there is nothing outside the frame

the artificial information environment, again

This poll question has been doing the rounds on social media for a couple of weeks now, with a lot of people getting quite upset with one another:

“If you had a choice between instantly receiving £50,000 or a 50% chance to win £1m, which would you pick?”

The debate has been split roughly between “five hundred thousand is more than fifty thousand, duh” and “actually fifty thousand pounds would make a huge difference to lots of people’s lives actually as you would know if you weren’t so privileged actually”. For what it’s worth, 73% of people polled by YouGov said they would take the certain money.

It seems that the Discourse, though, has focused on what it’s rational to do. From an economic perspective, what is the correct choice to make? What does the science of economics say about this dilemma?

[…]

[…]

[…]

Ok I’m gonna stop you right there. Put down the graph, stop talking about utility, stop talking about risk aversion. What the science of economics tells you is that this will never happen. Nobody is ever going to put you in any situation where you’re stopped in the street as a stranger and offered either tens of thousands of pounds for nothing, or a risk free gamble worth half a million. If they do, you have long since left the world of economic reality behind.

Whatever else economics might say about rationality, it definitely says that the idea of “giving someone a choice between taking £50,000, or a 50/50 chance at £1m” is stochastically dominated by the feasible alternative strategy of “not doing that”. The best you might hope is that a bored behavioural economics prof might offer you 5p or a quid, and hope to extrapolate the results.

We have circumnavigated this mulberry bush before on the blog. Human beings evolved to make choices in real world situations, not completely bizarre ones that would never happen. Intuitions drawn from hypothetical cases stripped of all context and content are not necessarily insights into rationality. Here’s another hypothetical:

“You receive an inheritance of $1 million from a grandparent. A stranger claims to be a long-lost relative and contests the will, but offers to settle for $950k. Your lawyer tells you that you have a 50% chance of winning in court. Do you take the settlement or defend yourself?”

Strangely, people who claimed to have urgent needs for a certain £50k over a possible million in the first case start get very argumentative about the second. One of the things we know about choice under uncertainty is that framing effects matter.

But framing effects are all there are! Decisions happen in frames. They aren’t departures from rationality, they are the normal process of normal decision making operating normally.

As a matter of history the laws of probability we're first studied in the context of games of chance. But a casino is a very weird man-made environment, not a laboratory of rationality. The fact that the heuristics and choice principles that have kept humanity from dying out over thousands of years don’t necessarily give the right answers to some kinds of exam question isn’t a “bias” or “innumeracy”, it’s a failure of the model to describe reality.