Approval Vote: reply to Bart Ingles

[Bart Ingles]

Craig Carey wrote:
[...]
> "Is Approval Voting an 'Unmitigated Evil?' A Response to Brams,
>  Fishburn, and Merrill," by Donald G. Saari and Jill Van Newenhizen,
>   Public Choice (1988), 59:133-147.
> 
> "A Case Against Bullet, Approval and Plurality Voting," by
>  Donald G. Saari and Jill Van Newenhizen, January 1985.
> 
> "The problem of indeterminacy in approval, multiple, and truncated voting
>  systems, Public Choice (1988), 59:101-120, by Donald G. Saari and
>  Jill Van Newenhizen,


The titles of the latter two apparently point out Saari's objection to
allowing voters to truncate ballots.  The version of Borda he favors
actually penalizes truncators more than the "standard" version.  To wit:

Sincere Borda points with three candidates, for a single voter with
preferences ABC:
A = 2, B = 1, C = 0

Points for same candidate who truncates (standard Borda):
A = 2, B = 0.5, C = 0.5  (or A=1.5, B = 0, C = 0)

Points for truncator in Saari's version:
A = 1, B = 0, C = 0

(I got this directly from Prof. Saari, in response to a question)

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

> >> It is not a method that tries particularly hard to elect their
> >>  first preference.
> >
> >The method doesn't try -- the question of how hard to try to elect a
> >first choice is left up to the voter.
> >
> 
> If the paper allows 30 Approval sub-votes, any voter can mark just
>  a single candidate as the best way to get the method to try hard.

Not sure what you mean by sub-votes -- the voter is allowed to give one
vote each to any candidate(s) he desires.  Thus if there are 30
candidates, the voter is allowed to cast anywhere from 0 to 30 votes (0
and 30 are both forms of abstention).

> ...
> >>  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.
> >
> >Not sure why you mention a voter with 3 votes -- is this something you
> >consider for other systems?
> 
> I was imposing a constraint that the counts be integral.
> How would you argue that such aa constraint should be imposed?.

The only constraint with approval voting is that a voter is allowed one
vote per candidate.

Are you sure you aren't confusing approval voting with cumulative
voting?  That would explain the "30 sub-vote" mention above, if you
intended other than 30 candidates.


> >>  In the voting booth the voter can't easily tell if D should
> >>  be voted for. The[re] may be >7 candidates so the voter may
> >>  imagine that voting for D gives him/her more power.
> >>  In this example voting for D is to the voter's disadvantage:
> >>
> >>              A     B     C     D
> >> 3 Voters:    3     3     3     3
> >>   Others:    6     7     8     9
> >>    Total:    9     9    11    12
> >> Winners  = {C,D}
> >>
> >>              A     B     C     D
> >> 3 Voters:    3     3     3
> >>   Others:    6     7     8     9
> >>    Total:    9    10    11     9
> >> Winners  = {B,C}
> >
> >You don't support your claim, since you don't show how many votes the
> >remaining candidates are likely to receive.  Voting for D may well be
> >the right choice if E,F, or G are also likely to receive 11 or 12 votes.
> 
> You need to interpret "there may be >7 candidates" to
>  "there are 4 candidates". Then the proof of subsequent preferences
>  harming candidates supported by earlier preferences is done and visible.
> 
> Of course, a single numerical example is able to allow the Approval Vote
>  to found to be failed by that rule.

If A, B, C, and D are the only candidates, and D is the least preferred,
then there would _never_ be any reason to vote for D under approval
voting.


> >This example is not really sufficient to predict voter strategy, since
> 
> You wrote about "efficiency" in text deleted, and questioned my using
>  3 votes for one voter, which indicates a viewpoint difference.

I mentioned "Condorcet efficiency" and "social utility efficiency", but
I haven't a clue what those have to do with using 3 votes per voter.


> Suppose a person was ignorant and didn't use enough Approval sub-votes.

He would presumably still have voted for his more highly-favored
candidates.  He may not have supported the necessary compromises, but
you can do the same with any other system.

The equivalent error in FPP would be to vote for a favorite who had no
chance of winning instead of a lesser-evil who might have one.

The equivalent error in STV aka AV aka PV aka IRV aka Musical Chairs
would be to rank sincerely, allowing a winnable 2nd-choice compromise to
be eliminated, instead of ranking the compromise 1st so that it survives
the next elimination round.