Deviates from Classic in a few ways:

1. non-deterministic leadership lottery: zero or more leaders per slot
2. Proved secure under adaptive adversary

Leadership Lottery:

$$ \phi_f(\alpha)=1-(1-f)^\alpha $$

Properties:

• $\phi_f(1) = f$
  • probability of winning the lottery for someone owning all stake is $f$
• $\phi_f(\sum_i\alpha_i)=1-\prod_i (1-\phi_f(\alpha_i))\leq\sum_i\phi_f(\alpha_i)$
  • $\phi_f$ is sub-additive, why is this desirable? bias against centralization?
• stake values $\alpha_i$ are normalized to $\alpha_i\in[0..1]$
  • if we don’t know total stake, we need to learn a normalizing term to adapt the difficulty (do we target $1-f$ slots empty)?