We identify the monotonicity axiom as a problematic cornerstone of normative theory on decision making, and propose sequential consistency as an alternative, weaker axiom, that is still strong enough to induce uniqueness of updates, yet sufficiently flexible to rationalize the Allais and Ellsberg preferences. It is generally believed that the monotonicity property is an indispensable feature of a normative preference ordering. Phrased as `if A is better than B in all states tomorrow, it must be better now’, its intuitive appeal is immediate. We also take it for granted, in case A and B are acts, or lotteries, that actually pay out in each state tomorrow. In other words, we adopt monotonicity in real monetary outcomes. Its extension to the general case, however, with A and B not yet resolved in tomorrow’s states, is less innocent than this phrasing suggests. At closer inspection, the word `better’ comes in two different forms: better if it comes to obtaining (often the tacit assumption), and better if it comes to the opposite perspective (returning, delivering, writing). We argue that the discrepancy between both perspectives, also referred to as endowment, or the gap between willingness to pay and accept, or the bid-ask spread, is inherent in most common preference orderings in the first place, rather than the effect of additional psychological phenomena. Now this undermines the seemingly absolutely compelling nature of the monotonicity axiom (see  for an elaborate discussion). Inspired by [1-3], we propose an alternative axiomatic framework for complete continuous preference orderings on finite state acts, in which the standard (conditional) monotonicity axiom is replaced by the much weaker axiom of sequential consistency (, mainly Def 4.1 and axioms A1-6). This extra flexibility gives room to combine uniqueness of updates, consequentialism, and dynamic choice consistency in a such a way that it accommodates the Allais and Ellsberg preferences without giving up a normative claim.
 B. Roorda and J.M. Schumacher (2015) Weakly Time Consistent Convex Risk Measures and their Dual Representations. To appear in Finance \& Stochastics, Open Access. DOI: 10.1007/s00780-015-0285-8
 B. Roorda and R.A.M.G. Joosten (2015). Dynamically Consistent Non-Expected Utility Preferences with Tuned Risk Aversion. Working paper
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