# [EM] Round Robin Tournament Showings

Ted Stern dodecatheon at gmail.com
Thu Aug 5 16:19:22 PDT 2021

```What if worst score is zero?

What if best and worst score are both zero?

What if best and worst scores are both small, but Log(R) is relatively
large?

WLOG, you could first restrict to the Smith Set, which would avoid such
troubles, but it seems a little fragile to me.

On Wed, Aug 4, 2021 at 11:30 AM Susan Simmons <suzerainsimmons at outlook.com>
wrote:

> Note if we replace A(X) approval of X with
> Log R(X), where R(X) is the ratio of X's best pairwise score to X's worst
> pairwise score, then ASM and RSM are the same
>
>
>
> Sent from my MetroPCS 4G LTE Android Device
>
>
> -------- Mensaje original --------
> De: Susan Simmons <suzerainsimmons at outlook.com>
> Fecha: 4/8/21 10:31 a. m. (GMT-08:00)
> A: election-methods at lists.electorama.com
> Asunto: Round Robin Tournament Showings
>
>
> After a Round RobinTournament concludes its pairwise contests how should
> we decide the finishing order (1st place, 2nd place, 3rd place, etc.) of
> the participating teams?
>
> Here's a solution that's reminiscent of Approval Sorted Margins:
>
> Since there is no precise analogue for a team's approval in this context
> we use the ratio R of its best score to its worst score to determine a
> tentative list order.
>
> Then as long as some adjacent pair of teams is out of order pairwise,
> among such pairs transpose the one whose members' R ratios are closest,
> i.e. with the smallest absolute value of log(R1/R2).
>
> The CW and CL (when they exist) will appear at opposite ends of the sorted
> list.
>
> And there is the same kind of reverse symmetry that ASM provides in the
> context of elections.
>
> In fact, we could call this method RSM or Ratio Sorted Margins, where the
> margins are the absolute differences of form
>  |log R1 - log R2|
> in analogy to the approval margins of form |A1 - A2|.
>
> People that are uncomfortable with approval cutoffs can use RSM instead of
> ASM ... no approval necessary ... ranked preference style ballots are
> perfectly adequate ...in fact, since it is a tournament method, the
> pairwise vote matrix is adequate by itself.
>
> No more excuses for clone dependent, intractable Kemeny-Young: just use
> RSM!
>
>
> Sent from my MetroPCS 4G LTE Android Device
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
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