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## Regarding Theorem 1.115 from the Seven Sketches
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Strategic preorders<em>‼︎</em>
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- $P$: preorder of strategies (e.g., ordered by risk)
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- $Q$: be a preorder of game states (e.g., ordered by payoff)
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- A function $f : P \to Q$ that finds the *best possible outcome* for a given strategy is **Left Adjoint**
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- Due to T1.115 this is equivalent to $f$ preserving **joins**
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-**Example:** being logical about "OR" choices, like "what's my best outcome if I can use strategy A *or* strategy B?"
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- A function $g: Q \to P$ that finds the **least risky strategy** required to **guarantee** a certain outcome is a **Right Adjoint**.
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- Due to T1.115, this is equivalent to $g$ preserving **meets**.
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-**Example**: being logical about "AND" requirements, like "what is the single safest strategy I must commit to if I want to guarantee I achieve an outcome of *at least* A **AND** an outcome of *at least* B?"
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