White and Perfors (2022) on Ambiguity Aversion in Vignettes

Joshua P. White and Andrew Perfors, “Ambiguity Aversion in Qualitative Contexts: The Role of Prior Beliefs,” May 22, 2022; available here.

• The idea is to test for ambiguity aversion in more-or-less familiar risky situations that are not about money, such as blind dates or election outcomes. Further, the issue of whether ambiguity aversion arises from people holding pessimistic beliefs about the actual odds facing them in ambiguous situations is explored.

• The three lab experiments employ Amazon Mechanical Turk (overall n>2000) and the analysis is pre-registered, including the data exclusion criteria.

• The 24 vignettes: Would you rather be in the risky situation or the ambiguous situation? Half of the vignettes concern potential gains (e.g., new job) and half concern potential losses (e.g., losing a job). 

• The results: ambiguity aversion is typically present on average in both the gain and loss framings; ambiguity aversion is greater, however, in the gain scenarios, and the amount of aversion varies quite a bit across scenarios. 

• The scenario that tracked an Ellsberg urn problem showed (easily) the highest ambiguity aversion. 

• For some individuals, the aversion to ambiguity seems to derive from pessimistic feelings about how ambiguity would be resolved. (The Ellsberg-style urn vignette – which involved a casino! – is particularly likely to be affected by pessimism.) But there remains a good deal of ambiguity aversion that does not derive from pessimistic beliefs (nor from "comparative ignorance," the concern that a decision maker is up against better informed folks – such as casino owners, perhaps?).

Chen and Schonger (2016) on Ambiguity Aversion

Daniel L. Chen and Martin Schonger, “Is Ambiguity Aversion a Preference?” TSE Working Paper No. 16-703, December 2016.

• Ambiguity aversion has been implicated in many real world phenomena, including the equity premium puzzle: the stock market operates under Knightian uncertainty (ambiguity), not risk, and so ambiguity-averse investors need compensation to buy stocks. Overly punitive plea bargains are acceptable to ambiguity-averse defendants…

• But perhaps the sort of behavior exhibited by the Ellsberg paradox is not really indicative of underlying preferences – perhaps it is mistake, the use of a decision heuristic in inappropriate circumstances. Perhaps people are not actually ambiguity averse.

• Maybe people (rightly) shy away from unfamiliar offers, especially when the person making the offer possesses superior information – and this is the situation when experimental participants are presented with the Ellsberg game. Subjects suspect that the experimenter actually knows how many red and blue balls are in the urn.

• Chen and Schonger set up an Ellsberg experiment where the experimenter is not the party responsible for the contents of the ambiguous urn; rather, the choices of other subjects determine the contents. 

• Every subject decides which of two symbols to send to the others. In experiment 1, the symbol that gets the most “votes” is the symbol that will appear in the “ambiguous” urn for other participants (which need not be the same for all participants, incidentally). 

• All experiments involve a toss of a fair coin, where the subjects can choose to bet on either heads or tails, along with the two ambiguous options. A correct outcome yields 4€. The choice of the bet is determined by taking the maximum of the valuations provided by each participant for each of the four bets. 

• People turn out to prefer the ambiguous bets! “For each of the 16 sessions, individuals were more likely to bet on a symbol with subjective uncertainty, and in all but 2 of the 16 sessions, both bets with subjective uncertainty were more popular than the bets with objective uncertainty [p. 15].” This remains true in design 2, where there is a full-on urn and not just a specific symbol chosen by others.

The Ellsberg Paradox and Ambiguity Aversion

• OK, this is not really an outline of an article, but at least there is an urn involved. The urn has a total of 90 balls inside of it. Thirty of the balls are black, and the other 60 balls are either red or blue. (That is, anywhere between 0 and 60 of those balls are red, and the remainder of the non-black, non-red balls are blue.) A single ball will be pulled at random from the urn. 

• Situation A: You can choose Bet 1A, which pays $100 if the ball that is chosen is black. Alternatively, you can choose Bet 2A, which pays $100 if the chosen ball is red. Which bet do you prefer? [Spoiler alert: most folks prefer Bet 1A.]

• Situation B: You can choose Bet 1B, which pays $100 if the ball that is chosen is either black or blue. Alternatively, you can choose Bet 2B, which pays $100 if the chosen ball is either red or blue. Which bet do you prefer? [Spoiler alert: most folks prefer Bet 2B.]

• The modal choices in these hypothetical urn-related decision problems, already spoiled for you, are to choose Bet 1A and Bet 2B. 

• These modal choices are inconsistent with expected utility maximization. A person who (strictly) prefers Bet 1A to Bet 2A, and is an expected utility maximizer, must believe that the probability of choosing a black ball (here, precisely one-third) exceeds the probability of choosing a red ball. A person who (strictly) prefers Bet 2B to Bet 2A, and is an EU maximizer, must believe that the probability of choosing a black ball is smaller than the probability of choosing a red ball (because the probability of winning via the blue ball is the same in either alternative, 2A or 2B).

• The disposition that (presumably) leads to these modal choices is termed ambiguity aversion. In Situation A, the subject knows precisely the probability of winning Bet 1A, but is unsure of the probability of winning Bet 2A. In Situation B, the situation is reversed, with Bet 2B being the option with the known probability (precisely 2/3) of winning.

• The modal choices, inconsistent with expected utility maximization, are an example of what has become known as the Ellsberg Paradox, after the analysis given by Daniel Ellsberg in "Risk, Ambiguity, and the Savage Axioms," Quarterly Journal of Economics 75(4): 643-669, 1961 [pdf here]; Ellsberg's version is on pages 654-655. The version in this post follows closely the presentation in the Introduction (pages 3-4) by Adam Oliver in Behavioural Public Policy, Adam Oliver, ed., Cambridge University Press, 2013.

Kocher, Lahno, and Trautmann (2015) on Ambiguity Aversion as Exceptional

Martin G. Kocher, Amrei Marie Lahno, and Stefan T. Trautmann, “Ambiguity Aversion is the Exception.” CESifo Working Paper No. 5261, March, 2015 [pdf available for download here].

[A later (and differently titled) version of this paper appears as Martin G. Kocher, Amrei Marie Lahno, and Stefan T. Trautmann, “Ambiguity Aversion is Not Universal,” European Economic Review 101: 268-283, January 2018.]

• In light of the Ellsberg paradox, many researchers believe that people are averse to ambiguity: people will accept known risks over ambiguous ones even when such choices are rather costly. 

• But ambiguity aversion has only been robustly demonstrated for choices involving uncertain gains, and where the probability of achieving a gain is moderate. What about quite unlikely risks, or prospects involving losses, or mixed (gains and losses) gambles? 

• Kocher et al. conduct a laboratory experiment with more than 500 participants. The main result is that for moderate likelihood gain prospects, ambiguity aversion exists (consistent with the prior literature). But outside of the moderate likelihood gain domain, aversion is harder to find, and even ambiguity seeking sometimes is common. Further, there’s a good deal of ambiguity neutrality in all conditions. 

• Previous work predicts: ambiguity aversion for moderately likely gains and for low likelihood losses; ambiguity seeking for low likelihood gains and moderately likely losses. Kocher et al. hypothesize ambiguity aversion for mixed gain/loss prospects. 

• In the first stage of the experiment, it is only in the moderate likelihood gain domain that ambiguity aversion (still, in a minority of participants) is indicated. Most people (in all domains) are ambiguity neutral. Once the effectively neutral folks are purged from the data set, what remains is the predicted pattern: ambiguity aversion in the gains domain for moderate likelihoods, and in the losses domain for low likelihoods; ambiguity seeking for low-likelihood gains and moderate likelihood losses. 

• For mixed gain/loss prospects, once again ambiguity neutrality dominates. When the neutrals are removed from the data set in this domain, the only statistically significant finding is ambiguity seeking for a .1 (average) chance to win 10 euro paired with a .9 (average) chance to lose 10 euro.