[EM] single elimination tournaments

[Simmons, Forest]

Suppose that after the ballots come in and after the pairwise matrix has been published, any and all are allowed to submit single elimination tournament schedules in the form of binary trees of minimum possible depth (approximately log base two of the number of candidates).

All of these tournaments are then carried out on the basis of the pairwise matrix, recording the winning and losing votes at each branch of the trees.

Then the tournament whose (fill in your suggested criterion) is the tournament used to select the winner.

For example, the tournament whose maximum losing vote is minimal is the tournament that selects the winner.

Example:

49 C,  24 B,  27 A>B

T1:  ((A,B),C)  the losing votes are 24 and 27 with max 24.

T2: ((A,C),B)  the losing votes are 27 and 49 with max 49.

T3:  ((B,C),A) the losing votes are 49 and 24 with max 49.

 So T1 is the winning single elimination tourney, whose winner is C.

 

Forest

 



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