‘Power index’ measures provide a kind of ‘coalitional potential’ score that varies depending on how many actors or blocs are competing, what their resources (votes) are, and what the winning threshold in a situation is. Although this measure does not really grip ‘power’, it does reveal an important structural aspect of situations, and does so in a low information way valuable in many research contexts. But most knowledge we have of how ‘power indices’ operate is based on majority rule thresholds. There is an important and largely unexplained terrain of ‘reinforced majority’ or consensus decision-making that stretches from majority rule up to unanimity rule. This paper shows systematically how the normalized Banzahf index operates for all thresholds levels between 51 and 98 per cent, in situations involving either three or four actors and blocs. It also surfaces some fundamental rules and operational suggestions that are useful for extending the analysis to encompass situations with more actors. Consensual decision contexts emerge as a new and rich field for better understanding institutional analysis and design.
