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Talk:Fairshare between two and more: Difference between revisions
→Fairness example and cycles: For a different set of numbers.
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===Fairness example and cycles===
I saw Horsts' Perl program above, and recognized that the idea of fairness is hard to bring across so I thought I might do
The set of numbers in this case are not a linear progression, so we (maybe), see the emergence of Thue-Morse as being the most "fair" calculated as the spread in final amounts per person.
'''For all cases we will have have three people A B and C to choose the best at their turn, from the same, ever decreasing pots of money.'''
====18 then 27 Fibonacci numbers====
<pre>Numbers: [2584, 1597, 987, 610, 377, 233, 144, 89, 55, 34, 21, 13, 8, 5, 3, 2, 1, 1]
Order: ABC_ABC_ABC_ABC_ABC_ABC : Simple Repetition
A gets: 2584 + 610 + 144 + 34 + 8 + 2 = 3382
B gets: 1597 + 377 + 89 + 21 + 5 + 1 = 2090
C gets: 987 + 233 + 55 + 13 + 3 + 1 = 1292
Maximum difference in amounts = 2090
Order: ABC-BCA-CAB_ABC-BCA-CAB : Simple Rotation
A gets: 2584 + 233 + 89 + 34 + 3 + 1 = 2944
B gets: 1597 + 610 + 55 + 21 + 8 + 1 = 2292
C gets: 987 + 377 + 144 + 13 + 5 + 2 = 1528
Maximum difference in amounts = 1416
Order: ABC-BCA-CAB-BCA-CAB-ABC : Thue-Morse Fairshare
A gets: 2584 + 233 + 89 + 13 + 5 + 2 = 2926
B gets: 1597 + 610 + 55 + 34 + 3 + 1 = 2300
C gets: 987 + 377 + 144 + 21 + 8 + 1 = 1538
Maximum difference in amounts = 1388
Numbers: [196418, 121393, 75025, 46368, 28657, 17711, 10946, 6765, 4181, 2584, 1597, 987, 610, 377, 233, 144, 89, 55, 34, 21, 13, 8, 5, 3, 2, 1, 1]
Order: ABC_ABC_ABC_ABC_ABC_ABC_ABC_ABC_ABC : Simple Repetition
A gets: 196418 + 46368 + 10946 + 2584 + 610 + 144 + 34 + 8 + 2 = 257114
B gets: 121393 + 28657 + 6765 + 1597 + 377 + 89 + 21 + 5 + 1 = 158905
C gets: 75025 + 17711 + 4181 + 987 + 233 + 55 + 13 + 3 + 1 = 98209
Maximum difference in amounts = 158905
Order: ABC-BCA-CAB_ABC-BCA-CAB_ABC-BCA-CAB : Simple Rotation
A gets: 196418 + 17711 + 6765 + 2584 + 233 + 89 + 34 + 3 + 1 = 223838
B gets: 121393 + 46368 + 4181 + 1597 + 610 + 55 + 21 + 8 + 1 = 174234
C gets: 75025 + 28657 + 10946 + 987 + 377 + 144 + 13 + 5 + 2 = 116156
Maximum difference in amounts = 107682
Order: ABC-BCA-CAB-BCA-CAB-ABC-CAB-ABC-BCA : Thue-Morse Fairshare
A gets: 196418 + 17711 + 6765 + 987 + 377 + 144 + 21 + 8 + 1 = 222432
B gets: 121393 + 46368 + 4181 + 2584 + 233 + 89 + 13 + 5 + 2 = 174868
C gets: 75025 + 28657 + 10946 + 1597 + 610 + 55 + 34 + 3 + 1 = 116928
Maximum difference in amounts = 105504
</pre>
Thue-Morse is best in ''this'' case.
Hmmm, I feel a blog coming on...
--[[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 03:50, 26 June 2020 (UTC)
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