Why do simple heuristics perform well in choices with binary attributes?

Simple heuristics, such as deterministic elimination by aspects (DEBA) and equal weighting of attributes with DEBA as a tiebreaker (EW/DEBA), have been found to perform curiously well in choosing one out of many alternatives based on a few binary attributes. DEBA and EW/DEBA sometimes achieve near-perfect performance and complement each other (if one is wrong or does not apply, the other is correct). Here, these findings are confirmed and extended; most importantly, a theory is presented that explains them. The theory allows calculating the performance of any model, for any number of binary attributes, for any preferences of the decision maker, for all sizes of the consideration set, and for sampling alternatives with as well as without replacement. Calculations based on the theory organize previous empirical findings and provide new surprising results. For example, the performance of both DEBA and EW/DEBA is a U-shaped function of the size of the consideration set and converges relatively quickly to perfection as the size of the consideration set increases (this result holds even when the preferences of the decision maker are worst-case scenarios for the performance of the heuristics). An explanation for why DEBA and EW/DEBA complement each other is also provided. Finally, the need for a unified theory of multiattribute choice and cue-based judgment is discussed