Probability theoretic “better” is intransitive. See non-transitive dice
Imagine your life is a dice, and you have three options:
4 4 4 4 4 1
You live a mostly peaceful life, but there is a small chance of doom.
5 5 5 2 2 2
You go on a big adventure: either a trasure or a disappointment.
6 3 3 3 3 3
You put all your cards in a lottery for epic win, but on fail, you will carry that with you.
If we compare them: peace < adventure < lottery < peace, so I would deny transitivity.
The intransitive dice work because we do not care about the margin of victory. In expected value calculations the same trick does not work, so these three lives are all equal, with expected value 7⁄2
Probability theoretic “better” is intransitive. See non-transitive dice
Imagine your life is a dice, and you have three options:
4 4 4 4 4 1
You live a mostly peaceful life, but there is a small chance of doom.
5 5 5 2 2 2
You go on a big adventure: either a trasure or a disappointment.
6 3 3 3 3 3
You put all your cards in a lottery for epic win, but on fail, you will carry that with you.
If we compare them: peace < adventure < lottery < peace, so I would deny transitivity.
The intransitive dice work because we do not care about the margin of victory. In expected value calculations the same trick does not work, so these three lives are all equal, with expected value 7⁄2