Context-dependent effects of branches in decisions under risk

This paper investigates how the number of branches in a prospect influences decision makers' preferences. I propose that individuals may use differences in branch number as a justification when choosing between prospects, but that this heuristic applies only when multiple probabilistic options are available for comparison. Accordingly, the impact of branch number on choice depends on decision context, particularly the alternatives presented alongside the target prospect. In choices between two prospects offering probabilistic gains, preference for a prospect increases when it offers more gain branches than the alternative. For example, more people choose a target prospect offering a 20% chance to win $14 and a 20% chance to win $15 (otherwise $0) over an alternative offering a 60% chance to win $10 (otherwise $0) than when the target offers a 40% chance to win $15 (otherwise $0). However, the effect disappears when the alternative is a sure gain and reverses when the prospect is presented in isolation. The data also indicate rapidly diminishing sensitivity: preference increases when a prospect's branches rise from one to two while the alternative has a single branch, but additional branches yield little or no further gain in attractiveness. Additional studies examined moderators of the effect and extended the findings to losses and to decisions involving valuations of human lives. Together, these results challenge existing models of risky choice by demonstrating the context dependence of branch effects, and they carry practical implications for financial and policy decisions under uncertainty.