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Dynamics of Rule Revision and Strategy Revision in Legislative Games

Dynamics of Rule Revision and Strategy Revision in Legislative Games

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Dynamics of Rule Revision and Strategy Revision in Legislative Games

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  1. Dynamics of Rule Revision and Strategy Revision in Legislative Games Moshe Looks Ronald P. Loui Barry Cynamon Washington University in St. Louis, USA Looks/Loui/Cynamon

  2. Basic Idea • Legislators don't always • Say what they mean nor • Mean what they say • Hart: there is a limit to the use of language… • Sometimes the rule-makers don't even agree • Be deliberately vague • Toss the issue to the courts Looks/Loui/Cynamon

  3. Legislation is Worth Studying • Rules change • Often they change in response to: • Agents behaving badly • Agents discovering unintended strategies • North there is institutional learning… • Legislate to perform strategy extinction Looks/Loui/Cynamon

  4. How to Study Legislative & Institutional Dynamics? • Multi-agent systems simulation • Can we build a model that exhibits the interesting phenomena? • Agent modeling • Institutional modeling • Plausible dynamical modeling • Would anyone (outside AI) be able to work with rules: • As text? • As logic fragments? • As procedures? Looks/Loui/Cynamon

  5. Idea! • All edict takes the form of • an objective function on k variables • to be maximized • Legislative revision = change of function • Legislative abridgement = projection • Onto subspace • I.E., use only a subset of the variables Looks/Loui/Cynamon

  6. Target Phenomenon I • Tenure-granting colleges often publish rules: • Will count journal publications • Will count student evaluations of teaching • Will count amounts of external research funding • Legitimately interested in • Productivity • Intellectual impact • Teaching ability • Published criteria: • Observable • Apparently precise Looks/Loui/Cynamon

  7. Target Phenomenon I • Those seeking tenure subvert the spirit of the rules by: • Joining long co-author lists • Reporting research in minimal-publishable-units • Avoiding teaching difficult courses • Giving inflated grades • Doing research for the sake of funding • Adding their names as Co-PI to big projects • In the worst case, there is misdirection • Papers written for the resume, not for the scholarship • Teaching aimed at good feedback, not long-term student growth • Research aimed at getting funding, not intellectual impact Looks/Loui/Cynamon

  8. Target Phenomenon I • Tenure Committees Respond by • Normalizing papers by author count • Evaluating the five best publications • Measuring student performance objectively • Capping funding amounts that can be reported • Requiring co-PI's to show students supported on funds • Candidates for tenure respond in situ to new reqirements • They don't toss their resumes & start from scratch Looks/Loui/Cynamon

  9. Target Phenomenon II • Tax regulations seek to encourage charitable deductions including (as cases are decided): • Donations of books to book sales • Donations of cars to non-profit organizations • Donations to arts performance organizations Looks/Loui/Cynamon

  10. Target Phenomenon II • Taxpayers respond by • Buying books for the purpose of donating them • Donating cars that do not run • Donating to performance companies in exchange for free tickets • Over time, through legislative misdirection • agents optimize the wrong function Looks/Loui/Cynamon

  11. Target Phenomenon II • Tax regulators respond by • Requiring receipts showing purchase amounts • Allowing deduction for only car’s value realized on sale • Reducing amounts of donations by any quid-pro-quo considerations • Taxpayers respond again by donating less • New abridgement repairs short-term misdirection • Successful strategy extinction or scenario extinction • In time, different legislative misdirection Looks/Loui/Cynamon

  12. Our Model • There is a veridical value function: • V(x, y, z, …) • “known” to the legislators • At any time, there is an abridgement of V: • A(x, z) • A function of fewer variables • More generally, use a projection of V • public Looks/Loui/Cynamon

  13. Our Model II • At any time, an agent’s strategy/position is • A point in V-space • (9, 10, 1, …) • With de jure value A(9, 1) • With de facto value V(9, 10, 1, …) • Agents occupy admissible positions • E.g., declare that (0, 0, 0, …) is prohibited • Admissibility is not known to all • Admissibility is discovered through search • Admissibility can also change with time Looks/Loui/Cynamon

  14. Our Model III • A legislature can respond: • Change the set of admissible positions • Change the function A (OUR FOCUS) • An agent can respond: • Search for point with higher A-value • Learn from other agents • Where are the high A-values • Where are the admissible points Looks/Loui/Cynamon

  15. Simulations • Example: Greedy Non-Omniscient Agents • Look at neighborhood around current point • Move to highest point with highest A-value • Bound how much they can move • Example: Imitative Non-Omniscient Agents • Move toward average of others • If it is better than where you are • Bound how much they can move Looks/Loui/Cynamon

  16. Looks/Loui/Cynamon

  17. Simulations • Example: Incentivizing the Average • Revise A so AverageAgent maximizes V • Project V onto line between global opt and avg position • Mix(A,A') to bound difference • Example: Extinguishing the Worst • Find d* = maximum V  A • Choose A' to minimize A'(d*) • Diff(A,A') is bounded Looks/Loui/Cynamon

  18. Simulations • How quickly can the legislator act? • Dominant legislature • Revises as quickly as agents, bounds generous • Parity • Revises as quickly as agents, bounds on par • Dominant agents • Agents revise more quickly, bounds on par Looks/Loui/Cynamon

  19. Looks/Loui/Cynamon

  20. Background Functions • In addition to V, A, add • B which models • The public "spirit" of the laws • E.g., B is a time-average of A over a period • Agents who maximize B are more robust to changes of A • B contains additional knowledge about A Looks/Loui/Cynamon

  21. Background Functions • Taxonomy of agents: • A-maximizer at the expense of B is a rat • A-maximizer s.t. high B is a literalist • B-maximizer s.t. high A is a wolf • B-maximizer at the expense of A is an idealist • Imitative A-maximizer is a sheep • Novel A- but not B-maximizer is an exploiter • Novel A- & B-maximizer is a producer Looks/Loui/Cynamon

  22. Conclusions • Result? A model with rich and appropriate dynamics • Main contribution: depicting legislative phenomena in mathematical economics (or ICMAS) clothing • Would like A-B-V triad to be memorable • Main idea: there must be a reason to revise • Agents learn • Legislative misdirection accrues • Much legislation is repair of old abridgement Looks/Loui/Cynamon