  A proposed measure of voting power should satisfy two conditions to be
plausible: first, it must be conceptually justified, capturing the intuitive
meaning of what voting power is; second, it must satisfy reasonable postulates.
This paper studies a set of postulates, appropriate for a priori voting power,
concerning blockers (or vetoers) in a binary voting game. We specify and
motivate five such postulates, namely, two subadditivity blocker postulates,
two minimum-power blocker postulates, each in weak and strong versions, and the
added-blocker postulate. We then test whether three measures of voting power,
namely the classic Penrose-Banzhaf measure, the classic Shapley-Shubik index,
and the newly proposed Recursive Measure, satisfy these postulates. We find
that the first measure fails four of the postulates, the second fails two,
while the third alone satisfies all five postulates. This work consequently
adds to the plausibility of the Recursive Measure as a reasonable measure of
voting power.
