You get them to pay you for one, in terms of the other. People will pay you for a small chance of a big payoff in units of a medium chance of medium payoff. People will pay you for the certainty of a moderate reward by giving up a higher reward with a small chance of failure. All of the good examples of this I can think of are already well-populated business models, but I didn’t try very hard so you can probably find some unexploited ones.
I get that you can do this in principle, but in the specific case of the Allais Paradox (and going off the Wikipedia setup and terminology), if someone prefers options 1B and 2A, what specific sequence of trades do you offer them? It seems like you’d give them 1A, then go 1A → 1B → (some transformation of 1B formally equivalent to 2B) → 2A → (some transformation of 2A formally equivalent to 1A’) → 1B’ ->… in perpetuity, but what are the “(some transformation of [X] formally equivalent to [Y])” in this case?
You can stagger the bets and offer either a 1A → 1B → 1A circle or a 2B → 2A → 2B circle.
Suppose the bets are implemented in two stages. In stage 1 you have an 89% chance of the independent payoff ($1 million for bets 1A and 1B, nothing for bets 2A and 2B) and an 11% chance of moving to stage 2. In stage 2 you either get $1 million (for bets 1A and 2A) or a 10⁄11 chance of getting $5 million.
Then suppose someone prefers a 10⁄11 chance of 5 million (bet 3B) to a sure $1 million (bet 3A), prefers 2A to 2B, and currently has 2B in this staggered form. You do the following:
Trade them 2A for 2B+$1.
Play stage 1. If they don’t move on to stage 2, they’re down $1 from where they started. If they do move on to stage 2, they now have bet 3A.
Trade them 3B for 3A+$1.
Play stage 2.
The net effect of those trades is that they still played gamble 2B but gave you a dollar or two. If they prefer 3A to 3B and 1B to 1A, you can do the same thing to get them to circle from 1A back to 1A. It’s not the infinite cycle of losses you mention, but it is a guaranteed loss.
“People will pay you,” as in different people, true, but I really doubt that you can get the same person to keep paying you over and over through many cycles. They will remember the history, and that will affect their later behavior.
My cards on the table: Allais was right. The collection of VNM axioms, taken as a whole, is rationally non-binding.
You get them to pay you for one, in terms of the other. People will pay you for a small chance of a big payoff in units of a medium chance of medium payoff. People will pay you for the certainty of a moderate reward by giving up a higher reward with a small chance of failure. All of the good examples of this I can think of are already well-populated business models, but I didn’t try very hard so you can probably find some unexploited ones.
I get that you can do this in principle, but in the specific case of the Allais Paradox (and going off the Wikipedia setup and terminology), if someone prefers options 1B and 2A, what specific sequence of trades do you offer them? It seems like you’d give them 1A, then go 1A → 1B → (some transformation of 1B formally equivalent to 2B) → 2A → (some transformation of 2A formally equivalent to 1A’) → 1B’ ->… in perpetuity, but what are the “(some transformation of [X] formally equivalent to [Y])” in this case?
You can stagger the bets and offer either a 1A → 1B → 1A circle or a 2B → 2A → 2B circle.
Suppose the bets are implemented in two stages. In stage 1 you have an 89% chance of the independent payoff ($1 million for bets 1A and 1B, nothing for bets 2A and 2B) and an 11% chance of moving to stage 2. In stage 2 you either get $1 million (for bets 1A and 2A) or a 10⁄11 chance of getting $5 million.
Then suppose someone prefers a 10⁄11 chance of 5 million (bet 3B) to a sure $1 million (bet 3A), prefers 2A to 2B, and currently has 2B in this staggered form. You do the following:
Trade them 2A for 2B+$1.
Play stage 1. If they don’t move on to stage 2, they’re down $1 from where they started. If they do move on to stage 2, they now have bet 3A.
Trade them 3B for 3A+$1.
Play stage 2.
The net effect of those trades is that they still played gamble 2B but gave you a dollar or two. If they prefer 3A to 3B and 1B to 1A, you can do the same thing to get them to circle from 1A back to 1A. It’s not the infinite cycle of losses you mention, but it is a guaranteed loss.
“People will pay you,” as in different people, true, but I really doubt that you can get the same person to keep paying you over and over through many cycles. They will remember the history, and that will affect their later behavior.
My cards on the table: Allais was right. The collection of VNM axioms, taken as a whole, is rationally non-binding.