Randomization vs. selection: How to choose in the absence of preference?

Decision makers sometimes have to choose between alternative options about which they have no preference: either they judge the options equally valuable (indifference) or they have no judgment about their relative value (noncomparability). Choosing randomly is generally considered a natural way to deal with such situations. This paper shows, however, that systematic randomization between noncomparable options may lead to a chain of decisions resulting in monetary losses (a money pump). Furthermore, these losses can be avoided by deliberately selecting one of the noncomparable options instead of randomizing. Thus, randomization among noncomparable options is costly relative to deliberate selection. On the other hand, randomization among indifferent options is costless relative to deliberate selection.