vote optimum strategy, and this may give an edge to
 >> party Y's second choice over party X's second choice. But strategic
 >> equivalence does not mandate that the resulting strategies be
 >> identical when the initial probabilities are different. So this does
 >> not run contrary to the strategic equivalence assertion.
 >
 >Then I don't see the significance of the strategic equivalence, at 
 >all.
 >If my strategy is going to be different for the exact same election 
 >with
 >the exact same voter preferences, with the only difference being 
 >whether
 >Approval or CR is used, then I don't see why they should be treated >as
 >being equivalent in any important way.

It will only be different if you have the information about how voter 
strategy (or non-strategy) will affect the outcome in the CR case. In 
the real world of public elections, I don't see that kind of 
information as something that would be available. That is why, in my 
opinion, the strategic equivalence is significant -- a 
strategically-minded voter in a real-world election will make the same 
assumptions in a CR election as in an approval election.

 >I think CR deserves a lot more attention than it's received.  In many
 >ways, it's a generalization of various other systems.  By 
restricting >the
 >range of values in one way, CR can be made to simulate Approval.  By
 >restricting them in another way, it can simulate Borda.  There are 
 >entire
 >classes of variants that, to my knowledge, haven't been explored at 
 >all --
 >because CR is dismissed as being "not worth pursuing."

Straight CR -- unrestricted ratings over a fixed range -- is "not 
worth pursuing" in the sense that it offers "advantages" that nobody 
should take advantage of (those that do take advantage of them will be 
taken advantage of). Incidentally, that argument is based on your 
statement A, not statement B, so the quote you gave from 
electionmethods.org is a bit sloppy.

Variations of CR have been discussed here in the past. Around three 
years ago Forest and I had an exchange about normalized CR 
(specifically with an L2 norm, though this can be generalized to any 
L-norm). L1-normalized CR is strategically equivalent to Plurality. L2 
projects everyone's vote onto the surface of an N-sphere. It has the 
interesting property that your optimum vote exactly matches the 
strategic values you calculate for each of the candidates; in a 
zero-info election this means your optimum strategy is to cast a 
sincere CR vote. If only we could guarantee every election to be 
zero-info...

 >> Instead of forcing us to try to conceive of such a case, why not give
 >> an example?
 >
 >I did, in a previous email.  I'll include it at the end of this 
 >reply.  It
 >makes additional assumptions about how to convert between sincere CR
 >ballots and sincere Approval ballots (which probably aren't 
 >justified) but
 >the general idea is still clear, I believe.

That example is in the same category as the "exception" I pointed out. 
Including assumptions about how some voters will fail to maximize the 
strategic value of their vote, changes the probability inputs to the 
strategy equation.

 >> The truth of statement B is not dependent on its being equivalent to
 >> statement A, so you have a straw man argument.
 >
 >I was making two different points.  The first was that A and B do 
not >mean
 >the same thing, nor does A imply B simply in virtue of the meaning 
of >the
 >statements.  You already made it clear that you agree with that 
 >point, but
 >my reason for raising it was that others sometimes seem to think 
 >they're
 >semantically equivalent.
 >
 >The second point I was trying to argue was that A doesn't imply B at 
 >all,
 >but that was based on my misunderstanding of what "strategic 
 >equivalence" entails.

I haven't seen anyone claim A implies B, although if you have been 
reading this list more closely than I, you might have caught something 
I missed. The electionmethods.org quote about CR might have carelessly 
substituted B for A, but that's not the same as claiming A implies B.

 >I was never trying to argue directly from the first point to the 
 >second,
 >so there was no straw man argument in play.

It would be a straw man if it was intended to suggest that others were 
arguing from the first statement to the second, which I guessed to be 
the case based on your statement in that original post:

 > Now, the point I would like to make clear is that A and B are not
 > synonymous, nor does A logically imply B.

  -- Richard