On Jun 8, 2009, at 2:14 AM, Jan Kok wrote:
On Sun, Jun 7, 2009 at 9:22 PM, Dave
Ketchum<[email protected]> wrote:
On Jun 7, 2009, at 8:33 PM, Jan Kok wrote:
On Sun, Jun 7, 2009 at 3:58 PM, Dave Ketchum<[email protected]
>
wrote:
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.
I was not disagreeing with Paul (at least not with the passage I
quoted). The point of my post was to show that both Paul and Warren
were right about some of the things they were saying, and to shed
some
light on what may have been the core of their misunderstanding.
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?
Warren said "equal amount of information". Paul (sort of) said
"ranked
ballots have more info". So which is it, equal or more? If both are
right, doesn't that seem like a paradox? I went on to explain why it
only _seemed_ like a paradox, i.e. there was no paradox.
(ignoring Jan's naming error),
Naming error? Not sure what you're talking about.
Paul is assigning B&C equal ranks , with A liked less. Then you
have C as
least liked. Makes the studying difficult.
Where did I say C was least liked? I don't see it.
Go up to the paragraph before the one-word "Paradox" paragraph. You
do not explicitly say that C is least liked, but ending with C being
possibly not voted for implies least liked.
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.
Yes, I agree that a ranked ballot contains info that can't be
found in
the corresponding Approval ballot.
And I assert equally that an Approval ballot contains info that
can't
be found in the corresponding ranked ballot.
How do we get here?
Too much starting from a dream, and then proceeding as if the dream
made sense.
Think of 20 candidates. Expect many voters to NOT want to rank all
20; expect many voters to feel two or more are liked equally by them
and thus deserve the same rank.
While some can wish for voters to be forced to rank all and no two
with the same rank, those thinking more seriously can wish to minimize
demands on the voters:
NOT required to rank all, so a voter who thinks Plurality can
vote for a single candidate.
CAN assign the same rank to two or more, so a voter who thinks
Approval can express the same thoughts.
NOT required to rank all.
With these possibilities a ranked vote can contain more information
than is possible for an Approval vote.
I already explained that:
"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.)"
So the Approval ballot contains the information that the voter
"approves" C, i.e. likes C better than the expected outcome between A
and B. You can't tell that from the ranked ballot B>C>A. Therefore:
"an Approval ballot contains info that can't be found in the
corresponding ranked ballot."
If you simply say "ranked", voters can do equal ranking, which
permits
ranked voters to vote ballots IDENTICAL to approval by giving all
approved
IDENTICAL ranks. All without losing rank's ability to support
multiple
ranks.
I think we're wandering off into the weeds here. The original
discussion, or at least the part I read, was only about 2 and 3
candidate elections, _strict rankings_ vs. Approval voting with vote
for all and vote for none not considered.
Yes, if you allow equal rankings, then you can vote Approval-style
with such ranked ballots. But then it needs more bits to represent
that type of ballot.
Ranking has no need to ban equal ranking, that supports voters'
occasional
desires for such. No great strain to count such - A=B is simply
counted by
NEITHER counting A>B nor A<B.
Sure.
Going back to your initial statement:
It matters what is said, not whether speaking in different
languages
affects
whether different information can be contained in the same size
statement.
I'm not sure what the point is that you are trying to make. Maybe
you
are saying that the type of information you gather from a ballot is
more important than the number of bits needed to represent that
info.
(Which would be a subjective statement.)
Suppose there are 16 candidates.
Then a 16-bit string can have a bit for each candidate indicating
whether or not approved.
Can have 4 bits for each approved candidate, and a 4-bit field
indicating how many approved by this voter. Certainly takes less
space if
total number of approval fields is less than 3*number-of-voters.
Again, I think we're drifting away from the original topic.
But matters not. What matters is ability to recognize voters' use of
ability promised to them - and to count this.
I'd say that's one of _several_ things that "matter" if you are going
to do voting reform activism in the real world.
Cheers,
- Jan
Dave Ketchum
What follows wanders into straining the voting method beyond Approval
or ranking.
Dave Ketchum
I'd say that the exact number of bits needed to represent a ballot
is
not all that important - especially if the discussion is limited
to 2
and 3-candidate elections! In general, more bits _might_ mean that
the
voting method can make a better choice of winner. But more bits also
could mean more complicated ballots, asking voters for more
information than they want to bother with giving, and can make it
harder to summarize the ballot data so that it can be posted outside
polling places for the public to check. If you want less info, go
for
Approval. If you want lots of info, go for fine-grained Score Voting
(e.g. 0-99). If you want something in between, go for coarse-grained
Score Voting (e.g. 0-3).
Other than number of bits, some things that matter are: whether
voters
or legislators would accept a given ballot style and associated
voting
method (i.e. how hard is it to "sell" the voting method); how much
and
what sort of strategic voting is encouraged by a particular voting
method, and the effect that has on election outcomes - for example
Plurality voting encourages choosing the lesser evil, which
maintains
a two-party duopoly and limits voters choices; how well does the
voting method do at picking the "best" candidate for winner (i.e.
Warren's Bayesian Regret calculations); cost of implementation,
including voting machine upgrades and voter education; how
vulnerable
the voting method is to fraud; and so on.
Cheers,
- Jan
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