This order-dependence reveals that weak dominance lacks the modal robustness required for genuine dominance reasoning, suggesting weak dominance is not a weakened form of the same relation but a categorically different one.

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Categorically different(arguing that weak dominance is not a weaker version of strong dominance, but something entirely separate): Fundamentally different in kind or type, rather than just different in degree or strength—like how a dog differs from a rock, not just like how a large dog differs from a small one.
Modal robustness(describing what genuine dominance reasoning should have): The quality of remaining reliable and unchanged across different possible scenarios or conditions.
Order-dependence(describing how weak dominance reasoning changes based on order): When the result or validity of something changes depending on the sequence or arrangement of steps—like how mixing ingredients matters in baking.
dominance reasoning(game theory): A form of iterative reasoning in game theory where players eliminate dominated actions from consideration, which may reduce the game and render further moves dominated
weak dominance(Game theory, iterated deletion of dominated strategies): Strategy s1 weakly dominates s2 if a player does at least as well with s1 as with s2 for any reply by the opponent, and strictly better on at least one reply

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