love_reduces_sigma
plain-language theorem explainer
Love reduces global imbalance as measured by sigma in the virtue signature model. Researchers modeling ethical decisions via Recognition Science would reference this when distinguishing love from other virtues like justice that preserve sigma. The proof simplifies the love definition and normalizes the resulting numerical value.
Claim. The sigma effect of the Love virtue is negative: $sigma_{Love} < 0$.
background
The module defines Born-profile signatures for DREAM virtues, each with family loadings across four families and a sigma effect on global imbalance. Sigma from the Abilene Paradox context is the charge given by the gap between private preference and public vote: +1 if private stay but public go, -1 for the reverse, and zero for truthful agents. Love is specified with loading only on family 0 and sigma_effect set to -1, making it the unique virtue that directly reduces sigma. Justice preserves sigma with zero effect, and the module establishes that the 14 virtues form a basis of distinct signatures.
proof idea
One-line wrapper that simplifies the love definition to expose sigma_effect = -1 and then applies numerical normalization to verify the strict inequality.
why it matters
This result confirms love's unique negative impact on sigma, as highlighted in the module documentation where love alone changes the imbalance measure among the virtues. It fills the role of establishing the negative sigma effect in the chain of theorems on virtue signatures, supporting the framework's ethical structures. No direct downstream uses are listed, but it underpins distinctions in how virtues affect recognition-theoretic imbalance.
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