  Comonotonicity ("same variation") of random variables minimizes hedging
possibilities and has been widely used in many fields. Comonotonic restrictions
of traditional axioms have led to impactful inventions in decision models,
including Gilboa and Schmeidler's ambiguity models. This paper investigates
antimonotonicity ("opposite variation"), the natural counterpart to
comonotonicity, minimizing leveraging possibilities. Surprisingly,
antimonotonic restrictions of traditional axioms often do not give new models
but, instead, give generalized axiomatizations of existing ones. We, thus,
generalize: (a) classical axiomatizations of linear functionals through
Cauchy's equation; (b) as-if-risk-neutral pricing through no-arbitrage; (c)
subjective probabilities through bookmaking; (d) Anscombe-Aumann expected
utility; (e) risk aversion in Savage's subjective expected utility. In each
case, our generalizations show where the most critical tests of classical
axioms lie: in the antimonotonic cases (maximal hedges). We, finally, present
cases where antimonotonic restrictions do weaken axioms and lead to new models,
primarily for ambiguity aversion in nonexpected utility.
