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SPEAKER: |
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TITLE: |
"The 'Proper' Relative Size of Prizes and Rewards Based on Difficulty of Achievements" |
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DAY: |
Wednesday, November 12, 1997 |
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TIME: |
3:30 p.m. [Coffee in BSB-202 at 3:00 p.m.] |
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PLACE: |
BSB-108 |
How much larger should be the reward of a winner in a competition than that of the runner-up? How should the "purse" be divided between the participants, finalists or top-finishers? To answer these questions, we need to quantify the relative difficulty of finishing in different positions, before the actual achievement realizations are known. This problem was posed by Galton and Pearson in 1902. They proposed a scheme for competitions which award two prizes, and where the achievement distribution is normal. I discuss the merits of their idea and propose an alternative scheme which is defined for any number of prizes and is simple and distribution free. It also is shown to possess some desirable monotonicity properties.
If rewards are to be a function of the difficulty of (observed) achievements, a yardstick based on historical performance in the activity in question is needed. The International Amateur Athletic Federation devised such scoring methods for individual events in combined events competitions such as decathlon and pentathlon. I attempt to formalize the manner in which rewards could be based on the distribution of past achievements. Properties of the measures proposed are compared.
Dr. Yigal Gerchak obtained Bachelor and Masters degrees from Tel-Aviv University and a Ph.D. degree in Management Science from University of British Columbia. He is presently a Professor in the Department of Management Sciences at University of Waterloo. His research interests include operations management, modeling health management, decision analysis, Bayesian statistics, operations research, applied probability and mathematical statistics. He has published extensively on these areas. Dr. Gerchak has served in the editorial board of several journals including IEE Transactions, Operations Research, Manufacturing & Service Operations Management and Operations Research Letters. Dr. Gerchak has been a member of the program committee of several international conferences and was the organizer of the 1990 Multi-Echelon Inventory Systems Conference held at University of Waterloo.
The following articles have been provided by Dr. Gerchak to be used as background for his talk. They are on reserved at Thode Library (STATS 770: Statistics Seminar).
[1] Gerchak, Y. (1997). "On the 'Proper' Relative Size of Prizes in Competitions: Galton and Pearson Revisited," submitted for publication (9 pages).
[2] Gerchak, Y. (1997). "Rewards Based on Difficulty of Achievements," submitted for publication (6 pages).