As reported in [7], [8] and [12], there is a small theory of voting bodies which can serve as an excellent example for letting students at upper secondary school level actively participate in a process of mathematizing a situation and mathematical model building. One of the exciting problems which come up in going through this process concerns the existence of non‐measurable voting bodies. The answer to this question is positive as was first proved in the first (1944) edition of [13]. In [9] and [10] it has been shown on an elementary level that there are a variety of examples of non‐measurable voting bodies which can be related to finite geometries (see also [5] and [14]). Also in [9] and [10], the question of necessary and/or sufficient conditions for non‐measurability was discussed and some sufficient conditions were formulated and applied. In this paper a condition is formulated which is both necessary and sufficient. The proof exceeds the level of school mathematics. As is explained in [11], this characterization of measurability of voting bodies is basically related to the characterization of additivity of ranking orders on finite Boolean lattices given in [2] and [6].