[EM] range ballots chew up slots; "unsupported" range voting claims

[Jan Kok]

On 8/19/05, Abd ul-Rahman Lomax <abd at lomaxdesign.com> wrote:
> At 09:05 PM 8/18/2005, Warren Smith wrote:

> >I do not especially recommend running range elections in this style.
> >I would much prefer it if there were voting machines specifically designed
> >for range voting.  However, because range voting CAN be done on
> >plurality machines as a stopgap measure, that makes it a lot
> >more adoptible than many other forms of voting, for
> >example IRV, which CANNOT be done on many kinds of plurality machines.
> 
> I question this assertion. It depends on the number of candidates. Yes,
> combination presses would be much more difficult to use in IRV, but Mr.
> Smith and the others who have written about the use of these machines for
> Range have assumed one lever per rating value. In IRV, levers equal to the
> number of candidates (minus one, but at least one net) is required for each
> candidate -- last place being indicated by no press. So for four
> candidates, three levers per candidate are needed.
> 
> I've said this before, so that the assertion continues to be made about IRV
> and voting machines does disturb me. Indeed, IRV and Range require,
> actually, the same kind of ballots, if you want granularity sufficient to
> give a unique rating to each candidate. That is, you could vote in the IRV
> fashion on any Range ballot. The only way that Range may handle more
> candidates than IRV on a ballot is by requiring equal rankings for some
> candidates, if the voter wants to express an opinion on all candidates.

Yes, Range, IRV, Condorcet and others can use the same kind of _ballot_.

Warren (and my) claim is that existing voting _machines_ that are
designed to handle Plurality elections, _can_ handle Range Voting. 
But if the machine simply counts and reports how many ballots had each
hole punched or filled in, or how many voters pulled each lever, that
information is not sufficient to conduct an IRV, Condorcet, etc.
election.

Consider my favorite IRV example:

35 A>B>C
25 B>A>C
40 C>B>A

The ballots could look like this:

A  1 2 3
B  1 2 3
C  1 2 3

where the "1", "2" and "3" are holes that can be punched or marked, or
levers that can be pulled.

The 35 A>B>C voters would mark their ballots as

A  *1 2 3
B  1 *2 3
C  1 2 *3

where the "*" indicates the mark/punch/pull.

The other voters would cast their votes appropriately.

There are two problems with running this IRV election on dumb
plurality voting machines:

1.  The machine probably doesn't have the flexibility to check that
the ballots are properly marked.  A plurality voting machine could
check that only one rank is chosen for each candidate, but could
probably not check for two candidates assigned the same rank.

2.  When the polls close, the following counts would be available from
the above example:

     1   2  3
A 35 25 40
B 25 75   0
C 40   0 60

Assuming all the ballots were filled out correctly, we can see that B
had the fewest first-choice votes and should be eliminated.  The
problem is, we can't tell from the counts how many of the B-first
voters voted for A second, and how many voted for C second, so we
don't know how to redistribute the votes to the other candidates.

(The Australian solution is to announce the first preference counts on
election night, and to send all the ballot papers to the central
election offices.  For those races where no candidate got a majority
of first preferences, the ballots are counted and shuffled over the
next several days.  In close races, with absentee ballots trickling
in, sometimes it takes two or three weeks to figure out who the winner
is.  We could do a similar thing in the US, of course.)

A dumb voting machine that just totals up the punches, as above, could
easily handle Range Voting elections.  Suppose, just for illustration,
that the same voters would vote in an RV election so as to get the
following totals:

     0 1 2 3 4  5 6 7 8  9
A 40 0 0 0 0 25 0 0 0 35
B   0 0 0 0 0 75 0 0 0 25
C 40 0 0 0 0   0 0 0 0 60

Then we can trivially compute the ratings as follows:

A = (0*40 + 5*25 + 9*35) / (40 + 25 + 35) = 440 / 100 = 4.4
B = (5*75 + 9*25) / (75 + 25)  = 600 / 100 = 6.0
C = (0*40 + 9*60) / (40 + 60) = 540 / 100 = 5.4

(Note, by the way, that the counting can be done at the voting
locations, and just the numerators and denominators (440 / 100, 600 /
100, 540 / 100) transmitted to the central election office for
combining to get the final ratings.  With IRV, the amount of data that
needs to be transmitted to the central office is considerably greater,
and is considerably more difficult to understand, making it harder to
audit.)

Cheers,
- Jan