nickeye
07-19-2002, 04:23 AM
good one from July's Scientific American...
A mathematically inclined judge uses a unique form of arbitration to settle monetary disputes. As in most arbitrations, the plaintiff and defendant present their evidence to the judge. But before the plaintiff begins, he writes down on a piece of paper how much money he thinks he should get--let's call the amount P--and puts the paper in a sealed envelope. Then the defendant writes down how much she is willing to pay--call it D--and puts that number in a separate envelope.
The judge does not know P or D. Once the plaintiff and defendant have presented their evidence, the judge determines an equitable monetary award, called J. But in this form of arbitration, the amount actually paid to the plaintiff is determined by comparing J with P and D. If J is closer to P, the defendant pays P; if J is closer to D, the defendant pays D. For example, say the plaintiff thinks he deserves $18 million, the defendant thinks she should pay nothing, and the judge decides the complaint is worth $8 million. Because $8 million is closer to zero than to $18 million, the plaintiff gets nothing.
Your challenge is to find the best strategy for the plaintiff. Suppose the judge hints that his award will be between $3 million and $10 million, with all numbers in that range having the same probability of being chosen. How much money should the plaintiff request to maximize his expected compensation?
<center><img src="http://njpconsulting.homestead.com/files/eyeballhead.jpg"></center>
A mathematically inclined judge uses a unique form of arbitration to settle monetary disputes. As in most arbitrations, the plaintiff and defendant present their evidence to the judge. But before the plaintiff begins, he writes down on a piece of paper how much money he thinks he should get--let's call the amount P--and puts the paper in a sealed envelope. Then the defendant writes down how much she is willing to pay--call it D--and puts that number in a separate envelope.
The judge does not know P or D. Once the plaintiff and defendant have presented their evidence, the judge determines an equitable monetary award, called J. But in this form of arbitration, the amount actually paid to the plaintiff is determined by comparing J with P and D. If J is closer to P, the defendant pays P; if J is closer to D, the defendant pays D. For example, say the plaintiff thinks he deserves $18 million, the defendant thinks she should pay nothing, and the judge decides the complaint is worth $8 million. Because $8 million is closer to zero than to $18 million, the plaintiff gets nothing.
Your challenge is to find the best strategy for the plaintiff. Suppose the judge hints that his award will be between $3 million and $10 million, with all numbers in that range having the same probability of being chosen. How much money should the plaintiff request to maximize his expected compensation?
<center><img src="http://njpconsulting.homestead.com/files/eyeballhead.jpg"></center>