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    Home/Original/inverse
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    Inverse View

    It is not the case that There is a threshold effect at 33% such that Fairmen's population proportion determines whether Fairmen tend toward extinction or fixation.

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.The 33% threshold assumes a well-mixed, infinite population, but real evolutionary dynamics involve spatial structure and assortative interaction that alter fixation thresholds.
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    • 2.Brian Skyrms's lattice simulations in 'Evolution of the Social Contract' show Fairmen can achieve fixation from far below 33% when agents interact with neighbors rather than random strangers.
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    • 3.Therefore, the threshold is not a fixed property of the strategies but an artifact of the mean-field assumption embedded in the replicator dynamics model.
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    Reason for 2 of 2
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    • 1.The replicator dynamics framework treats strategy frequencies as continuous deterministic variables, but finite populations exhibit stochastic drift that can override selection pressure near threshold boundaries.
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    • 2.Nowak and May's work on stochastic evolutionary game theory demonstrates that drift can carry populations across deterministic thresholds, making 'extinction or fixation' a probabilistic rather than categorical outcome.
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    • 3.The claim's sharp threshold language thus misrepresents a gradient of fixation probabilities as a binary bifurcation point.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.When each strategy is used by 33% of the population, all strategies have an expected average payoff of 1/3.
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    • 2.If the proportion of Fairmen drops below 33%, Fairmen do not meet each other often enough to compensate for losses against Greedies.
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    • 3.If the proportion of Fairmen rises above 33%, Fairmen's extra gains from meeting each other compensate for their losses when they meet Greedies.
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