When making a purchase of wine, a restaurant is given the choice of 3 barrels, A, B or C. The restaurant wishes to choose the best, and, if barrels are ranked in true order of quality, their loss function will be equal to the rank of the chosen barrel minus 1. The restaurant employs two expert wine tasters who independently sample the barrels and rank them in order of quality. Each taster guesses the correct order with probability 2/5, guesses each of the two orderings which differ from the true by interchange of a single neighbouring pair with probability 1/5, and guesses each of the three other orderings with probability 1/15. The expert tasters nominate orders BAC and ACB. Using a prior distribution which gives probability 1/6 to each of the 6 possible true orders, find the posterior distribution of the true order. Hence find the Bayesian decision which tells the restaurant which barrel to choose.