A tournament to decide which notes to devote attention to polishing

Kragen Javier Sitaker, 2017-07-19 (2 minutes)

I should start publishing some of these notes. But how to select? There are 236 of them! Maybe read through four of them today, pick the two that seem to have the most potential, improve them, then repeat the process the next day, then do the same with the four winners.

To find some that are in the top, say, 10%, we need three or four such tournament levels. Four tournament levels look like this:

            Day 1: A B C D
            Day 2: E F G H
        Day 3:     A B E F
            Day 4: I J K L
            Day 5: M N O P
        Day 6:     I J M N
    Day 7:         A B I J
            Day 8: Q R S T
            Day 9: U V W X
        Day a:     Q R U V
            Day b: Y Z α β
            Day c: γ δ ε ζ
        Day d:     Y Z γ δ
    Day e:         Q R Y Z
Day f:             A B Q R

That should give two items that would, in the perfect-fairness case, be in the top 6.25% of the essays, with four revisions, at the cost of reading an essay 60 times (reading 32 unique essays) and doing 30 revisions. The two-of-four comparison system obviously deviates somewhat from perfect fairness, although, if the comparisons are reliable, it will find the best two; but the runners-up may not be the #3 and #4 best. (In the above example, C and D could have been the #3 and 4 best, but still be eliminated on day 1 because of having the bad luck of sharing the same day with A and B, if those were #1 and #2.)

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