In Anscombe and Aumann’s (1963) domain, there are two types of mixtures. One is an ex–ante mixture, or a lottery on acts. The other is an ex–post mixture, or a state– wise mixture of acts. These two mixtures have been assumed to be indifferent under the Reversal of Order axiom. However, we argue that the difference between these two mixtures is crucial in some important contexts. Under ambiguity aversion, an ex–ante mixture could provide only ex–ante hedging but not ex–post hedging. Under inequality aversion, an ex–ante mixture could provide only ex–ante equality but not ex–post equality. For each context, we develop a model that treats a preference for ex–ante mixtures separately from a preference for ex–post mixtures. One representation is an extension

whose paper [7] provided us with motivation, the experimental design and part of the experimental evidence. Usual disclaimers apply. This paper was written while Giovanni

Fairness emerges as a relevant factor in redistributive preferences in surveys and experiments. We study experimentally the impact of varying the probability with which players are assigned to initial positions in Ultimatum Games (UGs). In the baseline case players have equal opportunities of being assigned the proposer position –arguably the more advantaged one in UGs. Chances become increasingly unequal across three treatments. We also manipulate the inter-temporal allocation of opportunities over rounds. We …nd that: (1) The more initial chances are distributed unequally, the lower the acceptance rates of a given o¤er; consequently, o¤ers increase; (2) Being assigned a mere 1% chance of occupying the proposer role compared to none, signi…cantly increases acceptance rates and decreases o¤ers; (3) Players accept even extreme amounts of unequal chances within each round in exchange for overall equality of opportunities across rounds. Procedural fairness –both static and dynamic- has clear relevance for individuals.