[EM] information content of ballots (and intelligent people)

[Jan Kok]

I understand quite well Warren's point that for 2 and 3-candidate
races, and with full ranking required, and equal ranking not allowed,
then Approval (with the "silly" votes excluded) and ranked ballots can
be encoded in the same number of bits. And yes, there is certainly an
algorithm for turning a binary number like 100 back into a ranking. Or
for turning an 8-bit number into 3 Approval or 3 ranked ballots.

In his most recent post to EM, Paul wrote:

> If "ranked ballots provide more information than approval ballots" is a
> MYTH, then Mr. Smith should be able to decide from {B C} > {A} which
> of {C B} is preferred by the approval voter over the other.

In other words, Paul is saying that the ranked ballot "B>C>A" contains
some information (namely B>C) that is not contained in the Approval
ballot "{B,C} are approved".

I think the answer to this seeming paradox is that the ranked and
Approval ballots contain the same amount but _different kinds_ of
information. In fact the Approval ballot contains information that can
not be determined from the ranked ballot: in the above example, can
you tell from the ranked ballot whether C would be "approved" by the
voter? ("Approved" meaning the voter considers C to be better than the
outcome expected if A and B were the only candidates.)

To state it more simply: does the voter like C a lot or not much at
all, compared to the likely winners? You can't tell from the ranked
ballot. The Approval ballot at least gives you a hint.