DEAR ALLSTAT LIST:
A MANAGEMENT STRATEGY COLLEAGUE OF MINE IS INTERESTED IN THE FOLLOWING
ISSUE. CONSIDER THE MISS AMERICA PAGEANT. SUPPOSE THAT
(1) BEAUTY IS NORMALLY DISTRIBUTED ACROSS THE US WITH NO DIFFERENCE
BETWEEN STATES
(2) EACH STATE CHOOSES THEIR MOST BEAUTIFUL WOMAN TO SEND TO THE
PAGEANT.
(3) THE PAGEANT JUDGES CORRECTLY RANK THE 51 STATE CANDIDATES FROM
MOST TO LEAST BEUATIFUL.
OBVIOUSLY CALIFORNIA HAS A BIG ADVANTAGE OVER MARYLAND BECAUSE OF
ITS MUCH BIGGER POPULATION. THE QUESTION OF INTEREST IS: WHAT IS THE
DISTRIBUTION OF THE RANK OF A STATE'S CANDIDATE AS A FUNCTION OF THE
POPULATION OF THAT STATE (AND PRESUMABLY ALL THE OTHER STATES)?
THE QUESTION IS EASY TO STATE AS A QUESTION ABOUT THE ORDER STATISTICS
OF A SET OF EXTREMES. THE SCIENCE OF STATISTICS OF EXTREMES BEING WELL
DEVELOPED, I FIGURED THERE ARE PROBABLY MANY PUBLISHED PAPERS ON THIS
AND SIMILAR PROBLEMS. PERHAPS THERE ARE ALSO PUBLICATIONS IN THE SPORTS
STATISTICS LITERATURE.
WHY IS MANAGEMENT SCIENCE INTERESTED IN SUCH ISSUES? BECAUSE IT IS AN
ARTICLE OF FAITH THAT SOME FIRMS/COUNTRIES HAVE SUSTAINABLE COMPETETIVE
ADVANTAGE WHICH EXPLAINS THEIR CONSISTENT SUPERIOR PERFORMANCE. BUT A
CASE CAN SOMETIMES BE MADE THAT PERFORMANCE CAN BE EXPLAINED IN TERMS
OF A STATISTICAL PROCESS WHERE THERE IS NO DIFFERENCE BETWEEN FIRMS
AND COUNTRIES.
CHRIS J. LLOYD
AUSTRALIAN GRADUATE SCHOOL OF MANAGEMENT
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