Optimal quorum for the model of computational grid with redundancy

We consider a model of grid computing system solving numerous similar problems. Computers produce correct answers with some known probability. Each problem is solved up to the fixed number (quorum) of identical answers; this redundancy allows reducing the risk of accepting a wrong answer. The cost function is the sum of computational time and penalty in case of wrong answer. We reveal the conditions when such redundancy is advantageous and how the optimal quorum can be determined. We compare results for different numbers of possible answers and show that behavior of the model is similar.