This paper proposes a novel technique for allocating information gathering actions in settingswhere agents need to choose among several alternatives, each ofwhich provides a stochastic outcometo the agent. Samples of these outcomes are available to agents prior to making decisions and obtaining further samples is associated with a cost. The paper formalizes the task of choosing the optimal sequence of information gathering actions in such settings and establishes it to be NP-Hard. It suggests a novel estimation technique for the optimal number of samples to obtain for each of the alternatives. The approach takes into account the trade-offs associated with using prior samples to choose the best alternative and paying to obtain additional samples. This technique is evaluated empirically in several different settings using real data. Results show that our approach was able to significantly outperform alternative algorithms from the literature for allocating information gathering actions in similar types of settings. These results demonstrate the efficacy of our approach as an efficient, tractable technique for deciding how to acquire information when agents make decisions under uncertain conditions