Proposer selection in EIP-7251

Immediate settlement, or single-slot finality (SSF), is a long-term goal for Ethereum. The growing active validator set size is placing an increasing computational burden on the network, making SSF more challenging. EIP-7251 aims to reduce the number of validators by giving stakers the option to merge existing validators. Key to the success of this proposal therefore is whether stakers choose to merge their validators once EIP-7251 is implemented. It is natural to assume stakers participate only if they anticipate greater expected utility (risk-adjusted returns) as a single large validator. In this paper, we focus on one of the duties that a validator performs, viz. being the proposer for the next block. This duty can be quite lucrative, but happens infrequently. Based on previous analysis, we may assume that EIP-7251 implies no change to the security of the protocol. We confirm that the probability of a validator being selected as block proposer is equivalent under each consolidation regime. This result ensures that the decision of one staker to merge has no impact on the opportunity of another to propose the next block, in turn ensuring there is no major systemic change to the economics of the protocol with respect to proposer selection.