1. 1JURIX 05Looks/Loui On Game Mechanisms and Procedural Fairness Moshe Looks Ronald P. Loui Washington University in St. Louis, USA

2. 2JURIX 05Looks/Loui Fairness Distributive Fairness (who gets what?) Procedures –Can determine distributions –Can also determine predicates Procedural vs. Substantive Fairness –Substantive refers to outcomes (equal split) –Procedural refers to construction of outcomes

3. 3JURIX 05Looks/Loui Procedural Fairness Procedure justifies outcome –If properly conducted –Parties contribute inputs –Outputs are constructed upon inputs+chance –Justify procedure independently Disputants –Agree to play a game –Bound to outcome of game –Like contracts Society prescribes procedures

4. 4JURIX 05Looks/Loui Fairness as Appropriateness Structural Fairness –Symmetry of rules –Equality of opportunity –Exchangeability of endowments & resources Teleological Fairness –Justifiable asymmetry –Based on social roles –Ultimatum game: Let's flip a coin …. But it's MY envelope… Let's flip a biased coin –Rawls: role ex-ante exchangeability vs. positional ex-ante exchangeability

5. 5JURIX 05Looks/Loui Procedural Fairness Personally at stake: –Procedures for argument need to be Fair Efficient Appropriate I, Tom Gordon, Gerard Vreeswijk, Arno Lodder, and Rohit Parikh believe –Correctness of computation ~ fairness of procedure –Past student efforts: Anne Jump, Alan Bisarya, Ricky Wofsey, James Rosen, Alex Schiller

6. 6JURIX 05Looks/Loui What Formalism? JKP! (jon-ken-po/rock-paper-scissors) is –One play of simultaneous choice from {J, K, P} –! = Check for winner (possibly indeterminate) JKP! n –As many as n rounds of JKP until winner –More decisive than JKP n-1 JKP! * –As many rounds as needed –Uncountably decisive

7. 7JURIX 05Looks/Loui More Formalism HEADS is –One play of {INC A /.5; INC B /.5} = HEADS –HEADS k BEST! is best of k rounds of HEADS p k BEST! reduces effect of error/chance in p! –Two counferfactuals: If p has an A-bias, the probability of p k BEST!  A … p k BEST! is more like p*BEST! than p k-1 BEST! –Larger k takes more time, can spread distributions

8. 8JURIX 05Looks/Loui More Formalism Chance determination of procedure –CHANCE1 p = {p A /.5; p B /.5} –Determines by chance who moves first –Effect of chance depends on later choice: CHANCE1 NAMEHIGHESTNUMBER! CHANCE1 TICTACTOE! CHANCE1 CHESS! CHANCE1 GO! Also Chance determination of endowments –CHANCE$A CHANCE$B MONOPOLY –Endowment difference reducible to procedural choice –Except when claiming strategic-familial resemblance

9. 9JURIX 05Looks/Loui More Formalism Baseball Innings –INN A = BATS A BATS B –Apparent game is INN A 9 BEST! –Actual game is INN A 9 BEST! XTRA A –XTRA A = (INN A BEST!)* –Chance/Choice ontology is unclear with games of physical skill –(derivably possibly) Fairer Procedures (no home info advantage): INN A 9 BEST! CHANCE1 XTRA CHANCE1(INN 9 BEST! XTRA) (CHANCE1 INN) 9 ! (CHANCE1 INN BEST!)* MERIT1(INN 9 BEST! XTRA)

10. 10JURIX 05Looks/Loui Q2 and Other Arguments Nested quantifiers (Q2) P is solvable (for A) iff –there exists a s A s.t. for every s B, A wins –TICTACTOE is solvable for 5+ yr olds –TICTACTOE is unsolvable for many Reject many dominant strategy arguments –Players not omniscient, non-optimal –Optimal play depends on population/opponent –s A  A Some reductions: –x CHANCEWIN! = CHANCEWIN!

11. 11JURIX 05Looks/Loui Aspects with Formalizable Tradeoffs MERIT: Degree to which rules promote a skill –Management of risk –Tactical lookahead CHANCE: –Meritocracy of good luck DECISIVENESS/EFFICIENCY: –Amount of input required –Potential to be indeterminate SPREAD: –Range of outcomes

12. 12JURIX 05Looks/Loui Future Axioms CHANCE1! –Removes specific asymmetry –Usually increases ex-ante exchangeability –Usually decreases merit, ex-post exchangeability p k BEST! –Magnifies meritocracy of p! –Decreases decisiveness/efficiency JKP! –Functions like an unbiased chance mechanism

13. 13JURIX 05Looks/Loui Prospects Main technical problem was notation for procedures Main problem now is that the subject is large and unexplored Trying to make simple self-contained observations is challenging Building inventory of procedural primitives We are at a naïve stage Rawl's "pure procedural justice" and "veil of ignorance" welfare arguments DO seem naïve to us!