Impossibilities for strategy-proof committee selection mechanisms with vetoers

When a group of voters selects a committee out of a set of candidates, it is common and often desirable to endow these voters with some veto power. I present impossibility results showing that even limited veto power makes many mechanisms of interest manipulable. This applies in particular (i) to mechanisms the range of which contains a degenerate lottery in which a committee is chosen for sure and (ii) to mechanisms that are constructed from extensive game forms with a finite number of strategies. These impossibilities hold on a large set of domains including the domain of additive preferences, and even when probabilistic mechanisms are allowed and voters can report cardinal preferences.