[EM] Manual Construction of Smith Set

[Richard, the VoteFair guy]

Thank you Forest, Colin, and Kristofer for answering my question about 
how to manually identify the Smith set.

I now better understand how to do this on paper.

However, I'm still uncertain how it could be done in a public setting 
such as on stage in a school auditorium, with an audience watching to 
ensure the process is fair. (And creating a video of the process.)

Doing calculations on paper would not be acceptable because 
non-math-savvy viewers would regard it as untrustworthy "magic."

Forest's idea of pulling out a calculator and doing matrix calculations 
is very clever, but of course that's not the kind of "manual" process 
that would be meaningful to an audience.

What I think can be followed is to do the pairwise counting with people 
who are "pairwise counters."  Each one focuses on just one pair of 
candidates. Perhaps a video screen behind each person can show the 
ballot being looked at and the screen can show the current pairwise 
counts for that pair.

At the end of this process perhaps each pairwise counter can use a 
felt-tip pen to write a sign that say something like:

Alder
wins over
Cedar

But what would be a good audience-visible process -- using people on the 
stage -- that converts these win-loss signs into the Smith set?

Your answers use the word "sort."  How could this sorting process be 
represented using the signs and some people on a stage?

Of course when there's a Condorcet winner, finding the candidate who has 
a win count equal to one minus the number of candidates is simple.

But what happens when there is no Condorcet winner?

It would be acceptable for an announcer to say things like "If Alder won 
over your other pairwise candidate, please hold your sign up high, 
otherwise keep your sign low. ... I see that Alder has 4 pairwise wins."

Such wins/losses can be written on different signs that say something like:

5 wins for Alder

But what can be shown as an action for a non-simple case, such as the 
following one in Wikipedia?

5 wins for A

5 wins for D

4 wins for G

3.5 wins for C

2.5 wins for F

1 win for B

0 wins for E

(Half indicates a tie.)

So, does anyone have a suggestion for how some interactions on stage can 
clearly -- and hopefully simply -- show how to resolve this more complex 
kind of situation?

Richard
The VoteFair guy