[EM] Round Robin Tournament Showings (correction)
Susan Simmons
suzerainsimmons at outlook.com
Wed Aug 4 15:09:25 PDT 2021
The ratio R(X) should be ...
... the smallest pairwise support for X divided by the greatest pairwise opposition to X.
In the sports context that would be the ratio of X's smallest score to the greatest score against it.
In terms of the pairwise matrix ... it is the smallest entry in X's row divided by the largest entry in X's column.
The entry in row i of column j is simply the number of points team i scored in the game against team j.
In the election context it is the number of ballots on which candidate i was strictly preferred over candidate j ... plus the number on which they were both voted equal Top and half the number on which they were voted equal but not Top or Bottom.
I hope everybody gets this corrected definition of the ratio R.
Sent from my MetroPCS 4G LTE Android Device
-------- Mensaje original --------
De: Susan Simmons <suzerainsimmons at outlook.com>
Fecha: 4/8/21 11:30 a. m. (GMT-08:00)
A: election-methods at lists.electorama.com
Asunto: Re: Round Robin Tournament Showings
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
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