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

[Dave Ketchum]

It matters what is said, not whether speaking in different languages  
affects whether different information can be contained in the same  
size statement.

Paul is stating, correctly, that reading a ballot that only approves  
{B C} provides no information as to the voter's desires  being B>C,  
B=C, or B<C - only preferring them over A.

On Jun 7, 2009, at 2:57 PM, Jan Kok wrote:

> 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.)

Paradox?  (ignoring Jan's naming error), Paul's approval ballot is  
approving {B C} as if equally liked, and unable to imitate rank's  
ability to include relative liking of the two.

The approval voter had to omit voting for A to indicate lesser liking  
for A, while the rank voter could indicate lesser liking for A in the  
ranking.
>
> 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.