# [EM] Approval vs. CR (again)

Richard Moore moore3t1 at cox.net
Tue Jan 27 19:44:01 PST 2004

```On Tue, 27 Jan 2004, Bill Lewis Clark wrote:
> In reading through some of the archives, I've come across a point that
> apparently needs some clarification.
>
> (A) The optimal strategy in CR is to always vote the maximum or
minimum.
>
> (B) CR is strategically equivalent to Approval.
>
> Now, the point I would like to make clear is that A and B are not
> synonymous, nor does A logically imply B.

You may be reading to much into the statement "CR is strategically
equivalent to Approval". What this statement means is just the
following: If S is an optimum strategy for an Approval election, and
S' is the equivalent CR strategy (in which an S' ballot is one that
gives 100% rating to all candidates approved in S and 0% rating to all
candidates disapproved in S), then S' is also an optimum strategy for
CR, if the probabilistic information used in determining the strategy
is the same in both cases.

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.

> It's conceivable that the optimal strategy for CR may, in some cases,
> require the voter to assign maximum values to a candidate that
wouldn't be
> approved under Approval's optimal strategy (and similarly, minimum
values
> for a candidate that *would* be approved.)

Instead of forcing us to try to conceive of such a case, why not give
an example?

> Now, it may be that these cases never actually come about (because they
> require unrealistic assumptions about how to convert sincere CR ballots
> into sincere Approval ballots) but the point is that A and B cannot be
> assumed to equivalent simply in virtue of the meaning of the statements
> (which seems to have been the case on at least a few occasions in the
> past.)

The truth of statement B is not dependent on its being equivalent to
statement A, so you have a straw man argument.

-- Richard

```