[EM] Approval: One Man One Vote: fails or passes[?] (was Re: What are we all about?

Craig Carey research at ijs.co.nz
Sat Jul 27 03:28:38 PDT 2002

 >RE: What are we all about?
 >From: Joe Weinstein
 >Subject: RE: What are we all about?
 >Date: Wed, 24 Jul 2002 12:56:42 -0700
 >James Gilmour writes:  "If I've got it right, Approval Voting breaks the
 >first and most fundamental rule of democratic representation: "one person,
 >one vote".
 >JAMES, you've got it WRONG - or at any rate [got it] USELESS[ly ...]
 >If the rule is construed narrowly to mean just one mark allowed on a marked
 >ballot, there are very few voting systems that would qualify.  In fact maybe
 >none apart from the existing lone-mark plurality.  (Certainly not IRV, for
 >Rather, in any reasonable interpretation, the rule MEANS 'one person, one
 >ballot' (of equal inherent power to each other cast ballot).

Joe is saying that "any [i.e. most] reasonable" interpretation[s] of
"one man one vote", will have a trait of taking no notice of the set of winners.

Privately and months ago, I received an argument from Mr Hager that said
American "idiom" led to a conclusion that the Approval methods is not so
flawed. They go into the booth and tehy get a single paper. It is very
different in Britain where some consideration of who wins occurs. Anyway,
Mr Weinstein has got just the same argument.

This statement is a bit complex and torn apart by text in the parentheses:

 >Rather, in any reasonable interpretation, the rule MEANS 'one person, one
 >ballot' (of equal inherent power to each other cast ballot).

Approval Votes in general do not have equal inherent power. Being true,
it can be hard for an Approval advocate to get the defences looking

I ask members to imagine that the parentheses are actually not there.

Anyway Joe has got the definition of "one man, one vote" wrong. It
does not require equality of power. For example, the Alternative Vote
negates the power of votes thus it is not equating powers. But it is my
opinion that it is passed by a "one man one vote" test.

The test is somewhat easy to get past and it even looks like the Block
Vote and the Cumulative Vote (and SNTV/FPTP) can get past that test.


 >However, if you INSIST on the narrow interpretation, then Approval voting is

[Ideally can't write about "insist[ing]" while there was not really an
admission in the text that the other was understood. If any sees
evidence of understanding please correct me.]


Here I produce a definition of "one man one vote". First we construct a
number saying what the power of a ballot paper is, when compared against
FPTP papers (i.e. Approval papers with a single checkbox filled). Then
the method is failed if that number is greater than 1.0.

Devise an example showing that checkbox Approval fails:

    (1) limit the papers so that all papers have exactly 2 checkboxes

    (2) Replace that paper with any linear combination of Approval FPTP
      papers. Optimise the combination so that the total count (weight) of
      the FPTP papers is minimized. That returns a number. Then maximise
      that number of all possible election examples. All the added papers
      have non-negative weights

It is surely going to be the case that the final number resulting won't
be smaller than 2.0.

Mr Weinstein said that the other had a narrow interpretation and also
gave a wrong and vague definition of "one man one vote". It is not
obvious that a plausible method that is "worse" than Approval could be
devised, under the consideration of that "one man one vote" test.

The standard Borda method also fails: ti has a power of 4/3 in 3 candidate
1 winner elections; and I showed that here (using some software rather
than quite explicit algebra):

|  http://groups.yahoo.com/group/politicians-and-polytopes/message/173
|     Date:  Sun Mar 31, 2002  8:27 am
|     Subject:  Borda method is corrupt at 4/3 = power

That 4/3 would get worse as more candidates are added.
That was Borda with these weights for subtotals of candidates A,B,C

(A)  2, 1/2, 1/2
(AB) 2, 1, 0
(ABC) 2, 1, 0

Borda can be rejected: it allocates too much power to some papers.

An aim behind rejecting Approval is to withhold from public voters a
need to consider how to manipulate and Approval election. Thus there
may be less opposition to Approval if the elections using are tiny
little elections (Long Beach elections) rather than anything election
where the public would vote. We need to show that the facts are not
available to anticipate an Approvalists defence where it is stated
that the public in an Approval election would be provided super
calculators that would advise them on how to manipulate an Approval

Since the Approval method is being checked by a Boolean function
and the method is completely failed by that test, then why not
boldly say that the method fails?. [The document was long enough
that that highly relevant truth could have been slipped in without
increasing its overall size by much.]

Joe had an "it's simple" argument. Indeed, it would be simple to a
voter that can't see how to gain power in an Approval election and
who then voted using too few preferences. Unlike with the Alternative
Vote, to say that Approval is simple is saying that it is not
being manipulated well and thus some voters are missing out on the
power they could have had. [I have not got a quote I can copy here].

 >still meaningful, as a short-hand way of voting on each of a list of
 >propositions.  Namely, look at each race for an office as a list of the
 >Is candidate A acceptable? (In response you get one vote opportunity:
 >"yes"=check, or "no"=blank).
 >Is candidate B acceptable? (again you get one vote opportunity).
 >Is candidate C acceptable?
 >So long as at least one candidate IS acceptable to 50% or more of the
 >voters, so that one or more of the propositions pass, the passed
 >propositions will result in the office going to the candidate with the
 >highest number of yes votes, i.e. the Approval winner.

The percentages don't actually sum to 100% ?. Should the figures be
re-normalised, Mr Weinstein ?.

The readers of this list know that people here could not figure out
how to best manipulate Approval. Presumably a computer could get the
best way of maximising influence figured out rapidly. Public voters
don't have computers for that task and if they did then it would not
help them.

I don't see any research of Approvalists that shows just what type of
people are helped by Approval's sloshy power excesses.

Wherever there is a bit of dodginess in the advocating arguments then
there could be a presence of bias too.

I guess I am only writing back to Mr W rather than criticising the
Approval movement.

Craig Carey

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