[EM] Manual Construction of Smith Set

[Forest Simmons]

First day in basic training ,"boot camp", 'cruits line up single file ...
keep switching places with neighbors that are out of order according to
height ... it doesn't matter which out of order pair goes first ... as long
as you agree that shorter 'cruits need to be ahead of taller ones in the
lineup. After n*(n-1)/2 or fewer swaps, no shorter recruit will be preceded
by a taller one.

It may sound chaotic, but that's the way they did it 55 years ago at Ft.
Bliss, TX.
You can do it more systematically by giving "right of way" to the pair in
front of you. Or by waiting until everybody ahead of you has settled into
order before you move into your proper position among them.

A merge sort would be a nice dance: start by counting off ... the evens
merge with the odds in front of them ... then adjacent pairs merge into
adjacent quadruplets ... the adjacent quads into adjacent octuplets, etc.

Now back to pairwise defeat ...

Let's say you have reached the point where you have a pairwise defeat chain
from front to back.

Give a flag to the candidate at the head of the line. While any body behind
the flag defeats the flag bearer, transfer the flag to the one of these
that is furthest from the front (i.e. closest to the back).
EndWhile

The final position of the flag is the cutoff position of the Smith Set...
the Smith set is the initial segment down to and including the flag holder.

El mié., 12 de ene. de 2022 7:46 p. m., Richard, the VoteFair guy <
electionmethods at votefair.org> escribió:

> 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
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
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