<p>My textbook says that "if a weak preference relation is complete and transitive, the strict preference relation MUST be asymmetric and negatively transitive". Now, I think I understand why it must be asymmetric - all strict preference relations are asymmetric, correct? However, I don't understand why it is negatively transitive. If the weak preference is transitive, couldn't the strict preference also be transitive?</p>

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2019-02-09T06:50:13.577Z
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iBooot
<microeconomics><preferences>
If a weak preference relation is complete and transitive, why is the strict preference relation negatively transitive?
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# If a weak preference relation is complete and transitive, why is the strict preference relation negatively transitive?

(Asked by: username_0 on 2019-02-09)

My textbook says that "if a weak preference relation is complete and transitive, the strict preference relation MUST be asymmetric and negatively transitive". Now, I think I understand why it must be asymmetric - all strict preference relations are asymmetric, correct? However, I don't understand why it is negatively transitive. If the weak preference is transitive, couldn't the strict preference also be transitive?

**Tags:** microeconomics, preferences

> **Comments:**
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