Approval Voting fish (3)

[Craig Carey]

(This message is believed by me to be not worth reading by most.)


At 16:30 03.03.00 , MIKE OSSIPOFF wrote:
>
I have deleted paragraphs containing the word "compromise"
 (an undefined noun).
Typos apologised for.
...


>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.
>

The mistake is that you seemed to miss that that can be regarded
 as an optimisation problem. [One that can't be defined.]


>Allowing negative votes, and specifying a limit to the sum of
...
>But constraining the sum of the votes, or their absolute value,
>is an unnecessary constraint on voter freedom. With flexible
>points, limited only by a maximum & minimum that one can give
>to a particular candidate, the strategically informed voter would
>want to give the maximum to some and the minimum to the rest. You
>wouldn't allow that, would require voters to make difficult choices
>that they don't have to make in Approval.

That is what the method should do: approximately allocate a minimum
 to candidates just to cahnge them from losers to winners.

(While that is worded as an optimisation problem, a defining of the
 optimisation problem seems to be not able to be done. There would
 not be a problem solving the problem.)

These difficult decisions on how to decide the weights are somewhat
 done by methods other than the Approval Vote.

...
>> >But it can be shown that, if one wants to maximize one's utility
>> >expectation in the election result, when using a flexible point
>> >system, one's best strategy is to give the maximum points to
>> >all the candidates for whom you'd vote in Approval, and to give
>> >the minimum points (usually zero or some large negative amount)
>> >to all the candidates for whom you wouldn't vote in Approval.
>>
People do not want to maximize the utility expectation.

Expectation is a word from statistics (yes?).

Are there some probabilistic ideas that are a basis for your defence of,
 or derivation of, the Approval Voting method?. Use of probability would
 lead to a sub-optimal rule failing method.

What is a "utility expectation" ?. This is a simple question able to
 be answered with a precise definition (just like my request for SARC
 to be defined).


>>A use of an undefined term, "maximum". It is a function of variables.
>>This definition: "1/(number of [sub-votes] cast by that candidate)"; got
>>  excluded. That would be an attempt to press down the "hump" and
>>  create respectability.
>
>Sorry I didn't define "Maximum". It means "largest", or, in this
>case, "largest permitted".

A maximum is a function that eliminates variables. I don't see any
 variables in what you wrote, around 'maximum'. "Permitted" would be a
 Boolean function of some variables too. It is a constraint and the
 variables it depends on are not at all stated. Both terms are very
 undefined.

>
>I don't know what you mean by "1/(number of votes cast by that
>candidate)". If I excluded it it's because I never heard of it,

  1/(number of sub-votes cast by that voter)

>and don't know what it means. The candidates don't cast votes
>in the election. Ok, you mean "voter" rather than "candidate",
yes
>and I suspect that you want to limit the voter to a maximum
>total number of votes. That's the proposal that we don't know

No, that is worded to show a consideration of internal variables.
I would not want to define a rule that uses internal variables of
 the Approval Voting method. So ideas like "points" and so on are
 not due a consideration in any comparative consideration.

>the strategic consequences of, but which obviously forces
>some strategic decisions that Approval doesn't force.


...
>No, based on FPTP voting, and comments by FPTP voters, maximization
>of utility expectation is what voters want to do. I don't understand
>your definition of power, but the voters' goal seems to be as I've
>said.

It is not clear what that "utility expectation" means. Real voters need
 not wish to maximise that when allowed to have themeselves and the
 method freely alter weights, with a freedom that allows the Approval
 Vote to result. So nothing good about the Approval Vote formula is able
 to be inferred from surveyed electorate members' opinions on mathematical
 theory about FPTP.

...
>Utility doesn't mean power. It's a numerical measure of how good
>it would be, for a certain voter, if a certain candidate won.
>It could be defined as the merit of that candidate, as judged by
>that voter.

So it defined to be something that ignores voter's interests. Further
 it achieves a disregard for their interests too. For example, it can
 punish voters more harshly than STV's transfer values would, if they
 use few votes.

...
>>Your assurance seems [to be] false. Suppose the election had 300
>>  candidates and voters could pick 80 of them, and 9 days before
>>  the election, an article on the origins of democracy in the GB,
>>  had comments from the House of Lords on the idea of each person
>>  having one vote. Should the uneducated be told by state advertising
>>  to NOT cast just one vote?.
>
>I assume that there will be only one winner. I don't know why
>you limit voters to voting for only 80 of the 300 candidates,
>but if voters are allowed 80 votes, then, for most of them, casting
>only one vote is contrary to their best strategic interest. So
>yes, voters should be made aware of that fact in that situation.
>

So there is admitted to be a serious problem that properly requires
 education on how to strategically vote.

Unfortunately the ratios of the powers of votes can be so very large
 (or very small), that education won't be good enough. It is almost
 clear that a good method is the best option.

VOTERS NEED TO BE EDUCATED On How To Strategically Vote, with the
 Approval Voting method.


>>If Borda can be modified then so can the Approval Vote:
>>
>>Unfortunately for Borda, there is no sequence of weights, with the
>>  sequence being of any length equalling the number of preferences on
>>  the voting paper, where specifying or not specifying the last
>>  preference makes no difference to the winners.

That is false once the unstated constraint of the weight for the last
 preference being 1, is removed.

>
>If you specify every rank position except for your last choice,
>then it will be obvious who's the last choice to whom you're
>giving zero votes.
>
You can't say "obvious" and mean true, because some preferential voting
 methods fail that. You should be writing on relative values, not absolute
 values ("zero votes").
In fact the Approval Voting method fails that rule, and standard Borda
 (as recently defined), passes that rule or test, which is that there is
 invariance of outcome wrt. specifying and not specifying, the last
 preference.

...
:>Consider that the Approval Voting method has papers requiring that
>>  voters use sequential numbers, just like as for STV. In the counting
>>  room, the presence or absence of a number is considered rather than
>>  the value of the number. [This permits the intent of voters to be not
>>  considered and no known.]
>
[response omitted because it followed the wrong written meaning]

...
>IRV is the name under which the Alternative Vote is being
>promoted in the U.S. Single-winner STV. IRV stands for
>Instant Runoff Voting. I use that name because it's used by
>the promoters who are pushing that method here.

IRV = AV

...
:>That is an key question: can all of the method's problems be made to
>>  fully vanish by saying it is not a preferential voting method?.
>
>No, but it isn't reasonable to criticize it for not being what
>it doesn't claim to be. A paintbrush isn't a paint-spraying machine,
...
Just to rephrase that: the Approval Voting method is a preferential
 voting method that accepts (can accept) the same papers that the
 AV Alternative Vote method. (Both are a set function of a vector of reals.)

...
>With IRV, a voter's preferences aren't reliably counted, since
>the fact that they voted X over Y isn't counted if X is eliminated
>before that voter's traveling vote reaches X.

Every vote is ignored unless it close to traversing a point across
 a win-lose boundary, i.e. near to having an effect.


>> >realize is that most rank methods are worse, because the
>> >preferences that you vote aren't reliably & fully counted, and,
>>
>>This is what is meant by "Fully":
>>
>>Voter X casts ONE vote, and the Approval sub-votes are for
>>    A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T
>>
>>Voter Y casts  ONE vote, and the Approval sub-votes are for:
>>    A
>>
>>Is the Approval Vote 'fully counting' the vote of voter Y, when
>>  Voter Y has about 1/20th the power to influence of voter X, (or
>>  exactly 1/20, as the number of candidates approaches being infinite).
...

The public education, that Mr Ossipoff was indicating needed, was to
 educate voters that their vote could have 1/20 of the power that it
 should have.

What is it about the "utility" function that is desired by voters, to
 such an extent that would explain why voter Y has:
  (1) a need to be educated, and 
  (2) a need to have a very weak influence in the election outcome.

Mr Ossipoff wrote that preferences voted for, should be "fully ..."
 counted, and then did not say why the weight for the vote was about
 1/20 of what it should be, if the vote was full.

...
>Nothing wrong with expressing your opinion, and others can
>judge for themselves whether the arguments presented support
>your claim.
>

Can any explain that the basis of the method: does it have a trace of
 plausibility to it?. Whereas for large problems, Condorcet can't find
 an answer for
 0.999999999999999999999999999999999999999999999 of all elections,
 this promoted Approval Vote will give some of the more mathematically
 unskilled voters a power of this when voting: 0.0000001.

Are utility functions desirable.

Please define all concepts around this utility value and functions.
It was an expectation.

I have a method and it is based on 3 axioms that are known, The Approval
 Vote has axiom hasn't it?.


>I claim that Approval is the 2nd best proposal because of the
>criteria that it meets, and which nearly all rank methods fail.
>WDSC, FBC, & SARC. Actually, as I said, no method other than

I skipped over WDSC and apologies for that.

>Approval meets FBC or SARC. Condorcet meets some valuable
>criteria that Approval doesn't meet, but other rank methods
>fail those too.

FBC is contrived valueless overly weak rule.

This is SARC.

:Strong Adverse Results Criterion (SARC):
:
:If a group of voters share the same preferences, and if they
:all vote the same way, in a way that could, with some configuration
:of the other people's votes, produce an outcome better than any
:outcome that they could get in any other way, then the fact that
:they showed up & voted in that way should never cause their
:favorite to lose, or cause their last choice to win, if that
:wouldn't have happened had they not showed up & voted.
:

Should "favorite" be pluralised?. If singular is correct then the
 Approval Vote fails SARC.

The words "their last choice" refers to something that in general
 does not exist and it is a constraint imposed too late saying that
 if there are N candidates then the number of Approval-sub-votes must
 equal N-1.
Also the words "some configuration" appear late enough to prompt doubt
 that the paragraph translates readily into an existential logic
 formula. "Some configuration" in the paragraph really means "for all
 configurations".

"Outcome better than" is largely undefined. It is anybody's guess
 whether winners set W1 is better than winners set W2 when
 #(P.W1) > #(P.W2), where C is the candidates receiving sub-votes
 (and "." is set intersetion and "#" is the 'cardinal number of').
 That failure to define does not occur when only 1 winner is elected.
 Is  more that 1 winner specifically ruled out?.

If you were to say that SARC applies when there is just one winner,
 then isn't this SARC a definition that applies to any preferential
 voting method. It is good to see that the Approval Voting method has
 rules that draw it into comparative competitve assessments.

>> >> >Favorite-Betrayal Criterion (FBC):
>> >> >
>> >> >By voting a less-liked candidate over his favorite, a voter should
>> >> >never gain an outcome that he likes better than any outcome that
>> >> >he could get without voting a less-liked candidate over his
>> >> >favorite.
>>...
:> >The words "over his favorite" doesn't mean that the Approval sub-votes
>>
>> >remains constant. It changes during the voting, as more people
>> >arrive at the polls. However, after the polling is over, then
>> >the number of votes does remain constant, as it would with any
>> >method. I'm not sure why you say that that makes the criterion
>> >less valuable.
>>
>>This is a rule that people will not consider to be important.
>>It says that adding a later preference shall not advantage a candidate
>>  of an earlier preference. This is a rule that I would not bother
>>  to impose upon a method. Is seems to be a cntrived rule that came
>>  into existence to full up a nearly empty set of good qualities that
>>  the Approval Vote has.
>
>Are you saying that it's good for a voter to have strategic
>need to vote a lower choice over his favorite?
>
>If you believe that, then we've found the source of our
>disagreement.
>

The FBC is very badly defined. What are the constraints on the number of
 winners and the number of sub-votes?. What is a favorite?. How is
 liking defined?. Why not just write this weak rule in a mathematical
 formulation, using existential logic?.

In the meantime let's assume the Approval Vote has very few good properties.

...
>But at least FPTP doesn't force you to give some points to all
>but one of the candidates.
>

That is not such a good point actually, at least when truncated preferences
 are allowed in the Borda method. Bart says that can be done, with a 3
 candidate vote for (A..) having the weights (wrt. (A,B,C)): (1.5, 0, 0):


At 17:46 03.03.00 , Bart Ingles wrote:
...
>The titles of the latter two apparently point out Saari's objection to
>allowing voters to truncate ballots.  The version of Borda he favors
>actually penalizes truncators more than the "standard" version.  To wit:
>
>Sincere Borda points with three candidates, for a single voter with
>preferences ABC:
>A = 2, B = 1, C = 0
>
>Points for same candidate who truncates (standard Borda):
>A = 2, B = 0.5, C = 0.5  (or A=1.5, B = 0, C = 0)
>
>Points for truncator in Saari's version:
>A = 1, B = 0, C = 0
>
>(I got this directly from Prof. Saari, in response to a question)
>
>-------------------------------------------------