This week we had two posts on the foundations of rationality and two on whether there’s been a recent surge in government spending.
I claim these things:
Claim One: I have here a mystery pet that might be a dog and might be a cat. If you prefer dogs to cats, you’ll prefer a dog to the mystery prize — and vice versa.
Claim Two: If you prefer dogs to cats, then you’ll prefer an 11% chance at a dog to an 11% chance at a cat — and vice versa.
Claim Three: The same things are true if you replace “dog” and “cat” with any other prizes you care to think of.
Claim Four: The desirability of a lottery depends only on the prizes and the probabilities of winning.
Claim Five: If you accept Claims One through Four, then you must answer either A to both of the following questions or B to each of the following questions:
Question 1: Which would you rather have:
- A million dollars for certain
- A lottery ticket that gives you an 89% chance to win a million dollars, a 10% chance to win five million dollars, and a 1% chance to win nothing.
Question 2: Which would you rather have:
- A lottery ticket that gives you an 11% chance at a million dollars (and an 89% chance of nothing)
- A lottery ticket that gives you a 10% chance at five million dollars (and a 90% chance of nothing)
Claim Five, as I’ve explained in the earlier posts, is a logical necessity. So if you want to defend inconsistent answers to Questions 1 and 2, then you are forced to deny at least one of Claims One through Four. It would be very helpful if participants in the ongoing discussion would specify exactly which claim they dispute.
I’ll have more to say about rationality — and a variety of other topics — over the next week.