N = 100. Each person privately presses red or blue. If blue votes exceed 50, everyone lives. Otherwise red lives and blue dies.
Other voters comprise fixed-blue, fixed-red, and persuadable masses. Persuadables have score X ∼ Normal(μ, σ) and press blue exactly when their post-message score is nonnegative.
Blue preaching shifts reached persuadables by +δ; red preaching shifts them by −δ. Reach ρ is deterministic.
qₘ = fixed blue + persuadable × ((1 − ρ)Pr[X ≥ 0] + ρPr[X + shiftₘ ≥ 0]).
Kₘ ∼ Binomial(99, qₘ). Your red press requires K ≥ 51 for universal survival; your blue press requires K ≥ 50.
U = self multiple × 1[self survives] + 99 × (others surviving / 99)survivor exponent.
For each press, the workbench retains the better preach. It then compares the two optimized press branches.