  Corruptive majority attacks, in which mining power is distributed among
miners and an attacker attempts to bribe a majority of miners into
participation in a majority attack, pose a threat to blockchains. Budish
bounded the cost of bribing miners to participate in an attack by their
expected loss as a result of attack success. We show that this bound is loose.
In particular, an attack may be structured so that under equilibrium play by
most miners, a miner's choice to participate only slightly affects the attack
success chance. Combined with the fact that most of the cost of attack success
is externalized by any given small miner, this implies that if most mining
power is controlled by small miners, bribing miners to participate in such an
attack is much cheaper than the Budish bound. We provide a scheme for a cheap
corruptive majority attack and discuss practical concerns and consequences.
