It’s very simple. We have the following assumptions (axioms):
for any two states, you prefer one over the other, or, you are indifferent, we will say A > B to mark A is preferred over B, A~B to say that you are indifferent, and A ≥ B to say you are either preferring A or you are indifferent.
if A ≥ B and B ≥ C, then A ≥ C, and at the same time A ~ C iff both A ~ B and B ~ C.
~ is equivalency relation (behaves like =)
The conclusion of above assumptions is no cycles. Now, each of them seems as a reasonable assumption. Sure, we can choose different set of axioms, but why? What are we trying to model?
It’s very simple. We have the following assumptions (axioms):
for any two states, you prefer one over the other, or, you are indifferent, we will say A > B to mark A is preferred over B, A~B to say that you are indifferent, and A ≥ B to say you are either preferring A or you are indifferent.
if A ≥ B and B ≥ C, then A ≥ C, and at the same time A ~ C iff both A ~ B and B ~ C.
~ is equivalency relation (behaves like =)
The conclusion of above assumptions is no cycles. Now, each of them seems as a reasonable assumption. Sure, we can choose different set of axioms, but why? What are we trying to model?