When random choice adds ambiguity instead of reducing it

Consider two bets: one pays according to the temperature in Athens, the other according to the temperature in Beijing. Someone unfamiliar with either city may find both probabilities ambiguous. Would tossing a fair coin to choose between the bets make the prospect more attractive?

In their theoretical preprint, Yutaro Akita and Kensei Nakamura develop a model in which this random selection offers no advantage over the better individual bet. Before the coin toss, both cities’ temperatures matter to the overall prospect; afterward, the person still faces an ambiguous bet. The authors use this example to motivate a distinction between disliking ambiguity and disliking an increase in the ambiguous events relevant to a payoff.

Why timing matters

The paper distinguishes two kinds of objective randomization. Ex ante randomization selects a bet before the uncertain state is realized. Ex post randomization mixes outcomes within each state, after that state is realized.

In the authors’ framework, the second operation can hedge ambiguity by smoothing the pattern of payoffs across states. The first does not provide that kind of hedge: it selects which ambiguous act the person will face. It can also make additional ambiguous events relevant to evaluating the prospect.

The resulting behavioral requirement is precise. If someone ranks one prospect above another, randomizing between them cannot beat the preferred prospect. This need not mean that the mixture is worse than both, or that every randomization produces a strict penalty.

Choosing a perception at a cost

The authors call their framework the costly ambiguity perception model. An ambiguity perception is a set of probability distributions, or priors, that the person considers possible.

For a given perception, each act is evaluated using its lowest expected utility across those priors. The person then behaves as if choosing the perception that maximizes the probability-weighted average of these evaluations across the lottery’s acts, minus a cost. One perception is used to evaluate the whole lottery.

Narrowing a set of possible priors weakly increases its cost. A more refined perception can improve the worst-case evaluation, but that improvement must justify the expense. A prospect involving fewer ambiguous events may therefore be easier to evaluate favorably: the person can concentrate refinement where it matters.

This is an “as if” representation, not a directly observed mental mechanism. The authors discuss contemplation, optimistic belief distortion and adjustment of ambiguity attitudes as possible interpretations of its optimization process.

Explaining difficult choice patterns

One application concerns Machina’s reflection example. A box contains balls in four colors, with known totals for two pairs of colors but unknown numbers within each pair. Different bets make either one pair’s uncertain composition or both pairs’ compositions relevant to the payoff.

The paper shows that its model can favor bets involving fewer relevant ambiguous events in the characteristic reflection pattern. Its worked example obtains strict preferences under a symmetric, strictly decreasing refinement-cost function when the cost multiplier is sufficiently low. The authors also provide a parameterized example accommodating Machina’s separate 50–51 thought experiment.

These are mathematical demonstrations of what the model can explain, not new experimental findings. The paper cites earlier experimental support for the reflection pattern.

Randomization reveals otherwise hidden differences

The authors establish an axiomatic characterization: seven behavioral requirements are jointly equivalent to having their representation. Alongside randomization attitudes, these include consistent rankings, continuity, respect for statewise dominance and an unbounded utility range.

A second main result concerns identification. Within convex cost structures, the authors identify a smallest feasible collection of ambiguity perceptions. Once the utility function and feasible collection are fixed, the cost function is unique and can, in principle, be recovered from certainty equivalents—unambiguous alternatives judged equivalent to the prospects being evaluated.

Observing randomization choices is essential. In one constructed example, two models agree on every individual act. Yet one values each of two opposing acts at one-half and their equal-probability ex ante lottery at one-quarter, while the expected-utility model does not impose that reduction. These are utility values, illustrating how agreement on individual bets can conceal disagreement about randomized combinations.

What remains untested

The framework also distinguishes comparative ambiguity aversion from the stronger notion of aversion to additional ambiguity. Under its conditions, the latter corresponds to a particular ordering of optimal perceptions toward less refinement; the two attitudes are not generally interchangeable.

The paper’s contribution is theoretical. Its finite-state setting, utility assumptions and behavioral axioms delimit the results. The authors leave testing when their proposed role for ex ante randomization is empirically reasonable to future experiments. Their central claim is therefore a testable account of choice, not evidence that people universally evaluate ambiguity this way.