Approval Voting fish (2)

[Craig Carey]

At 16:30 03.03.00 , MIKE OSSIPOFF wrote:
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>>Mr Ossipoff makes the remarkable error of saying "wrong", here:
That was a mistake to write that
>>--------------------------------
>> >>Subsequent preferences act against earlier preferences.
>> >
>> >Wrong. I'm glad you brought that up, because it's a good way
>>--------------------------------

So the "wrong" is itself "wrong". I should have foreseen that.

In the following I delete all comments by Mr Ossipoff that contain
 the word "compromise". It would be better to number preferences,
 especially once they are in an ordered list. 

>
>When you said "preferences", I, perhaps mistakenly, assumed
>that you meant preferred candidates. If you meant pairwise
>preference votes, then I did make an error there--an error
>in interpreting your wording.

...
>>My main complaints about the Approval Voting are:
>>
>>* Subsequent preferences harm candidates supported by earlier
>>   preferences, and voters will know that, and then find the decision
>>   (a strategic voting decision) on deciding how many Approval
>>   sub-votes to use, difficult. With FPTP and STV there is no similar
>>   strategic voting problem.
>

Here is text from an earlier message that got deleted and was absent
 from Mr Ossipoff's first reply. It is my second example of later
 preferences harming canidates supported by earlier preferences. In
 the 2nd, the number of candidates equals the number of preferences,
 and while people would say a voter should not do that, it
 nevertheless suffices to allow the proof to be made.

At 13:19 03.03.00 , Craig Carey wrote:
:
:Proof that the 1 winner [Approval] Vote method allows subsequent
: preferences to act against earlier preferences (invariance on
: truncation, that test that passes STV). (This example is also a
: proof that the Alternative Vote fails P2 and P1.)
:
:Paper = A>B  (A B .)
:Candidate:   A   B   C
:2 Voters:    2   2   0
:Others:     60  61  62
:Total:      62  63  62
:Winner = B
:
:Paper = A>B>C  (A B C)
:Candidate:   A   B   C
:2 Voters:    2   2   2
:Others:     60  61  62
:Total:      62  63  64
:Winner = C
:
:The alteration is this: (AB+)--(ABC+)
:That is a P2 violation since a change occured when the last preference
: was filled in, and it is also a P1 violation since [an] alteration
: was made in (ABC+) at and/or after the preference for B (i.e. the 2nd
: preference), and B changed from a loser into a winner.
:

(So "Subsequent can preferences harm candidates supported by earlier
 preferences, in the Approval Voting  method".)


...
>But where you're really inexplicably wrong is where you say that
>FPTP has no similar problem. ...

"Similar problem" here, means the problem of deciding how many Approval
 sub-votes to cast. That is a strategic voting problem entirely absent
 from STV/AV and FPTP/SNTV.

...
>So all you need to know to vote in Approval is which candidate
>you'd vote for in FPTP. And if you prefer the mathematical strategy,

That is false in general.

>it's almost identical with Approval & FPTP, no difference in
>complexity. (But it's been pointed out that a laborsaving
>shortcut is possible with Approval, but not with FPTP).
>
>But the biggest mis-statement was when you said that single-winner
>STV has no such problem. If you'd read my uninteresting letter,

It is not clear to me what meaning you have for the word 'problem':
 either the difficulty of deciding on how many sub-votes to cast
 or the very similar problem of subsequent preferences disadvantaging
 earlier preferences. Both those problems are absent from STV &
 FPTP/SNTV. Perhpas you referred to this paragraph:

:* Subsequent preferences harm candidates supported by earlier
:  preferences, and voters will know that, and then find the decision
:  (a strategic voting decision) on deciding how many Approval
:  sub-votes to use, difficult. With FPTP and STV there is no similar
:  strategic voting problem.


>you'd know that I said that single-winner STV has horrendously
>complicated strategy, and that I've never heard of any mathematician

For the issue of the discourse here, STV is perfect, i.e. perfect in that
 it requires no strategic voting at all in this matter, because of its
 property of: subsequent preferences never disadavantaging candidates
 named by earlier preferences. That is different from "complicated
 strategy". 

>willing to wade into that problem. When I say "IRV", I'm referring
>to what you'd call "single-winner STV".

((Why not just follow the British nomenclature?.))


>>
>>* The method makes no attempt to keep the power of voters about
>>   equal. Hence it would be a method not suitable for a land having
>>   leaders that sought a method that 'fairly summed votes'. It is
>>   a method that a court could only criticse scathingly.
>
>Every voter has the power to vote or not vote for any candidate.
>All voters equally have that same power. Votes are "fairly summed"
>if we add up every vote than anyone chooses to give to a candidate.

Maybe instead of "power" in the 1st sentence there you meant freedom.
The statement "All voters equally have that same power." is false; and
 I assume power has the commonly understood meaning.

Anticipating a need to be precise about the definition of that word,
 I defined "power" to be as follows:

At 13:19 03.Mar.00 , Craig Carey wrote:
...
:They may want to counter contrary hopes of other voters, and from the
: above it is shown that when voters have the same utility value,
: then they have different power. (I would try to define power as the
: ability to offset other votes where those votes do not have a 2nd
: preference.) Perhaps you had stated voters aims after imposing


>
>Maybe you're still talking about a voter's probability of changing
>the election outcome. I told you that that isn't what voters are

I rarely write about probabilities in preferential voting theory.

>concerned about. They want to maximize their utility expectation.

That is something that no voter alive wants to do.

...
>You're again criticising Approval because it isn't a pairwise
>count method. ...

No I am not critising the method on that grounds and the comment
 is false. You are free to disprove my previous sentence using
 evidence. The next paragraph contained the word "compromise".

...
>You still haven't named any criteria that Approval fails, and
>your favorite methods pass. I've named 3 criteria that Approval
>passes and which Borda & IRV & FPTP fail.

It fails the "truncation resistance" property that STV has. It
 also a open flop against my P1 and P2 rules.

>>
>>______________________________________________________________
>>
>>At 11:53 02.03.00 , MIKE OSSIPOFF wrote:
...
>I told you why Approval is an improvement on Borda. Below in
>this letter you disagree & I answer.

Missing axioms.

...
>>Borda has bigger weights for earlier preferences.
>
>You missed the point: Why should Borda tell you how many points
>you can give to candidates. That should be for you to decide.
>Make that improvement in Borda, and you get something strategically
>equivalent to Approval. Borda "has weights" for people you might
>not want to give any votes to. ...

You wrote that "Borda "has weights" for people you might not want to
 give any votes to. ...". That is referring to the truncation of
 preference lists. Those weights can be removed by subtracting in a
 way that leaves the set of winners unchanged.

Also, the comment "how many points you can give to candidates"
 indicates a viewpoint problem: if "points" means weights then those
 weights are data that is internal to the method. That data can be
 rescaled with altering the method.

>
>You might say that Approval also doesn't let you decide how many
>points to give the various candidates you vote for. No, but
>if you know what you're doing, and want to use your best strategy,
>you'll give the same point score to all of the ones that you
>give anything to. In other words, you'll vote as in Approval even
>if you're free to choose how many points you give to the candidates.

You've assumed constraints but not stated them. This is mathematics:
 there is no need to hide constraints yet write long paragraphs, or
 write long messages without describing the constraints' axioms, etc.


>>
>> >
>> >So, to start improving on Borda, suppose we let you give each
>> >candidate what _you_ want to give them. That would be a flexible
>> >point system. It would be a freedom-improvement on Borda.
>>
>>The sum of the absolute values of the weights would need to be
>>  constrained.
>
>If the allowed weights must be positive, and you limit how
>many points you may give, then congratulations, now you have
>a method that's strategically equivalent to FPTP. A distinct
>step down from Approval.

This is a greater than anything else you have written, it seems to me.
You comment would be disagreeable to persons with an STV viewpoint,
 where preferences soak up some of the vote, and what remains has its
 power 'transferred to' the next preference.

I believe that you made many mistakes and I might not reply more.

[end]