pull_raises_sigma
plain-language theorem explainer
The declaration proves that diverting the trolley raises the agency-imbalance cost relative to inaction. Decision theorists applying Recognition Science to moral dilemmas cite it to establish the strict J/σ tradeoff. The proof is a one-line wrapper that unfolds the sigmaCost definition and normalizes the constants.
Claim. Let $T$ be the inductive type with constructors pull and doNothing. Let $σ : T → ℝ$ be defined by $σ(pull) = 1$ and $σ(doNothing) = 0$. Then $σ(pull) > σ(doNothing)$.
background
The Decision.Trolley module recasts the classic trolley problem as a J/σ tradeoff inside Recognition Science. TrolleyChoice is the inductive type with constructors pull (active diversion) and doNothing (inaction). The function sigmaCost assigns the real value 1 to pull, reflecting the agency imbalance created by intervention, and 0 to doNothing, as stated in its sibling definition. This construction mirrors the sigmaCost pattern already introduced in NewcombParadox for predictor scenarios.
proof idea
The proof is a one-line wrapper. It unfolds sigmaCost on both constructors and applies norm_num to verify the numerical comparison 1 > 0.
why it matters
The result is used by tradeoff_strict to package the opposing movements on the two axes and by no_strictly_dominant_choice to show that neither option dominates both metrics simultaneously. It supplies the σ-raising half of the trolley instance of the J/σ tradeoff described in the module's treatment of philosophical paradoxes. The strict inequality highlights why the 14 DREAM virtues are invoked elsewhere to seek resolutions that avoid the forced tradeoff.
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