In this paper we propose a new party-system fragmentation measure as equivalent number of parties that fully takes into account the pivotal power of parties. The novel approach we adopt in the method of construction for an index of fragmentation allows us to take advantage of the theory of generalized means. We first construct the (class of) quasi-arithmetic mean(s) with Banzhaf power weight function for the party sizes and then, given the average size, we derive an equivalent-number of parties.