Approval Voting fish (4)

[Craig Carey]

(AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+)


Subject: Re: Approval Voting fish (3)

At 12:45 05.03.00 , MIKE OSSIPOFF wrote:
...
>>  not wish to maximise that when allowed to have themselves and the
>
>Maybe they "need not" wish to, but they usually do wish to.
>
>Voters want the best results they can get, and that's
>why they vote in a way that tries to maximize utility expectation.
>
They may prefer to avoid a method that presents that option.

...
>>So it defined to be something that ignores voter's interests. Further
>>  it achieves a disregard for their interests too. For example, it can
>
>It isn't clear why you believe that the matter of how good an
>outcome would be for a particular voter is something that
>"ignores...[and]...disregards" that voter's interests.
>
>It's as if you didn't even read the passage you were referring
>to. That's what I mean when I say that you should take a better look at what 
>we've said before you
>"refute" it.

This is far distant from the ideas of STV, where if a voter wants to
 narrowly promote a single candidate no less  than others can influence,
 then that voter can do so. You wrote "if a certain candidate won", you
 did not write "if a large group of certain candidates won.". In STV/IRV,
 if a single candidate is to be promoted then the voter can simply do
 that. I have yet to read WHY a vote for president should ideally
 be 1/44th of the vote of neighbours. There are some websites on the
 Approval Voting method.

What does the Approval Vote prove about the asserted partial desirability
 of utility ideas  when the most worthy candidate is also the
 candidate that voters would, if polled, say is the _only_ candidate that
 should be elected. I suppose it is a problem with the method.











(AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+)
(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)


Subject: Re: Approval Voting fish (3), selected replies

At 12:23 05.03.00 , MIKE OSSIPOFF wrote:
>
>
...
>>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.
>
>I hadn't heard about that rule before. In Approval it's always
>to your advantage to not vote for your last choice. Why would
>you want to?
>

That behaviour is not permitted by my P2.

What was the aim of the method designer(s) of the Approval Voting
 method in creating a method that gives a different outcome according
 to whether the last preference is or is not specified?.

Why should a 3 candidate 1 winner Approval Vote election have 15 papers
 when an STV election has 9 papers with unique effect (but 15 in fact).

 Why have the Approval Vote allow 6 options of making a votes that have
 no influence?. It is nice and symmetrical for sure. I do suggest that
 the designers of the method may have been groggy or something, given
 how it might have been tweaked into a better method before being
 published.



...
>There's a problem with using "AV" to stand for the Alternative
>Vote: In the U.S., "AV" is often used to stand for Approval
>Voting. When a term has 2 different meanings, it's important not
>to use it. I'll use "Alternative Vote", but if you say "AV",
>lots of people will think you're talking about Approval Voting.
>
I will go back to using STV since all the STV methods do have AV in
 common as far as I know.

...
>>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.)
>
>Wrong. Approval is not a preferential voting method, because
>"preferential voting method" means a rank-balloting method.
>Approval cannot accept the same papers that the Alternative Vote
>uses. You really must let Approval's proponents define it.

"Proponents"?: perhaps that refers to at least one of the people that
 wrote that the Approval Vote was monotonic.

 It is monotonic (no change in the length of a preference list), if
 the Y(X) function below is used.

In a 3 candidate election, STV accepts the 15 numbers described by X,
 and the Approval Vote will accept the 7 papers described by Y.
 If Approval Vote proponents did not define Y, it is too late now.

X = (A,  AB, AC, B,  BC, BA, C,  CA, CB, ABC, ACB, BCA, BAC, CAB, CBA)
P = (a0, ab, ac, b0, bc, ba, c0, ca, cb, abc, acb, bca, bac, cab, cba)

Y = ({A},{B},{C}, {A,B}, {B,C}, {C,A},         {A,B,C}        )
P = (a0, b0, c0,  ab+ba, bc+cb, ca+ac, abc+acb+bca+bac+cab+cba)


...
>
>Voters don't need to be educated on how to vote strategically.
>They already do in FPTP, and surely they will in Approval too,
>in the way that I've described to you so many times.
>

That is different: they don't have a problem with nothing but the
 rectangle of paper in front of them, in FPTP. I.e. the problem
 how many sub-votes to cast, when any one could cause a complete
 loss to one of their more preferred candidates they could have
 got if they used less votes. To say they want to maximise their
 utility is hard to follow: some voters want to elect particular
 candidates and that is quite inconsistent with an aim of maximising
 utility.


>>
>>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
>
>The voter doesn't have a need to be educated. I don't oppose
>education, and my web article on mathematical strategy for Approval
>and FPTP shows that, but voters know how to strategize without
>education, and their strategy would carry over easily to Approval,
>as I've often described to you.

Has anybody got an estimate on the probability that the method will
 be used in US state and government elections?.

...
>>Are utility functions desirable.
...
>I defined utility by saying that it's a numerical measure of the
>desirability of having a candidate win.
>

In STV, if a preference says a paper wants a particular candidate to
 win, then approximately the method does its best (despite the
 system) and if it can't get that candidate elected, then the STV
 method gives up on that candidate and does as best as the method
 actually does, to get the next using the remain weight of the paper.

 That method has nothing much to do with desires, or (if any could
 imagine it), an arithmetic summing of desires or desirability.
 However, as far as I can determine, the Approval Vote has nothing
 to do with utilities. Sure experts may connect the two.
 

...
>some valuable criteria, one of which is my minimum requirement
>for an adequate method (WDSC).


That seemed to be a rule that will quite reject STV and also
 truncation resistance. I regard truncation resistance as one of
 the most important rules to be held.

...
>>FBC is contrived valueless overly weak rule.
[Reply on FBC omitted. It could well be a not a valuable rule for
 methods other than the Approval Vote ....]



I just comment on this in case you wish to fix up the definition
 of SARC.

>>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.
>>:

The words "a group of voters share the same preferences" means a paper
 has a weight that may be >1, I suppose.

>>
>>Should "favorite" be pluralised?. If singular is correct then the
>>  Approval Vote fails SARC.
>
>Wrong again. The fact that you can vote for more than 1 candidate
>in Approval doesn't mean that you have more than 1 favorite.
>
>If you think Approval fails SARC, then you neglected to give an
>example where you think that happens.

My conclusion "Approval Vote fails SARC" is wrong. A better conclusion
 would be to say that the definition is bad. 
I later presumed that your definition was roughly done and better
 definition existed elsewhere (except for the comments about the
 word "some").

I want to avoid commenting on SARC because it is similar to my
 multiwinner participation axiom which I later regarded as being
 too weak to consider important if P1 was being imposed, at least
 until information to the contrary appeared.


:Subject: Re: [EM] Multiwinner participation rule. Reply to M. Schulze
:At 01:14 14.12.99 , Markus Schulze wrote:
:>Dear Craig,
:>
:>Craig Carey wrote (13 Dec 1999): ...
:>> -----------------------------------------------------------------------
:>> Definition: (Q2), "multiwinner participation axiom" rule. (13-Dec-99):
:>>
:>> (For All V)(For All p)(For All t) [
:>>    (0<=t)(#(p.W(V))<=#(p.W(V+tp))) .=>
:>>       (Satisf(W(V),p) <= Satisf(W(V+tp),p))]]
:>> -----------------------------------------------------------------------
:>> (Satisf(W,p) <= Satisf(X,p)) = (For All j=1..length(p)).[ G(W,X,p,j) ]
:>> G(W,X,p,j) = ((W.trunc(p,j-1) = X.trunc(p,j-1)) => (W.{p[j]}<=X.{p[j])})
:

>>
>>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.
>
>Come again? A voter's last choice generally doesn't exist?

Exactly, unless there are N-1 sub-votes marked on the paper. It is not
 minor if there is 1 winner since you wrote "or cause their last choice
 to win".

>Often someone has a last ....
...
>
>>Also the words "some configuration" appear late enough to prompt doubt
>>  that the paragraph translates readily into an existential logic
>
>I don't know what kind of logic you're using. How does the
>late appearance of "some configuration" prompt doubt about what
>"some configuration" means?
>
>>  formula. "Some configuration" in the paragraph really means "for all
>>  configurations".
>
>If I meant "for all configurations", then I would have said that.
>I said "some configuration" because I meant "some configuration".

I am not going to reply on the grounds that the wording is too hard
 to understand. I haven't formed an opinion on whether I was in the
 wrong. However...

A rule woudl check a preferential voting method against some test over
 ALL possible collections of papers, (or over ALL n-tuples of papers),
 or else the method simply isn't being tested. The word "configuration"
 in "some configuration" seems to mean some particular ballot counts.

(By existential logic, I mean Boolean operators plus "For All" and
 "There Exists".)


>***
>
>If anyone else is following this thread, will you let us know,
>and maybe comment on whether you want it posted to the list?
>
>***
>
>>
>>"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 intersection 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?.
>
>No. And though I don't know what that paragraph means, "outcome
>better than" was intended to mean "outcome that that group of
>voters like better than". I was trying to shorten the wording
>because it's a long paragraph.

The paragraph has gone. Anyway, your response caontains an error,
 in that it refers to voters. Suppose a voter, on being questioned
 for a fee paid by the Boulder theorists, lied about "likes".

>
>You don't say what you mean by "P". That leaves your paragraph
>without meaning. Also, the criterion says nothing about sub-votes,
>whatever they are.
>

P must be a paper, i.e. it is a list or vector (array).
 It needs to be auto-converted to a set, for the "." operator.

(To make a statement about all winners, rather than "P.Winners", can
  easily go seriously wrong as the number of candidates and/or
  winners approaches being infinite.)

...
>SARC doesn't say anything about how many winners there are.
>Ties are unusual in public elections, but the criterion doesn't
>assume that there aren't any.
>
>And yes, SARC applies to all methods. It's just that all but
>one fail it.

FPTP,

...
>> >> >> >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 Approval Vote is not upheld and advocated by these rules (SARC, FBC),
 because they are not serious rules.

Suppose there are 65,000 candidates and the FBC is testing a new STV
 formula: why is only one candidate considered even if the voter names,
 using the paper, 1,000 candidates?. Contrived is a word that could
 describe that. I don't want to fix the rule.

...

>But I'll save you the trouble of looking up "favorite": One's
>favorite candidate is the candidate whom one likes more than
>any other candidate. You say that there might be 2 that you
>like equally. Fine, but there might also be just one that you
>like better than all the others. That isn't unlikely, and
>the fact that your methods can violate the terms of the criteriion
>under those conditions means that your method fails the criterion.
>
>Look, Craig, you're new to this subject. That's ok; I'm sure that

These functions, which may contain "For All" operators from
 existential logic, do not have as input a lot of what your are
 attempting to explain they know of. The referring to voters is
 strictly irrelevant, yet your message often refers to voters when
 also referring to opinions, something typically never known in a
 voting room.
Here is a very clear example: SARC's definition contains the words:
 "last choice", when the number of preferences did not equal the
 number of candidates minus 1. The voter could pick one at random
 or give up and say that candidates not voted for were the last
 choices (botch the explanation), but neither the rule nor the
 method have any access to information allowing the discovery of
 what the last choice is (in this case).


>we all agree that people new to the subject should participate
>by asking questions and also by stating their opinions. But
...
>What it means to say that a method passes or fails a criterion
>may not be obvious, so let me clarify that, if under any
>conditions permitted by the criterion's premise, there can be
>even one example where the method being tested violates the
>terms of the criterion's conclusion, then the method fails the
>criterion.

...
>> >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):
>
>When giving zero to someone whom you don't rank requires you to
>give less to the candidate(s) you do rank, that has the same
>effect as being required to give point value to unranked candidates.
>
The fix for that is to normalize the weights, but you are declining to
 accept that the Approval Vote needs to have its weights normalized.
What is the problem?: that the power of a single person's vote varies
 according to the number of preferences/approvals/sub-votes cast?.








(AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+)
(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)


At 18:54 04.03.00 , MIKE OSSIPOFF wrote:
...
>>People do not want to maximize the utility expectation.
>
>You don't. Fine.
>
British select committees too, almost certainly.

...
>>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).
>
>SARC was defined in my first letter to you. Sorry I didn't
>define expectation. The utility expectation for one outcome
>is the probability of that outcome multiplied by the utility
>of that outcome. If you sum that over all the possible outcomes,
>that's the utility expectation of the event for you. In this
>case the event is the election, and an outcome is a candidate's
>election.

Not even 10**(-6) of vote should be miscounted if could be directed
 by the method towards a candidate that the paper preferred. These
 Approval Vote probabilities have standard deviations smaller than
 10**(-6) ?. Has anybody ever sampled an Approval Vote probability?,
 e.g. after an election, when it should be possible to get a truer
 estimate of the standard deviations involved,
My guess is that they are not defined and do not exist.








(AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+)
(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)


At 18:34 04.03.00 , MIKE OSSIPOFF wrote:
>>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
...
>>:The alteration is this: (AB+)--(ABC+)
...
>_do_ express. That can't be said for Borda or IRV. And
>it's easy to make a method protect preferences involving
>one's favorite to be cancelled by preferences among lower
>choices: Add a rule to eliminate your favorite before counting
>your preferences for lower choices. That's how IRV does it.
>Saved by being eliminated?
>

The part before the ":" seems to be wrong. The part after is
 obscure. Maybe it refers to STV's not peeking ahead at later
 preferences when deciding on whether or not to eliminate.


...
>If there's a candidate who's a compromise, and is likely to

[I have deleting text below containing the word "compromise".]

...
>sub-votes, but I'm not trying to claim that IRV is the same
>method as Approval, only that it has worse strategy dilemma,
>due to its failure of defensive strategy criteria, and the
>much greater complexity of its strategy.

It is not in itself significant to say that STV/IRV is complex:
 that's like saying its boundaries to win-regions have too many
 surfaces or are too rough. STV is an algorithmic method (i.e.
 like a compuer program), and it almost can't be improved to
 a simpler form. A more important question is: are the boundaries
 in the wrong places?.

>>:* 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".
>
>I don't call it "perfect" when IRV forces a voter to rank his
>2nd choice in 1st place to avoid the election of his last choice.
>Condorcet won't do that. Approval won't ever require you to
>vote a lower choice over your favorite.


The alteration described is either (AB {C+)-(B+A) or this:
 (AB {C+)-(BA+). P1 doesn't allow the 2nd (because of what
 happens to A), so suppose that the alteration questioned here, is
 the 1st.

 The alteration complained of is: (ABC+)-(B+AC)

  a  3   AB
  b  2    B
  c  4    C     : C wins iff (a<c)[Q or (a+b<c)]

   For STV, Q=(b<a).   For IFPP, Q=(2b<a+c)
   Approval: A:B:C = a:(a+b):c

  a  3   BA
  b  2    B
  c  4    C     : B wins iff (c<a+b)

   Approval: A:B:C = a:(a+b):c

The problem region is (a<c)[Q or (a+b<c)](c<a+b), = (a<c)Q(c<a+b)

IFPP and AV have the same problem. The region where the behaviour
 is not "perfect" (complained about) is a rather large region. It is
 so large that the complaint is under suspicion rather than the
 methods.

The complaint would be that B should win the first. This region is
 larger in IFPP, than it is in STV. The IFPP region is
 (a<c)(2b<a+c)(c<a+b). IFPP (but not STV) avoids this alteration
 (a P1 violation) by keeping B lose in the region: 
   (C{B+)-(AB{C+)   [Line *A*]

Both IFPP and AV avoid either of (or both of) these P1 violations
 by keeping B lose in the complained about region:
   (B{C+)-(C{B+),
   (B{A+)-(C+).

Either one or both of the latter has to be accepted or
 proportionality or truncation resistance for the 1st preference
 has to be given up, or your complaint has to be ignored ("IRV
 forces a voter to rank his 2nd choice in 1st place to avoid the
 election of his last choice.")

That's an explanation of why sometimes B wins (BA) and A and B
 lose (AB).

Once the problem appears inside that triangle, its is carried to
 larger problems through truncation resistance.

...
>Ok, I'll use "the Alternative Vote". I usually use "IRV", because
>the proposals that I'm opposing here, in the U.S., are called
>by that name.

[STV, one of the most intelligent methods.]

...
>> >concerned about. They want to maximize their utility expectation.
>>
>>That is something that no voter alive wants to do.
May be incorrect.
>
>Are you suggesting that voters in the United States aren't
>alive? :-) Instead of tackling that question, let me just tell

Would Brams & Fishburn want to maximise utility expectations?.


...
>But it's obvious really. The value of voting i over j depends

"Value"?. In STV theory, people, even churchpeople, talk about
 "winners".

>on how much better i is than j is, and on how likely it is that
>they'll be the 2 frontrunners. So vote for the person whose
>total value, summed over all the other candidates, is the greatest.
>
>That seems to be just what U.S. voters do. Take the example
...


You weren't subscribed to this list as I recall, at the time I
 started writing, which was September last year, I wrote on a
 formula of my own, named IFPP, based on my P1, P2, and P3.

For 3 candidates it is just the Alternative Vote, except that when
 any 2 candidates get less than 1/3 of the total vote by 1st
 preferences, then the candidate with the most votes by considering
 only 1st preferences, wins. It is the minimal change from STV
 that fixes [Line *A*] (better info may be elsewhere).

The 2 winner formula of that method is nothing but the 1 winner
 formula but with votes negated and winners called losers.


>> >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.
>
>If I hid something, that's still hidden from me. Voting in
>a flexible system as if it were Approval isn't a constraint; it's
>just your best strategy.

There were constraints that led to the choice of weights
 (1, 1, 1, 1, ... 1, 0, 0, 0, ... ).

Numbers like that don't come from nowhere. It is too narrow a view to
 say that voters maximise ... under the method: under such a method
 they could act strangely.

A lot of voters may want to elect their candidate, not figure out
 how to adapt to having 3-200 times more power than they reasoned that
 they deserved, knowing that actually using that power could cause one
 of their preferred candidates to lose. An option would be to use IRV
 instead.

The Approval Vote has problems like this:

(AB)-(A+)   not truncation resistant ({A}.Winners independent of 
                                truncating after candidate A)

There is no need to say it fails "a first preference loser can't become
 a winner rule". It does this: (AB+C)-(CA+). That  alteration is, under
 the Approval Vote, the same as (AB+C)-(A+C), which is just a failing of
 that rule requiring truncation resistance.





(AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+) (AB)-(A+)













Mr G. A. Craig Carey,   research at ijs.co.nz,   Auckland, New Zealand
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