Approval

[MIKE OSSIPOFF]

Bart Ingles said:

> >In whose estimation?  Prof. Saari?

Craig Carey said:

>Was that part of a quite public dispute?. I suppose Borda is better
>  since the Approval method is a Borda method but with the weights
>  (1, 1, 1, ...) for each preference.

It wasn't part of a public dispute. Saari probably knows better
than to propose Borda in public, since Borda can't be defended.

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.

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.

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.

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.


>The power a voter has will be a hump shaped curve with the
>  voters having no power if the number of votes they cast is zero
>  or if the number votes they cast is equal to the number of
>  candidates.
>
>Power
>  +
>  +                             +     +     +
>  +                       +                       +
>  +                 +
>  +           +
>  +     +
>  +-----+-----+-----+-----+-----+-----+-----+-----+-----+---->
>  0     1     2     3     4     5     6     7  Number of Votes

>Voters are expected to want to go into a voting booth and while
>  in there they want to (a) retain or (b) change the government.
>  They do not want to consider the latest, IF ANY, on hump shaped
>  curves.

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
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.

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.

>
>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.

>
>Subsequent preferences act against earlier preferences.

Wrong. I'm glad you brought that up, because it's a good way
of describing the difference between Approval and the method
known as the Alternative Vote, or Preferential Voting, or
Instant Runoff, or IRV, or MPV or PV. (I'll call it IRV here).
With IRV or FPTP, or most other methods, when you try to support
a candidate whom you might need as a compromise, that can require
you to cast a vote for that compromise, against your favorite.

That's never necessary with Approval. When you give a vote to
your compromise, and also to your favorite, you merely aren't
voting a preference between those two candidates.

The criteria that I defined in the letter to which you were
replying are intended to measure whether voters need to vote
anyone else over their favorite, or over someone whom they
like more. Approval passes. IRV & FPTP fail badly.

>
>Example: Suppose that in a election using a preferential vote,
>  a voter would have voted A>B>C>D. The voter very much (or
>  infinitely) prefers A to B to C to D.
>  Suppose the method was electing two winners.
>  Approval vote isn't a preferential method.
>  This voter is either important with 3 votes or the there are
>  3 voters.

I'm not into multiwinner methods, but Approval could be used
for that purpose too: Merely let people vote for as many candidates
as they want to, regardless of how many or how few will be
elected. But I won't defend that as a multiwinner proposal, since
I don't deal with multiwinner methods.

>Mr Brams or whomever might call it a simple method. I can't recall
>  who declared that the Approval method was simple. Perhaps it might
>  be called "a simple method for a simple people" (after carefully

To re-phrase your gracious wording, Approval's strategy, like that
of FPTP, is as simple or as complicated as the voter wants it
to be. With many things, no complex approach is needed, but those
who like those things can study it as complicatedly as they want
to.

You later say that Approval is worse than FPTP. No way. Approval
is simply FPTP, with more voter freedom added. More freedom isn't
a bad thing. FPTP only allows you to vote for one. With Approval
you can vote for only one if you choose to, or you can vote for
as many or as few as you choose to.

How should you vote in Approval? Vote for the same candidate you'd
vote for in FPTP, and for everyone whom you like better than him.
That isn't complicated.

>  excluding unavoidable comments from senators and congressmen who
>  probably haven't studied the method for long enough). But voters
>  may think it is more a method that demands that they be a nation
>  of Einsteins. The information they need to decide whether a voter
>  should list all of what they want or just a fraction of the
>  candidates they want elected, is completely unavailable to them
>  when they are voting, and even if accurate polls from the
>  previous day were available, it may be difficult to interpret
>  because the problems with the Approval Vote occur when candidates
>  have similar support.

If Approval required a nation of Einsteins, so would Plurality,
because, as I said earlier, if you can vote in FPTP, you can
vote in Approval. Sure, if you want to do it complicated, you
can, but that's just as true of FPTP. The mathematical strategy
for maximizing utility expectation is almost the same in Approval
as in FPTP, if you want to do the mathematical approach.

And what about IRV (aka PV)? I've never heard of any mathematician
calculating the mathematical strategy for PV, probably because
it's so horrendously complicated that even mathematicians want
nothing to do with it. Aside from PV's other disadvantages,
its complicated strategy is another reason why I hope it never
gets enacted here, and will fight it wherever it's proposed in
my country.

You said that the information that voters need for Approval
is completely unavailable. Not so. Voters now have frontrunner
probability information for our FPTP elections, and that's
the same information that'd they'd use for Approval, in the
same way. Voters now use that information to judge which candidate
is the "lesser-evil" for whom they need to vote. In Approval they
can vote for him & for everyone whom they like better.

>
>It would need to be shown that voters do actually know whether
>  they prefer candidates over other candidates rather than knowing
>  that they are indifferent to a group of three (lest a fourth wins
>  and makes the 2nd lose), or is it all four? (in those cases where
>  the three would win anyway).

No, Approval advocates don't need to show that voters are
indifferent between those for whom they vote. Voting all of
your preferences and having them all reliably & fully counted
is a nice luxury. You won't get that with the method known
as IRV or PV. PV doesn't reliably count the preferences that
you vote. It capriciously ignores some of your voted preferences.
At least Approval counts the preferences that you vote, even
though you can't vote as many preferences as you might like to.

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.


>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
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
not any that relate to majority rule or avoiding the need for
defensive strategy.

You agree that FPTP is genuinely simple, but in what way is
Approval less simple than FPTP? As I've described, the mathematical
strategy of the 2 methods is almost the same, with no difference
in complexity. Most people's Approval strategy would be just
like their FPTP strategy, and I'll repeat it: Vote for the
candidate you'd vote for in FPTP, and for everyone whom you
like better.


>
>
> >
> >Approval is one of the very best methods around. Only Condorcet
>
>A false statement there.

In terms of the need for defensive strategy, Approval
is the 2nd best proposal, as I said. If you think that something
else is better for single-winner elections, you could say what
you think is better, and what criteria it meets.

Information about mathematical Approval strategy can be found
at:

http://www.barnsdle.demon.co.uk/vote/sing.html

(note that the 2nd "a" in "barnsdale" is intentionally left
out, so it's "barnsdle").

At the table of contents, click on "Mathematical Strategy
for Approval & Plurality".

I'd like to add here, though, that if there really is no
frontrunner probability information, then your best Approval
strategy is to vote for all of the candidates who are above
average in merit, as you judge it. In FPTP, under those conditions,
your best strategy of course is to vote for your favorite.

***

People criticize Approval because it isn't a rank-method, because
it doesn't let you vote all your preferences. What people don[t
realize is that most rank methods are worse, because the
preferences that you vote aren't reliably & fully counted, and,
worse, people are strategically forced to completely abandon
their favorite sometimes, something that never occurs in Approval.

Yes rank balloting is a good thing, but only if it's counted
adequately. IRV, or PV, or the Alternative Vote doesn't count
it adequately.


>I don't have definitions for WDSC, NDDC, Bucklin. They could be
>  messages but I am aiming just to sustain an interest long enough
>  to get this message out.

Check the message to which you're replying. It contains definitions
of WDSC (also called NDDC), FBC, & SARC, the criteria that
I named to show why Approval is better than nearly all rank
methods.

I didn't define Bucklin, in order to save space, since no one's
proposing it. Bucklin says that each ranking gives a vote to its
top choice. If one or more candidates has a vote total exceeding
half the number of voters, then elect the one with the most votes.
Otherwise repeatedly have each ranking give a vote to its next
choice, until one or more candidates has a vote total exceeding half
the number of voters, or till every ranking has given a vote to
all its candidates, whichever happens first. At that time the winner
is the candidate with the most votes.


> >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.
> >
>
>I suppose the words "over his favorite" mean the number of votes
>  cast remains constant. That makes the criteria is significantly
>  less value.

The words "over his favorite" doesn't mean that the number of 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.

In any method you can vote A over B by voting for A & not for
B (If it's a rank method, of course that means you rank A but
not B). In a rank method you can also do it by ranking A higher
than B. That's what I mean by "over his favorite".

>
> >***
> >
> >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.
>
>So it may satisfy SARC, but the Approval vote shows bad properties
>  when voters change the number of votes they use.

What bad properties? What bad properties that aren't possessed
by IRV?

>
> >***
> >
> >FBC & SARC are met by no method except for Approval.
> >
> >***
> >
> >As I said, I personally prefer Condorcet's exclusive criterion
> >compliances. Or, putting it in more direct terms-- Approval
> >makes good use of previous elections, and will quickly home in
>
>[Makes no use of previous election's data]

Previous election data can be used with any method that requires
strategy, to the extent that it requires strategy. Condorcet
is distinguished by how little it needs strategy.

>
> >on the median candidate or party, but Condorcet will usually
> >go directly to the target in its 1st election. Also, I
> >like the luxury of being able to rank, with respect to each other,
> >the candidates whom I'd vote for in Approval, as I can do in
> >Condorcet or Bucklin. Additionally, with Condorcet, if the
>
>A problem with the Approval Vote is that it creates extremely
>  difficult stragic voting mathematical problems for individual
>  voters. They do not have the data or the time to allow them
>  to run computer simulations just in a hopeless aim of trying
>  to have their vote have no less influence than their
>  neighbours.

As I said, Approval's mathematical strategy is no more complicated
than that of FPTP, and a lot less complicated than that of IRV.

And, as with FPTP, voters don't need mathematical strategy.
If you can vote in FPTP you can vote in Approval, in the way
that I've described above.

>It is beyond imagination that the Democrats and the Republicans
>  would not be running their own simulations, etc. They have the
>  intelligence and the money: they jsut don't have the Approval
>  Voting method.

They most likely run simulations with FPTP too. They probably
don't want the Approval method because it would let people vote
for non-Republocrat parties & candidates. With Approval it
would be "goodby Republican/Democrat monopoly".

FPTP has the peculiar property that whatever 2 parties the
media convince people are "the 2 choices", that will be a self-
fulfilling prediction. People will think it would be pointless
to vote for any other party, and those 2 parties will be the only
ones that get any votes, fulfilling the media prediction that
they're the only viable choices. That's a Weber-Myerson equilibrium.
A vote totals outcome that is consistent with the vote totals
prediction(s) that led people to vote as they did, resulting in
that outcome. FPTP can have any 2 parties the frontrunners at
equilibrium. That isn't true in Approval. Suppose the Green
has enough support to be one of the 2 frontrunners, along with
the Democrat, but the media tell us that the  Republican &
the Democrat are the only viable choices. In Approval, all
the Greens, if they believe the media, will vote for the Democrat.
But they'll vote for the Green too. And the Green will end up
with more votes than the Republican, showing that the
Democrats & Republicans _aren't_ the frontrunners. The electorate
won't be stuck in a Weber-Myerson equilibrium in support of
2 parties falsely or mistakenly claimed to be the 2 frontrunners.

>Electorates may be better off with multiwinner First Past the
>  Post. At least FPTP/FPP is a true preferential method.

As I said, multiwinner electins can use Approval too, by
letting people vote for as many as they want. I don't debate
multiwinner methods.

>  Even Borda (2 versions perhaps) is a better, but by how much
>  is unclear. I believe FPTP IS a better method than the Approval
>  Voting method.

Borda is the absolute worst. Though IRV is no better than
Plurality, two methods tied for 2nd worst, Borda takes the prize
as the very worst.

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.

>
>How has the Approval Voting method evolved over the last decade
>  or years?.

Why should it evolve? Absolute simplicity is difficult to
improve on. You can propose a modification, but it wouldn't
be Approval then. There have been suggested modifications, but
none are popular with Approval advocates, because they sacrifice
simplicity.

Someone suggested letting people cast, in addition to their
Approval votes, a separate vote for their favorite. If that
separate vote shows anyone with a majority, then he wins. But
then I can't say that Approval doesn't require any balloting
changes. In communities where Runoff is in use, the minimal
change would be to simply use Approval in the first election,and
then still hold a top-two runoff among the 2 biggest votegetters.
That's called Runoff Approval. I have nothing against it as
a replacement for Runoff, and it would likely be easier to
enact.

You can propose modifications based on Approval, but what
makes Approval so winnable is that it's the minimal reform
for FPTP. Runoff Approval is the minimal reform for Runoff.
Approval, as I said, is nothing other than FPTP done right.

>
>I was unsure about Mr D. G. Saari criticisng [when was that?] the
>  Approval Vote because of that gentleman's limited commenting
>  on the Borda method, but Borda is a better method [check] and it
>  can be since the two are oiut of the same class [different
>  weights].

Borda is the worst voting system that I've heard proposed, having
majority rule violations & defensive strategy dilemmas even when
FPTP wouldn't.

Mike Ossipoff




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