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user 32748
Binary relations that reflect which states of the world an agent considers to be most desirable. Preferences are a fundamental ingredient in the axiomatic study of consumer choice decision theory.
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Non decreasing function for utility transformation
Since $u(x)$ represents $\succsim$, $\succsim$ must be rational. By completeness, $\neg (x\succsim y) \iff x \prec y$. Therefore, the claim that $$v(x) \geq v(y) \iff x\succsim y, \forall x, y$$ is eq …
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