Precinct canvassing and ranked-order

From: David Mertz <voting-project_at_gnosis_dot_cx>
Date: Thu Apr 29 2004 - 16:08:30 CDT

On Apr 29, 2004, at 3:28 PM, Douglas W. Jones wrote:
> Similarly, for STV/IRV systems, you treat the ABC race as 3 races, one
> for
> first place, one for second place, and one for third place, and
> reconcile
> votes that way as you're carrying votes forward from the precinct to
> the
> center. These numbers aren't the overall winners, just a convenient
> reconciliation rule. Again, cheaper than n!

I'm sure Doug must mean something other than what this seems to say (on
my reading). It looks like he is suggesting that a total of first
place, second place, etc. votes at a precinct contains enough
information to decide an IRV winner at an aggregate level. I had to do
a double-take to make sure I wasn't missing something in the algorithm
(Doug's thing SEEMS lossy, but I wanted an example to make sure). So
here's a concrete example.

Candidates are named 'A', 'B' and 'C'. When their names are
concatenated, that indicates a rank preference. Both precincts have a
low turnout of 3 voters each :-).

Precinct One:
-------------
Raw Votes: [ABC, BCA, CAB]
Place tallies: 1st: 1 A, 1 B, 1 C
                                        2nd: 1 A, 1 B, 1 C
                                        3rd: 1 A, 1 B, 1 C

Precinct Two:
-------------
Raw Votes: [CBA, BAC, ACB]
Place tallies: 1st: 1 A, 1 B, 1 C
                                        2nd: 1 A, 1 B, 1 C
                                        3rd: 1 A, 1 B, 1 C

As you can see, precincts One and Two are identical in terms of
canvassed place totals.

However, suppose that at the state (or county, city, whatever) level,
candidate A is eliminated from the first round. Incidentally,
different IRV variations might eliminate differently: e.g. least
winning (fewest #1s) versus most losing (most #3s). The second round
should look like:

Precinct One:
-------------
Adjusted Votes: [BC, BC, CB]
Place tallies: 1st: 2 B, 1 C
                                        2nd: 1 B, 2 C
                                        3rd: N/A

Precinct Two:
-------------
Raw Votes: [CB, BC, CB]
Place tallies: 1st: 1 B, 2 C
                                        2nd: 2 B, 1 C
                                        3rd: N/A

In the second round, precincts One and Two diverge... even though they
were identical in initial place totals.
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Received on Fri Apr 30 23:17:25 2004

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