I may have an insight to this, and I thought of 2 Allais related questions that are separate scenarios than that in the OP to express my idea. I’ll give them a different set of numbers to make it easier to tell apart. Here is the first scenario:
3A: You are given 2 million, with a 100% chance.
3B: You are given 2 million with 89 % chance, 1 million with 1% chance, and 5 Million with 10% chance.
4A: You are given 1 million with 89% chance, and 2 million with a 11% chance.
4B: You are given 1 million with a 90% chance, and 6 million with a 10% chance.
As far as I can tell, this is identical to the scenario, but with an extra 1 million dollars added to all positions. Personally, I now feel much better about picking 3A as opposed to 3B. (I’m worried, but not panicky/fretting.), whereas in the comparable section (1A/1B), I’m MUCH more fearful.
I was curious about why I might think this, and then thought of my second scenario:
This bet repeats 20 times. You must pick the same strategy each time. A rabbit is 1 day of Food, and a deer is 5 days of food. You begin with no food. If you go a full day without food, you will not have the energy to run from wolves at night and they will kill you. Food does not go bad.
5A: 100% chance of Rabbit.
5B: 89% chance of Rabbit, 1% chance of No food, 10% chance of Deer.
6A: 11% chance of Rabbit. 89% chance of No food.
6B: 10% chance of Deer. 90% chance of No food.
When do you die less? 5A, or 5B? When do you die less? 6A, or 6B?
I may have an insight to this, and I thought of 2 Allais related questions that are separate scenarios than that in the OP to express my idea. I’ll give them a different set of numbers to make it easier to tell apart. Here is the first scenario:
3A: You are given 2 million, with a 100% chance.
3B: You are given 2 million with 89 % chance, 1 million with 1% chance, and 5 Million with 10% chance.
4A: You are given 1 million with 89% chance, and 2 million with a 11% chance.
4B: You are given 1 million with a 90% chance, and 6 million with a 10% chance.
As far as I can tell, this is identical to the scenario, but with an extra 1 million dollars added to all positions. Personally, I now feel much better about picking 3A as opposed to 3B. (I’m worried, but not panicky/fretting.), whereas in the comparable section (1A/1B), I’m MUCH more fearful.
I was curious about why I might think this, and then thought of my second scenario:
This bet repeats 20 times. You must pick the same strategy each time. A rabbit is 1 day of Food, and a deer is 5 days of food. You begin with no food. If you go a full day without food, you will not have the energy to run from wolves at night and they will kill you. Food does not go bad.
5A: 100% chance of Rabbit.
5B: 89% chance of Rabbit, 1% chance of No food, 10% chance of Deer.
6A: 11% chance of Rabbit. 89% chance of No food.
6B: 10% chance of Deer. 90% chance of No food.
When do you die less? 5A, or 5B? When do you die less? 6A, or 6B?