selfishStrategy
plain-language theorem explainer
A selfish strategy on two agents sets one participant's sigma to zero while doubling the other's. Researchers analyzing ethical decision-making within Recognition Science would cite this to demonstrate how individual gain can increase overall sigma spread. The construction is given explicitly by case distinction on the agent index in the transformation rule.
Claim. For agents labeled as beneficiary $b$ and victim $v$ in a two-agent system, the strategy maps a sigma vector $s$ to a new vector where the $b$-component is 0, the $v$-component is $2 s_v$, and the remaining component is unchanged.
background
The module establishes that the Meta-Principle in Recognition Science requires the global sigma to approach zero. Here sigma denotes the discrepancy between an agent's private preference and public vote, following the definition from the Abilene Paradox analysis where sigma(a) equals the difference between private preference indicator and public vote indicator. A Strategy is formalized as a structure containing an apply function that transforms any finite vector of real-valued sigmas.
proof idea
The definition directly specifies the apply function using conditional expressions based on whether the index matches the beneficiary or victim.
why it matters
This definition provides the concrete example needed to prove that selfish strategies increase global sigma, as indicated by sibling declarations in the module. It illustrates a suboptimal path in the sigma equilibration process central to the Recognition Science ethics framework, where love is shown to minimize spread and achieve fastest equilibrium. It connects to the broader forcing chain by treating sigma as a defect measure analogous to J-cost in the foundation.
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