My resolution to this, without changing my intuitions to pick things that I currently perceive as ‘simply wrong’, would be that I value certainty. A 9⁄10 chance of winning x dollars is worth much less to me than a 10⁄10 chance of winning 9x/10 dollars. However, a 2⁄10 chance of winning x dollars is worth only barely less than a 4⁄10 chance of winning x/2 dollars, because as far as I can tell the added utility of the lack of worrying increases massively as the more certain option approaches 100%. Now, this becomes less powerful the closer the odds, are, but slower than the dollar difference between the two change. So a 99% chance of x is barely effected by this compared to a 100% chance of .99x, but still by a greater value than .01x, and the more likely option still dominates. I might take a 99% chance of x over a 100% chance of .9x, however, and I would definitely prefer a 99% chance of x over a 100% chance of 0.8x.
EDIT: Upon further consideration, this is wrong. If presented with the actual choice, I would still prefer 1A to 1B, but to maintain consistency I will now choose 2A > 2B.
My resolution to this, without changing my intuitions to pick things that I currently perceive as ‘simply wrong’, would be that I value certainty. A 9⁄10 chance of winning x dollars is worth much less to me than a 10⁄10 chance of winning 9x/10 dollars. However, a 2⁄10 chance of winning x dollars is worth only barely less than a 4⁄10 chance of winning x/2 dollars, because as far as I can tell the added utility of the lack of worrying increases massively as the more certain option approaches 100%. Now, this becomes less powerful the closer the odds, are, but slower than the dollar difference between the two change. So a 99% chance of x is barely effected by this compared to a 100% chance of .99x, but still by a greater value than .01x, and the more likely option still dominates. I might take a 99% chance of x over a 100% chance of .9x, however, and I would definitely prefer a 99% chance of x over a 100% chance of 0.8x.
EDIT: Upon further consideration, this is wrong. If presented with the actual choice, I would still prefer 1A to 1B, but to maintain consistency I will now choose 2A > 2B.