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

[Dave Ketchum]

On Jun 8, 2009, at 2:14 AM, Jan Kok wrote:

> On Sun, Jun 7, 2009 at 9:22 PM, Dave  
> Ketchum<davek at clarityconnect.com> wrote:
>>
>> On Jun 7, 2009, at 8:33 PM, Jan Kok wrote:
>>
>>> On Sun, Jun 7, 2009 at 3:58 PM, Dave Ketchum<davek at clarityconnect.com 
>>> >
>>> 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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