The resilience and censorship resistance of a blockchain depend on where the validators and proposers of that blockchain physically operate. We study the economic incentives behind this location choice, both with a single proposer and with multiple concurrent proposers. Formally, we study a game where proposers first choose locations and then compete in a first-price auction for an opportunity whose common value is driven by information from geographically dispersed sources. A single proposer minimizes variance-weighted delay, locating at a weighted median of the sources and co-locating with any dominant one. By contrast, with two proposers, information both observe equally early earns no rent, and each proposer's expected profit is proportional to the standard deviation of the information it receives before its rival. We show that the location game admits the jointly unobserved variance as an ordinal potential, so global solutions of a weighted two-median problem are equilibria. With two sources, one proposer locates at each, however weak one is. With more proposers and at least as many sources, equilibrium locations are distinct under regular bidding. Multiple concurrent proposers thus do more than limit any single proposer's control over inclusion: by rewarding exclusive rather than shared information, they create an economic force toward geographic decentralization.

翻译：暂无翻译