Abstract: This paper examines the relationship between the concentration of political power in legislative bargaining and the predictability of the process governing the recognition of legislators.  Our main result establishes that, for a broad class of legislative bargaining games, if the recognition procedure permits the legislators to rule out some minimum number of proposers one round in advance, then irrespective of how patient the individual legislators are, Markovian equilibria necessarily deliver all economic surplus to the first proposer. We also examine the extent to which alternative bargaining protocols can limit the concentration of power.