The Slippage Configuration Is Always the Least Favorable Configuration for Two Alternatives

Abstract

Performance guarantees for multinomial selection procedures are usually derived by finding the least favorable configuration (LFC)—the one for which the probability of correct selection is minimum outside the indifference zone—and then evaluating the procedure on that configuration. The slippage configuration has been proved to be the LFC for several procedures and has been conjectured to be the worst for some other procedures. The principal result of this article unifies and extends all previous results for two alternatives: the slippage configuration is the worst for all procedures that have a finite expected number of trials and always select the alternative with more successes. A generalization of the key inequality in the proof to an arbitrary number of alternatives is conjectured.

Keywords:

• Least favorable configuration
• Multinomial selection
• Ranking
• Selection
• Slippage configuration

Subject Classification:

• 62F07
• 62L10
• 62L15
• 60G40
• 60C05
• 62L15

ACKNOWLEDGMENTS

Thanks to David Goldsman for background information, reading a prior draft, and his encouragement. Thanks also to the Editor Nitis Mukhopadhyay and the referees for reviewing the manuscript and improving its formatting.

Notes

Recommended by David Goldsman