A Note on Limits on Incentive Compatibility and Griefing Factors

We show a fundamental tradeoff between extortion resistance and griefing resistance in the presence of non-uniquely-attributable faults: if extortion attacks in a consensus mechanism are unprofitable as long as portion h of participants refuses to be extorted, then the mechanism has a griefing factor of at least 1 2h − 1. We then discuss the notion of variable griefing factors, and propose a methodology for computing penalties for various participants given a particular honest (i.e. unextortable) minority assumption.