Classification of committees with vetoes and conditions for the stability of power indices

Decision making by a committee may be modelled by simple games. Some of the committee׳s members are equipped with a veto, i.e. they may stop an action temporarily or permanently (by transforming a winning coalition into a losing coalition). A classification of such committees and of power indices is presented in this paper. Special emphasis is given to particular characteristics of winning coalitions and, in consequence, to a priori power indices and conditions for their stability from the perspective of both axioms and parameters.