Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that Strict dominance implies weak dominance, but weak dominance does not necessarily imply strict dominance

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Under Savage's framework, rational preference requires complete state-space specification, making the strict/weak dominance distinction dependent on how states are individuated.
      ?

      Think about whether this reason is strong or weak

    • 2.If states are individuated finely enough to distinguish all payoff-relevant outcomes, every case of weak dominance collapses into strict dominance, dissolving the asymmetry.
      ?

      Think about whether this reason is strong or weak

    • 3.The apparent non-implication from weak to strict dominance is therefore an artifact of coarse state descriptions, not a fundamental logical asymmetry.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Pearce's 1984 rationalizability framework demonstrates that iterated elimination of weakly dominated strategies is order-dependent in ways that iterated elimination of strictly dominated strategies is not.
      ?

      Think about whether this reason is strong or weak

    • 2.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.
      ?

      Think about whether this reason is strong or weak

    • 3.If strict and weak dominance are categorically distinct relations rather than stronger and weaker instances of one relation, the claim that strict dominance 'implies' weak dominance mischaracterizes their logical relationship.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.A strictly dominated strategy fails to be a best response to any belief
      ?

      Think about whether this reason is strong or weak

    • 2.A weakly dominated (inadmissible) strategy may still be a best response to beliefs that assign probability one to states where the player is indifferent between the weakly dominated action and the admissible one
      ?

      Think about whether this reason is strong or weak

    • 3.These conditions are not symmetric
      ?

      Think about whether this reason is strong or weak

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.