The problem of no hands: responsibility voids in collective decisions

The problem of no hands concerns the existence of so-called responsibility voids: cases where a group makes a certain decision, yet no individual member of the group can be held responsible for this decision. Criteria-based collective decision procedures play a central role in philosophical debates on responsibility voids. In particular, the well-known discursive dilemma has been used to argue for the existence of these voids. But there is no consensus: others argue that no such voids exist in the discursive dilemma under the assumption that casting an untruthful opinion is eligible. We argue that, under this assumption, the procedure used in the discursive dilemma is indeed immune to responsibility voids, yet such voids can still arise for other criteria-based procedures. We provide two general characterizations of the conditions under which criteria-based collective decision procedures are immune to these voids. Our general characterizations are used to prove that responsibility voids are ruled out by criteria-based procedures involving an atomistic or monotonic decision function. In addition, we show that our results imply various other insights concerning the logic of responsibility voids.