When faced with a decision, people collect information to help them decide. Though it may seem unnecessary, people often continue to search for information about alternatives after they have already chosen an option, even if this choice is irreversible (e.g., checking out other cars after just purchasing one). While previous post-decision search studies focused on “one-shot” decisions and highlighted its irrational aspects, here we explore the possible benefits of post-decision search in the long run. We use a simple search task in which participants repeatedly decide whether to select the current alternative or continue to search for a better alternative. In a preliminary study we find that participants indeed conduct post-decision search even in unique environments, where information about forgone options cannot be used in future choices. In the main studies exposure to post-decision information was manipulated directly in unique environments, and was found to lead to better performance. The source of the observed improvement was further investigated with an explicit strategy elicitation methodology. We find that following exposure to post-decision information, people collect more data before generating thresholds. Thus, although post-decision search in unique environments might appear redundant, our results suggest it can help decision makers to modify their strategy and improve their future choices.

In this paper we estimate the expected error of a stochastic approximation algorithm where the maximum of a function is found using finite differences of a stochastic representation of that function. An error estimate of the order $n^{-1/5}$ for the nth iteration is achieved using suitable parameters. The novelty with respect to previous studies is that we allow the stochastic representation to be discontinuous and to consist of possibly dependent random variables (satisfying a mixing condition).

In this paper, in work strongly related with that of Coffman et al. [5], Bruss and Robertson [2], and Rhee and Talagrand [15], we focus our interest on an asymptotic distributional comparison between numbers of ‘smallest’ i.i.d. random variables selected by either on-line or off-line policies. Let X1,X2,… be a sequence of i.i.d. random variables with distribution function F(x), and let X1,n,…,Xn,n be the sequence of order statistics of X1,…,Xn. For a sequence (cn)n≥1 of positive constants, the smallest fit off-line counting random variable is defined by Ne(cn) := max {j ≤ n : X1,n + … + Xj,n ≤ cn}. The asymptotic joint distributional comparison is given between the off-line count Ne(cn) and on-line counts Nnτ for ‘good’ sequential (on-line) policies τ satisfying the sum constraint ∑j≥1XτjI(τj≤n) ≤ cn. Specifically, for such policies τ, under appropriate conditions on the distribution function F(x) and the constants (cn)n≥1, we find sequences of positive constants (Bn)n≥1, (Δn)n≥1 and (Δ'n)n≥1 such that

for some non-degenerate random variables W and W'. The major tools used in the paper are convergence of point processes to Poisson random measure and continuous mapping theorems, strong approximation results of the normalized empirical process by Brownian bridges, and some renewal theory.