A new framework is introduced that models group decision making by using simple group heuristics (SIGH). We report results of a set of simulations that systematically varied (a) the group members' strategies (compensatory unit weight model, UWM, and a noncompensatory lexicographic heuristic, LEX), (b) the distribution of cue validities (J-shaped vs. linear), and (c) the quantity and quality of shared information. Individual decisions were aggregated by using a majority decision rule (proportionality in case of ties). (1) The simulations revealed strong effects of the distribution of cue validities on group performance. When validities were linearly distributed, UWM gained an 8% better accuracy than LEX by considering all cues. Yet, if cue validities followed a J-shaped distribution, the much more frugal LEX surpassed the UWM by achieving a 16% higher accuracy. (2) This effect was robust across different quantities of shared information. (3) Systematic allocation of information in favour of valid or invalid cues showed that the performance of UWM mainly depended on mean validity, whereas the performance of LEX was more strongly affected by the degree to which the most valid cues were shared.