Talk:Fairshare between two and more: Difference between revisions
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--[[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 03:50, 26 June 2020 (UTC) |
--[[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 03:50, 26 June 2020 (UTC) |
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===Fairness and randomized rewards=== |
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I needed to further investigate Horst's work above finding repeated rotations being best, being best, and me finding that for Fibonacci (also above), Thue-Morse wins over repeated rotations. |
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I wrote something that for the rewards just took some random integers and ordered them highest to lowest; then used different orderings of three people selecting their best reward on the from that reward order. The winning ordering would have the least difference between peoples total reward, '''and crucially multiple orderings can have the win if they all have the same minimum spread of peoples winnings.''' |
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;Results: |
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<pre>## ALL SIMULATIONS BEING OF 3 PEOPLE TAKING TURNS TO TAKE EVER DECREASING AMOUNTS OF CASH FROM A REWARD_LIST. |
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Give summary stats on 250_000 repetitions of: |
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New reward_list = an ordered, random, selection of between 3 and 84 ints from the range 999_999 .. 0: |
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(Note: reward_list length is always a multiple of 3) |
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Each of the following 4 methods of ordering used to order this reward_list [ |
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"Randomised: Gen from repeat(shuffle('ABC')) eg ABC CAB ABC ABC BCA ...", |
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"Simple Repetition: Gen from repeat('ABC') eg ABC ABC ABC ...", |
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"Simple Rotation: Gen from repeat(rotate('ABC')) eg ABC BCA CAB, ABC BCA CAB, ... ", |
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"Thue-Morse Fairshare: Start _sequence_ not replicated later, but 'balanced' ABC's", |
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] |
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The ordering(s) with the LEAST spread of winnings per person wins the round. |
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SUMMARY |
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Wins for All 250_000 repetitions |
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order_by_thue_morse : 116_022 |
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order_by_rotation : 116_007 |
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order_by_randomise : 51_744 |
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order_by_repetition : 8_905 |
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Wins for All 88_099 repetitions where: len(reward_list) div 9 == 0 |
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order_by_thue_morse : 37_591 |
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order_by_rotation : 37_471 |
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order_by_randomise : 13_037 |
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Wins for All 115_767 repetitions where: len(reward_list) div 9 == 3 |
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order_by_rotation : 42_194 |
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order_by_thue_morse : 42_080 |
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order_by_randomise : 22_588 |
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order_by_repetition : 8_905 |
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Wins for All 88_812 repetitions where: len(reward_list) div 9 == 6 |
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order_by_thue_morse : 36_351 |
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order_by_rotation : 36_342 |
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order_by_randomise : 16_119 |
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Wins for All 26_679 repetitions where: len(reward_list) div 27 == 0 |
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order_by_thue_morse : 11_310 |
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order_by_rotation : 11_209 |
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order_by_randomise : 4_160 |
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Wins for All 62_423 repetitions where: len(reward_list) div 27 == 3 |
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order_by_thue_morse : 20_059 |
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order_by_rotation : 19_973 |
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order_by_randomise : 13_486 |
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order_by_repetition : 8_905 |
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Wins for All 35_168 repetitions where: len(reward_list) div 27 == 6 |
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order_by_thue_morse : 14_211 |
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order_by_rotation : 14_137 |
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order_by_randomise : 6_820 |
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Wins for All 34_589 repetitions where: len(reward_list) div 27 == 9 |
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order_by_rotation : 15_083 |
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order_by_thue_morse : 14_936 |
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order_by_randomise : 4_570 |
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Wins for All 26_598 repetitions where: len(reward_list) div 27 == 12 |
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order_by_rotation : 11_068 |
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order_by_thue_morse : 10_888 |
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order_by_randomise : 4_642 |
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Wins for All 26_654 repetitions where: len(reward_list) div 27 == 15 |
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order_by_thue_morse : 11_045 |
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order_by_rotation : 10_976 |
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order_by_randomise : 4_633 |
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Wins for All 26_831 repetitions where: len(reward_list) div 27 == 18 |
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order_by_thue_morse : 11_345 |
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order_by_rotation : 11_179 |
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order_by_randomise : 4_307 |
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Wins for All 26_746 repetitions where: len(reward_list) div 27 == 21 |
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order_by_rotation : 11_153 |
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order_by_thue_morse : 11_133 |
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order_by_randomise : 4_460 |
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Wins for All 26_990 repetitions where: len(reward_list) div 27 == 24 |
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order_by_rotation : 11_229 |
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order_by_thue_morse : 11_095 |
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order_by_randomise : 4_666 |
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</pre> |
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Thue-Morse wins for this case of random rewards, but not by much! |
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--[[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 12:04, 26 June 2020 (UTC) |