“Quiz time!” Recap

Last week's Quiz time! post about the Allais Paradox generated the most diverse and on-topic set of reader comments for a JEC post in awhile, so today I'm going to recap.

What I neglected to mention in last week's post is that a lot of people answer A-B-A or A-B-B rather than one of the two rational sets of answers, A-A-A or B-B-B. One explanation for this phenomenon is a psychological effect called the certainty effect.

The certainty effect happens when a person assigns a premium to a certain outcome for the sake of certainty. For example, imagine you have a 100% chance of winning $1 million. Now imagine your chance of winning decreases to 90%. How much worse do you feel at 90% than you did at 100%? Now further imagine your chance of winning decreases to 80%. How much worse do you feel at 80% than you did at 90%. Many people feel the change from 100% to 90% more acutely than they do the change from 90% to 80%, and they're willing to pay a premium for it. A common rationale is that the 100% chance is a sure thing while both 90% and 80% aren't sure things. Nevertheless, the decrease in probabilistic value from 100% to 90% is the same as the decrease from 90% to 80%. Objectively, if we were playing only the odds, we wouldn't favor certainty for the sake of certainty.

But should we play only the odds? There's more than one way to look at it.

Firstly, there's subjectivity in any chancy game. As last week's first question showed, some people would prefer to keep a sure $1 million, while some people would prefer to give up one of those percentage points to gain 10 percentage points of chance of doubling their winnings. But if you were strictly playing the numbers, then you would always pick the 10-for-1.

\[ (89\% \times \$1 \text{ million}) + (10\% \times \$2 \text{ million}) = \$1.09 \text{ million} \]

But to many people, the extra $0.09 million isn't worth risking $1 million—no matter what the odds are. They value winning differently than, say, a billionaire who likes thrills.

However, though we expect different people to value risk differently, we might expect everyone to be consistent with respect to their own risk valuations. But often this isn't the case, and that's what the three questions in last week's post together show when people say they would tolerate a 1 percentage point smaller chance of winning only when that decrease is from 11% to 10% and not when it's from 100% to 99%. That's akin to saying that sometimes the extra $0.09 million is worth risking $1 million for, but sometimes it isn't.

Is there a good reason to waver on that choice?