# Dominated lotteries in CPE

I have been looking into expectation-based loss aversion following Kőszegi-Rabin (2005, 2007). In particular, I find their choice-acclimating personal equilibrium (CPE) interesting, but it has a feature that I find rather odd.

My question is: Is there substantial evidence that people choose stochastically dominated lotteries? Are there experimental studies (in addition to the crazy one below) that can support this prediction of CPE? Or has someone cleverly exploited a data set to point out this behavior in the field?

Let me clarify what I am after:

In CPE, a player makes makes a consumption plan and expects to follow it through such that it becomes her reference point, and this plan must be better than any other available plan. That is, outcome lottery and reference lottery are the same.

For any choice set $$D$$, $$F \in D$$ is a CPE if $$U (F | F ) \geq U (F' | F') \quad \forall F' \in D$$.

If you want to know how $$U$$ looks like, here is the paper

In their Proposition 7, they show that people may choose stochastically dominated lotteries in CPE if losses hurt sufficiently badly. Let me quote the authors:

consider a lottery $$F$$ that yields $$w + g> w$$ with probability $$p>0$$ and $$w$$ with probability $$1 -p$$. Then \begin{aligned} U(w + F|w +F) &= [p (w + g)+(1-p)w] + [p (1-p) \mu (g) + p (1-p) \mu (-g) \\ &= w + pg [1- (1-p)\eta (\lambda-1)]. \end{aligned} If $$\eta(\lambda-1)>1$$, which is a calibrationally plausible situation, the decision maker prefers $$p=0$$ over a small $$p> 0$$. Intuitively, raising expectations of getting $$g$$ makes an outcome of no gain feel more painful. To avoid such disappointments, the person would rather give up the fragile hope of making gains. In fact, if gain-loss utility is sufficiently important, reducing exposure to sensations of loss is the decision maker’s central concern.

Avoiding disappointment does not sound completely crazy, but I wonder if such risk preferences are observed in situations "that matter". Their example with the prisoner seems extremely constructed to me. They also refer to an experiment by Gneezy, List and Wu, in which people pay more for a \$50 gift card than for a lottery over a \$50 and a \\$100 gift card, which seems outrageously crazy to me. I am inclined to say that these people just did not understand the questions.

Is there evidence that such behavior is prevalent?

Because -- if people play CPE and $$\lambda$$ estimates are on point -- it must be. Under CPE and the commonly used linear kinked $$\mu$$ with $$\eta=1$$, players prefer first-order stochastically dominated lotteries if $$\lambda >2$$. Conventionally, "losses loom about twice as large as gains", meaning $$\frac{1+\eta \lambda}{1+\eta } \approx 2 \Rightarrow \lambda \approx 3$$. There are multiple studies backing up this parameter estimate. Therefore, under CPE we should see these crazy risk preferences all the time. Do we? I certainly don't have that feeling.