# [EM] Condorcet How?

Wed Mar 24 01:42:19 PDT 2010

```robert bristow-johnson wrote:
>
> On Mar 23, 2010, at 9:01 AM, Terry Bouricius wrote:

[...]

>> Since the bill, as passed, actually
>> used a top-two contingent system (only the top two initial candidates
>> would advance), the tally would be relatively easy.
>
> so the regional venues would report 1st-choice tallies and *wait* for
> the central counting venue to indicate who the top two vote getters
> are?  then the regional venues do a pairwize tally between the two?  is
> that how it would be done?  that's possible, but it requires a two-way
> communication and a deferred counting action later in the evening of
> Election Day.

A top-two contingent system is actually summable. First, count
Plurality. Second, count the pairwise matrix. The Plurality count will
tell you who the two winners are, and then you just use the pairwise
matrix to find out which of these beat the other.

E.g. if the ballots are:

10: A > B > C
7: B > A > C
6: C > B > A

(23 in all)

the pairwise count is:
A beats B: 10 times
B beats A: 13 times

A beats C: 17 times
C beats A:  6 times

B beats C: 17 times
C beats B:  6 times

Plurality counts are: A: 10, B: 7, C: 6

Then A and B go to the second round. Since B>A is 13 but A>B is 10, B
wins. Both the Plurality counts and the pairwise matrix are summable, so
it works.

```