Mixed-Weight Committee Selection in Proof-of-Stake: Tunable Stake-Baseline Mixing with Exponential Tail Guarantees and Incentive Compatibility

Proof-of-Stake (PoS) blockchains often select committees in direct proportion to stake, which makes security sensitive to large validators and stake concentration.  In such settings, a purely stake-based lottery can sometimes produce committees whose adversarial share crosses the safety threshold, even if the global adversarial stake remains below one third.  This paper introduces a simple mixed-weight rule that combines stake with a bounded baseline distribution through a single mixing parameter $\lambda$.  The rule leaves committee size, rewards, and VRF-based sortition unchanged, but pulls weight away from highly concentrated positions.  Proved that, whenever the adversary is more concentrated than the baseline, the expected adversarial seats fall linearly in $\lambda$, while standard concentration bounds show an exponential drop in committee-capture probability.  While the mechanism relies on entity-level attribution (or high-cost identities) to prevent Sybil attacks, experiments on ten production PoS networks indicate that modest mixing (around $\lambda=0.3$) reduces expected adversarial seats by about one quarter and tightens worst-case guarantees by orders of magnitude.