Consider the algorithm for consensus in a synchronous system, which uses the following integrity definition: if all processes, whether correct or not, proposed the same value, then any correct process in the decided state would chose that value. Now consider an application in which correct processes may propose different results, e.g., by running different algorithms to decide which action to take in a control system’s operation. Suggest an appropriate modification to the integrity definition and thus to the algorithm.

What will be an ideal response?

A variant of the integrity condition is for any correct process to choose the majority of the proposed values (where the function majority is defined in the chapter to cover the case where there is no value occurring more often than all the others). Accordingly the algorithm needs to be adapted to choose the majority, not the minimum, of the values obtained from f+1 rounds.