  If a measure of voting power assigns greater voting power to a player because
it no longer effectively cooperates with another, then the measure displays the
quarrelling paradox and violates the quarrel postulate. We provide formal
criteria by which to judge whether a given conception of quarrelling is (a)
reasonable and (b) fit to serve as the basis for a reasonable quarrel
postulate. To achieve this, we formalize a general framework distinguishing
between three degrees of quarrelling (weak, strong, cataclysmic), symmetric vs.
asymmetrical quarrels, and reciprocal vs. non-reciprocal quarrels, and which
thereby yields twelve conceptions of quarrelling, which encompasses the two
conceptions proposed by Felsenthal and Machover and by Laruelle and Valenciano,
respectively. We argue that the two existing formulations of the quarrel
postulate based on these conceptions are unreasonable. In contrast, we prove
that the symmetric, weak conception of quarrelling identified by our framework
-- whether reciprocal or not -- is fit to serve as the basis for a reasonable
quarrel postulate. Furthermore, the classic Shapley-Shubik index and
Penrose-Banzhaf measure both satisfy the quarrel postulate based on a symmetric
weak quarrel.
