[EM] Manual Construction of Smith Set

[Richard, the VoteFair guy]

Thank you Ted!  And Kristofer and Forest!

I'm seeing that the secondary hand-written signs -- that show the win 
counts -- are not needed.

Instead, each person who represents a candidate holds all the 
hand-written pairwise win signs for which that candidate wins. The other 
name on the sign indicates who lost that pairwise comparison.

As Forest suggests, it would be easy for the "candidates" to sort 
themselves according to how many signs they are holding.

Then, as Ted suggests:

 > The one with the fewest defeats (the Copeland winner) moves to the right
 > of the line. If there is a tie, all tied candidates move right.
 >
 > The candidate(s) on the right is (are) asked, "Which candidates on the
 > left side of the line defeated you?" And as they are named, they come to
 > the right of the line.
 >
 > Each new right-side candidate is asked the same question, and any
 > left-side candidates named come to the right side.
 >
 > When none of the candidates on the right can name any other candidates
 > on the left who have defeated them, the Smith set is complete.

That makes sense.

Yet I believe that lots of audience members would give more trust to a 
method that eliminates candidates one at a time. This is the simplicity 
advantage that instant-runoff voting (IRV) has. In contrast, starting 
with the Copeland winner might seem like magic to people who fear math.

Would eliminating from the bottom always work?

In the Wikipedia example below, it does work. It identifies B and E as 
outside the Smith set, so the remaining candidates are in the Smith set.

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, my question is: Does elimination from the bottom always work?

My guess is the answer is yes.

Again, thank you for your help!

Richard Fobes


On 1/14/2022 3:02 PM, Ted Stern wrote:
> (re-sent as Reply to All)
>
> Hi Kristofer,
>
> There's a slightly easier way.
>
> Each candidate is asked "How many other candidates defeat you?"
>
> The one with the fewest defeats (the Copeland winner) moves to the right
> of the line. If there is a tie, all tied candidates move right.
>
> The candidate(s) on the right is (are) asked, "Which candidates on the
> left side of the line defeated you?" And as they are named, they come to
> the right of the line.
>
> Each new right-side candidate is asked the same question, and any
> left-side candidates named come to the right side.
>
> When none of the candidates on the right can name any other candidates
> on the left who have defeated them, the Smith set is complete.
>
> On Thu, Jan 13, 2022 at 2:34 AM Kristofer Munsterhjelm
> <km_elmet at t-online.de <mailto:km_elmet at t-online.de>> wrote:
>
>     On 13.01.2022 04:46, Richard, the VoteFair guy wrote:
>     > 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.)
>
>     My O(n^2) method would be pretty transparent, I think; it would just get
>     unwieldy very fast.
>
>     First you let each person represent a candidate, and then, for each
>     person, you have that person ask "do I beat A, B, C..." in turn. This
>     gives the number of candidates that candidate beats, i.e. the Copeland
>     score.
>
>     Let there be a dividing line: everybody to the right (say) of that line
>     is in the provisional Smith set, everybody to the left is not. Move the
>     Copeland winner to the right of the line.
>
>     Then ask each other candidate if he beats the first member, second
>     member, etc. of that set. If yes, move him up to the other side of the
>     line. If anyone was moved to the right of the line as part of this
>     round, restart from the first candidate to the left of the line once
>     you've asked all of them; otherwise, the process is done and the
>     candidates on the right constitute the Smith set.
>
>     -km
>     ----
>     Election-Methods mailing list - see https://electorama.com/em for
>     list info
>