Approval Voting fish

[Craig Carey]

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
--------------------------------

Apart from that, this message is a rather uninteresting.

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.

* 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.

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

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

______________________________________________________________

At 11:53 02.03.00 , MIKE OSSIPOFF wrote:
...

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,
 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.


>
>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.

>
>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.

>
>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.

>
>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.

>
>>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

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.


>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.


>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?.


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.
A method is a bad method if specifying or not specifying the last
 preference makes no difference. This means that if all the preferences
 are specified, then having the last preference equal 0, is very
 different from having it equal 1.


Proof: Consider a 2 candidate election, with the candidates being
 A and B.

A.   a0
AB   ab
B.   b0
BA   ba

Case 1:  1 = num prefs,  Weights = (1, 0)/1
Case 2:  2 = num prefs,  Weights = (K, 1)/(K+1),  K>1

What is K ?.

Sa = a0 + ab*K/(K+1) + ba*1/(K+1)
Sb = b0 + ba*K/(K+1) + ab*1/(K+1)
Winners = {A} if Sb < Sa, else  {B} if Sa < Sb.

Sa - Sb = (a0 - b0) + (ab - ba)(K-1)/(K+1)

To make the specifying of the last preference immaterial,
 1 = (K-1)/(K+1). However that function approaches K=1
 asymptotically.

This proves that Borda fails that P2 rule/axiom, which says that there
 should not be a change in the set of winners when votes are spread
 equally over the same vote but with subsequesnt preferences permuted
 out. Borda fails P1 too since it fails monotonicity (a proof is to
 alter the example I gave for the Approval Voting method).

-------------------

>>
>>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?.

>>
>>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
 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.]

Proof that the 1 winner Alternative 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 and 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.


...
>>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.

...
>
>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.
>

In FPTP, considerations of 


>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.

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

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


>
>
>>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).

>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

...
>In terms of the need for defensive strategy, Approval
>is the 2nd best proposal, as I said. If you think that something

That has to be ignored since you said subsequent preferences did
 no act against earlier preference (perhaps limiting that to
 one candidate elections).

...
>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").
>

Webpages needing promoting to search engines can be rapidly
 promoted using my Multithreaded Add-URL Javascript program:

http://www.ijs.co.nz/submit/submit.htm


...
>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?.

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.


>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).

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.

...
...
>> >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.

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


>
>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".

In general (or in an optimal method), the vote (CBA..) can
 have candidate A lose, but A can win if the vote were (C....).

...
>that outcome. FPTP can have any 2 parties the frontrunners at
>equilibrium. That isn't true in Approval. Suppose the Green
...
>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.

...
>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.

Approval Vote can take a place in the text books, in University
 text books.