Decision Making using Game Theory: An introduction for managers

169Indices of power: measuring influenceTable 8.11 Most pivotal position in the voting sequence for ‘controlled secondary’ board factions% times pivotal in 2nd % times pivotal in 3rdC 56 44L 56 44P 56 44T 56 44Table 8.12 Most pivotal position in the voting sequence for ‘out-of-state’ board factions% times pivotal in 2nd % times pivotal in 3rd % times pivotal in 4thL 18 68 14P 18 68 14R 0 100 0T 0 100 0r 0 100 0the winning side. Unfortunately, this is opposed by an equal andopposite desire on the part of those who have already formed awinning coalition not to accept superXuous members. Just as there isno incentive for the last voting faction to dissent, there is no incentivefor the Wrst three or four factions to form grand coalitions, sincethe last faction is never ‘important’. This idea is analogous to theminimal winning coalition theory referred to previously (Riker,1962), which states that if a coalition is large enough to win it shouldavoid accepting additional factions, since these new members willdemand to share in the pay-oV without contributing essential votesto the consortium.This idea of minimal winning coalitions forms the basis foranother power index – the Deegan–Packel index – which is discussedbelow.Other applicationsWhile this discussion has concentrated on school governance, analysisof this sort can easily be applied to other competitive voting situations,both within education and without. For example, when the forerunnerof the European Union was set up by the Treaty of Rome in 1958, there