Approval Voting fish--error explained

[MIKE OSSIPOFF]

>Mr Ossipoff makes the remarkable error of saying "wrong", here:
>--------------------------------
> >>Subsequent preferences act against earlier preferences.
> >
> >Wrong. I'm glad you brought that up, because it's a good way
>--------------------------------

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.

Yes, you'd be correct to say that when you vote for your favorite,
and that's a preference vote against everyone else, and then
you add a vote for a compromise, that acts against and cancels
out your preference vote for favorite against compromise.
So if that's what you meant, then of course your statement is true.

My answer to that is that Approval isn't a pairwise count method,
and doesn't claim to be one. So it isn't reasonable to criticise
it for not being a pairwise count method. Borda and IRV aren't
pairwise count methods either. If you want a pairwise count method,
and one that actually lives up to the promise of pairwise count,
then you want Condorcet's method. I have no disagreement with
you there; I too prefer Condorcet's method. For me, Approval's
advantage over Condorcet is that Approval could be easier to
propose, since it's such a minimal change from FPTP. If a
debate on what method to adopt has (in addition to Condorcet
advocates) Borda advocates, IRV advocates, Margins advocates,
etc., etc., and if no one convinces the others, then the
differences will go on forever, and there will never be agreement
on how to count rank ballots. That's where Approval could come
in especially helpful. If the rank-count debate is expected to
take some years, but be resolvable, even then Approval gives
quick improvement in the meantime, as I said.

***

But if by subsequent & earlier preferences, you _were_ referring
to candidates, then Approval _doesn't_ make you cast a vote
for your compromise against your favorite. Never a strategic need
to do that. Borda & IRV can force you to do that.

>Apart from that, this message is a rather uninteresting.

No manners. Do you believe that there's anything original about
your kneejerk objections to Approval?
>
>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.

Wrong again. If I vote for my favorite & a compromise, I'm not
harming my favorite; I'm merely not casting a vote between those
two candidates. In FPTP, however, if I vote for the compromise,
then I _am_ harming my favorite, casting a net vote against him.
Likewise with IRV (single-winner STV): If I try to ensure that
my vote for the compromise over someone worse gets counted, for
which I have to vote the compromise in 1st place, then I'm again
casting a vote for compromise over favorite, and thereby harming
my 1st choice candidate, compared to the situation if I didn't vote.

But where you're really inexplicably wrong is where you say that
FPTP has no similar problem. Since my letter was uninteresting, that
must be why you didn't read it, and therefore didn't know that
the voter in Approval doesn't have a problem that he doesn't
have in FPTP. I said several times that all the voter need do is
vote for the same candidate for whom he'd vote in FPTP, and for
everyone whom he likes more.

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,
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,
you'd know that I said that single-winner STV has horrendously
complicated strategy, and that I've never heard of any mathematician
willing to wade into that problem. When I say "IRV", I'm referring
to what you'd call "single-winner STV".

>
>* 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 you're still talking about a voter's probability of changing
the election outcome. I told you that that isn't what voters are
concerned about. They want to maximize their utility expectation.
And you haven't shown that other methods are better, even by
your questionable standard.

Any court that would scathingly criticize Approval would criticize
FPTP, IRV, or Borda doubly scathingly.

One of the Approval advocates that I've spoken with is an
elections judge.

>
>* It is not a method that tries hard enough to make a voter's
>   first preference be elected.

You're again criticising Approval because it isn't a pairwise
count method. FPTP tries harder to elect your favorite? :-)
Oh, you mean if you vote for your favorite instead of compromising?
Well you are free to vote only for your favorite in Approval. But
if you compromise in both methods, then FPTP will defeat your
favorite where Approval won't. Same with IRV if you seriously
try to protect your compromise.


>
>* (It is a method with bad theoretical properties).

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.


>
>______________________________________________________________
>
>At 11:53 02.03.00 , MIKE OSSIPOFF wrote:

[This probably refers to where I said that Borda can't be
defended]

>
>If Approval can be defended then so can Borda.
>My main complaint about Borda is that subsequent preferences act
>  against earlier preferences. Borda papers would be marked with
>  numbers, and since it is so similar to the Approval Voting method,
>  at least once the voters are allowed to cast any number of votes,

I've never heard of a Borda proposal that would allow voters to
limit the number of candidates whom they rank.

>  then the Approval Voting method would be a preferential voting
>  method too. In which case I can reject them both for being
>  preferential voting methods that have an instance where subsequent
>  preferences act against candidates receiving support from
>  earlier preferences.

I told you why Approval is an improvement on Borda. Below in
this letter you disagree & I answer.

>
>
> >
> >Since you say Borda is better than Approval, let's compare them.
> >Borda, in all the proposals that I've heard of, requires you to
> >give all but one of the candidates a vote, whether you want to or
> >not. And it rigidly forces you to give each candidate in your
> >ranking a specific number of points, regardless of what you'd
> >prefer to give them. Approval doesn't require you to give a vote
> >to anyone whom you don't want to.
>
>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. Tough luck. With Borda you have to
anyway.

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.

>
> >
> >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.

Allowing negative votes, and specifying a limit to the sum of
the absolute values of your point assignments is a new suggestion,
and I'm not sure what it would be like strategically. But I'll
bet that when it's checked out it won't be an improvement on
the much simpler Approval method.

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.

But right now neither you nor I can say what are the strategic
consequences of the point system you suggest (votes can be negative.
voter limited only  by total of absolute values). What I can
tell you now is that, as a voter, I don't want to have to choose
whether to fully support a compromise or to fully support better
candidates. Or whether to fully downvote the worst candidate,
or the worst one who's likely to win. Do you really want that
strategy dilemma? No such problem in Flexible Points, or in
Approval.



>
> >
> >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.
>
>A use of an undefined term, "maximum". It is a function of variables.
>This definition: "1/(number of 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".

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,
and don't know what it means. The candidates don't cast votes
in the election. Ok, you mean "voter" rather than "candidate",
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
the strategic consequences of, but which obviously forces
some strategic decisions that Approval doesn't force.

>
> >
> >So, when we improve on Borda by giving the voter more freedom
> >we get a flexible point system, but that's strategically equivalent
> >to Approval. So improving on Borda leads to Approval.
>
>Reasoning with a [disputed] missing link led to that finding.

Because you wouldn't improve on Borda in the same way that
I suggested. But though we don't know the strategic consequences
of your suggestion, it doesn't sound very good, due to the
strategy dilemmas that it creates, dilemmas that Approval doesn't
have.

 >
> >To maximize your chance of changing the election outcome, you'd
> >vote for half of the candidates. But voters have a different goal.
> >They want to maximize their utility expectation. Their strategy
>
>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
>  the assumption that the Approval Vote was being used.

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.


>
>
> >that they use in our Plurality (FPTP) elections is intended for
> >that purpose, though most voters won't put it that way if you
> >ask them.
>
>In FPTP, power = utility. I do not know what journals may define
>  "power" as.

I haven't used the term "power", except to say that in Approval
all voters have the same power to vote for whatever candidate(s)
they want to.

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 I assure you that voters needn't worry about that graph
> >that you posted. Their strategy is quite similar to the one
> >that they use in FPTP, but I'll get to that later.
>
>Your assurance seems is 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.

>
>
>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.

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.

The next material in your letter requires more study to
comment on it, and so, for now, I'll go on to your next
statement:

> >>It is not a method that tries particularly hard to elect their
> >>  first preference.
> >
> >Sure it is, if that's what _you_ want. You're free to vote only
> >for your favorite, if you feel that he has a good chance, or
> >if you don't like anyone else. But if you feel that you need
> >to support a compromise then you may, without abandoning your
> >favorite.
> >
>
>If there is one candidate that they really prefer over others,
>  should the voter put a black mark in all those 12 boxes?.

No, because that would mean voting for all of them. Maybe you'd
want to vote only for your favorite. That depends on whether
you believe that you need someone else as a compromise to beat
someone worse. If so, then vote for the compromise & for everyone
you like more. If you think you don't need a compromise, and that
your favorite can win, then you likely would want to vote for
him, just as you would then in FPTP.

>
> >>
> >>Subsequent preferences act against earlier preferences.
> >
> >Wrong. I'm glad you brought that up, because it's a good way
>
>I have already given an example proving that subsequent preferences
>  do act against earlier preferences, in the Approval Vote. I therefore

I mentioned, above, how I might have misunderstood what you
meant, leading to an erroneous statement by me. Your support
of a compromise cancels your preference for favorite over
compromise, but doesn't mean your net effect is to hurt your
favorite.

>  have deleted that argument that didn't actually support the false
>  assertion anyway. This is my primary objection against the Approval
>  Vote, so I will give a different example proving that the Approval
>  Vote does allow subsequent preferences to harm candidates supported
>  by earlier preferences.
>
>Consider that the Alternative 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.]

You haven't shown that the Alternative Vote would be like Approval
if voters didn't number the candidates in their ranking. I
don't think an Alternative Vote count would be possible at all
without numbering. If it were, I don't expect it would be
Approval.


>I don't know what IRV is. I don't mind saying so because others
>  reading this won't too.

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.

>
>If mathematicians had the latest AMD processor
>  (http://www.tomshardware.com/), then they could go a fair way
>  towards symbolically analyzing complex methods.

Maybe then they'd be able to analyze IRV's strategy.

>
>...
> >
> >I like Condorcet because it lets you vote more preferences &
> >have them counted. Fine. Would you oppose Condorcet? If so,
> >then that opposition is an example of why it could be difficult
> >to get a good rank method enacted. What if it turns out to be
> >a protracted, seemingly interminable battle over how rank ballots
> >should be counted? Part of the beauty of Approval is that it
> >neatly dodges that issue: There's only one way to count votes in
> >Approval: Add them up.
>
>I regard 1 winner Condorcet as a good method provided the paradox
>  parts are avoided, since it passes my P1 and P2. Fixing up the
>  paradox/undefined winner problems to get it to find the right
>  number of winners (my P3) quite presumably leads to a failure to
>  pass P1 & P2. [P1 implies that subsequent preferences do not
>  act against candidates supported by earliers preferences.]
>Notwithsatanding regarding Condorcet as a method with outstanding
>  properties, I regard pairwise comparing as an idea that is a dead
>  end.

Condorcet is intended to find one winner. The paradox of cycles
exists no matter what the method is. If there's a cycle, then
no matter what method you use, the winner that you pick will have
someone else who'd beat him in a 2-candidate election. Condorcet
differs because it directly addresses pairwise preferences of
the voters & of the public. We've posted a number of circular tie
solutions on this list.

Do you have a method in which support for a lower choice can never
hurt the chances of an upper choice? The Alternative Vote?
For one thing, contrary to what IRV promoters claim, the IRV
voter does sometimes have incentive to vote a short ranking.
In any case, though, the only reason why your support for lower
choices can't hurt your favorite in IRV is because IRV eliminates
your favorite when it gives a vote to your next choice. IRV
protects your favorite by eliminating him. Oh thanks a lot.
There was a proposal for a version of IRV that doesn't eliminate.
It was offered as a compromise to the IRVies, but they didn't
accept it.

>
>
> >
> >
> >>Surely it is better to stay with a genuinely simple method like
> >>  First Past the Post, or else use a well designed preferential
> >>  voting method like STV?
> >
> >I'm not talking about multiwinner methods. Approval is nearly
>
>I meant to write "multiwinner First Past the Post".
>
> >always proposed for single-winner elections. If you mean that
> >single-winner STV, aka IRV, PV, etc, is well-designed, then
> >maybe you'd like to tell me what criteria it meets. Certainly
>
>Subsequent preferences don't act against earlier preferences. It
>  seems to me that it is not all that far from passing monotonicity
>  (needs at least 21 voters to show a first problem).

Public elections have more than 21 voters.

A miss is as good as a mile. IRV fails Monotonicity. And, as
I said, the only reason why the vote that you give to a lower
choice doesn't hurt your favorite is because IRV eliminates your
favorite by that time. What it amounts to is that IRV saves your
favorite by killing him. A sort of electoral euthanasia.

But there is a method in which your participation in the election,
trying to get the best result you can, won't defeat your favorite
or elect your last choice: Approval. I defined SARC more precisely
earlier.

..
> >People criticize Approval because it isn't a rank-method, because
> >it doesn't let you vote all your preferences. What people don[t
>
>That is an key question: can all the methods 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,
but you're better off with a paintbrush than a badly malfunctioning
paint-spraying machine. Most rank-rules mess up badly and are
not as good as Approval.

I admit that there's a good case for preferring a _good_ rank
method. But not a bad one.


>
>Certainly with an appropriate viewpoint, no. The voters can enter
>  numbers specifying preferences and the Approval Vote can internally
>  convert them all into Boolean values. For FPTP the same can be
>  done internally: information about preferences after the 1st can
>  be discarded. It is up to the rule designers rather than the
>  advocates of methods.

I'm not sure what you mean there. If you collected rankings
and in some way converted the rankings to Approval votes, that
wouldn't be Approval. Approval starts with Approval votes,
giving each candidate either 1 or zero votes.


>
>
> >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":

In Borda, if I rank my candidate 1st & your candidate last,
then I'm voting my candidate over yours by the maximum possible
point difference. But if I vote your candidate 2nd, then I'm
giving him almost as many points as my favorite--just one point
less. That is what I mean by not fully voting my preference for
my candidate over your candidate.

In a Condorcet, my preference for my candidate over yours is
fully counted as long as I rank mine higher.

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.



>
>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).

Approval is fully counting Y's vote for A over each one of the
other candidates. But obviously Approval doesn't count your
preferences among the candidates you vote for, or among the
candidates you don't vote for. Approval isn't Condorcet. But
neither is Borda or IRV.

>
>This Approval Voting method is one of the dumbest methods that
>  has ever been presented to humanity. I am surprised you are
>  defending it, Mr Ossipoff.

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

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

>
>...
>...
> >> >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 number of votes
>
>                                                     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.


>
>It could be sharpened up by changing the word "adding" to "altering",
>  or changing the word "advantage" to "disadvantage". (In my reworded
>  definition).

I didn't say "adding" or "advantage". You can write a criterion
of your own of course.




> >Borda's majority rule violations make FPTP look good.
> >
> >I've quantitatively described here Borda's failures in that regard.
> >I'll do it again if requested. It will certainly come out if
> >anyone actually proposes Borda to the voting public.
>
>  [from below]
> >Borda is the worst voting system that I've heard proposed, having
> >majority rule violations & defensive strategy dilemmas even when
> >FPTP wouldn't.
>...
>
>
>Subsequent votes act against candidates selected by previous votes
>  in both methods.

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

Mike Ossipoff

______________________________________________________
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