  We study a basic sequential model for the discovery of winning coalitions in
a simple game, well known from its use in defining the Shapley-Shubik power
index. We derive in a uniform way a family of measures of collective and
individual power in simple games, and show that, as for the Shapley-Shubik
index, they extend naturally to measures for TU-games. In particular, the
individual measures include all weighted semivalues.
  We single out the simplest measure in our family for more investigation, as
it is new to the literature as far as we know. Although it is very different
from the Shapley value, it is closely related in several ways, and is the
natural analogue of the Shapley value under a nonstandard, but natural,
definition of simple game. We illustrate this new measure by calculating its
values on some standard examples.
