Optimal Dynamic Majority-Quorum Rules: Theory and Evidence

Bhargav Nagaraja Bhatt, Jonas Gehrlein and Kremena Valkanova

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Abstract: We study the optimal sequential aggregation of randomly arriving votes from a finite population to identify an unknown majority preference before a fixed deadline, trading off decision accuracy against the cost of delay. The optimal policy is a dynamic majority-quorum rule: a joint, time-varying threshold on vote lead and count, in which quorum and supermajority requirements emerge as the solution to an inference problem about non-participants' preferences. At each date, the continuation region is lens-shaped: the lead required to stop grows with turnout until too few voters remain to overturn it, and it vanishes at the deadline. We characterize conditions under which the boundary is monotone in the stakes, the arrival process, and time. Because the exact boundary admits no closed form, we derive a large-population approximation that reduces the two-dimensional rule onto a single sufficient statistic, and express the rule as a sequential significance test set by a single error tolerance. Calibrated on Polkadot governance data, an out-of-sample evaluation finds that our rule with a 2\% error tolerance halves decision times relative to the incumbent mechanism.

Date: 2026-10
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