What is the best generic agenda for SPE or Agenda Based Landau (ABL)?
I am assuming that (inclusive) pairwise information is available in the form of a matrix that has a row for each alternative... the j_th entry in the row for alternative i is the number of ballots on which alternative i is ranked preferable or equal to alternative j. In particular the k_th entry in row k is the number of ballots on which alternative k is ranked equal to itself, since it cannot be preferred ahead of itself. This number is sometimes referred to as the implicit approval for alternative k. (It must have some acceptability or why bother ranking it at all?)
Now within each row, sort the entries left to right from smallest to largest.
Now sort the rows among themselves by the value in the first entry of each row ... smaller to larger, top to bottom, and resolve ties by comparing entries further to the right as in dictionary order when they start the same way.
The more candidates, the more tie-breaking entries!
The method is "nothing, if not decisive!"
Now that the rows are in order, if you can remember which row goes with which alternative, you have your agenda!
This method can be adapted for round robin tournaments starting with the pairwise "score against" matrix.
The j_th entry in the i_th row is the score of team i in its match against tem j. The diagonal elements will all be zeros.
So once the entries within the rows are sorted from from smallest to greatest, every row will start with a zero. That's a good reason to go into overtime if necessary to resolve at least some of the ties.
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