redblue

N = 100. Each person privately presses red or blue. If blue votes exceed 50, everyone lives. Otherwise red lives and blue dies.

Other voters: fixed-blue mass, fixed-red mass, and persuadable mass. Persuadables have score X ∼ Normal(μ, σ). Press blue iff post-message score ≥ 0.

Blue preaching shifts reached persuadables by +δ. Red preaching shifts them by -δ. Reach ρ is deterministic.

q_m = fixed_blue + persuadable · ((1 - ρ)Pr[X ≥ 0] + ρPr[X + shift_m ≥ 0]).

K_m ∼ Binomial(99, q_m). Threshold for your red press: K ≥ 51. Threshold for your blue press: K ≥ 50.

U = self_multiple · 1[self survives] + 99 · (others_surviving / 99)^survivor_exponent.

For each press, the app keeps the better preach. It then compares best press-red against best press-blue, and shows the winning press plus its conditional preach.