When is a finite number of binary voting choices consistent with the hypothesis that the voter has preferences that admit a (quasi)concave utility representation? I derive necessary and sufficient conditions and a tractable algorithm to verify their validity. I show that the hypothesis that the voter has preferences represented by a concave utility function is observationally equivalent to the hypothesis that she has preferences represented by a quasiconcave utility function, I obtain testable restrictions on the location of voter ideal points, and I apply the conditions to the problem of predicting future voting decisions. Without knowledge of the location of the voting alternatives, voting decisions by multiple voters impose no joint testable restrictions on the location of their ideal points, even in one dimension. Furthermore, the voting records of any group of voters can always be embedded in a two-dimensional space with strictly concave utility representations and arbitrary ideal points for the voters. The analysis readily generalizes to choice situations over general finite budget sets.