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Debate Partitions

Debate Partitions. Restricted Versions of Games. Win restriction: [w x]: only games that x wins Fault restriction: [ fl x]: only games in which x makes a fault Control restriction: [c x]: only games that x controls [c x] = [w x] union [ fl x]

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Debate Partitions

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  1. Debate Partitions

  2. Restricted Versions of Games • Win restriction: [w x]: only games that x wins • Fault restriction: [fl x]: only games in which x makes a fault • Control restriction: [c x]: only games that x controls • [c x] = [w x] union [fl x] • Also add a complement restriction operation for each of the restriction operations: [!w x],[!fl x],[!c x] • [w x] union [!w x] = all debates • x!=y: [fl y] [fl x] = empty set of debates =[w y][w x]

  3. Focus on 2, 3, 4, 5 All debates 1 [!fl y] [w x] = [!c y] [w x] 2 [!w y] [fl x] = [!c y] [fl x] 3 [fl y] [w x] = [c y] [w x] 4 [w y] [fl x] = [c y] [fl x] 5 [!w x] [fl y] = [!c x] [fl y] 6 [!fl x] [w y] = [!c x] [w y] 7 [!c x] [!c y] c x c y x wins y at fault 1 5 3 4 2 6 y wins x at fault 7

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