The behavioural economics of Lotto

Lotto (and similar lotteries in other countries) presents a problem for economists' assumption of rational behaviour. A rational, risk-averse person should never choose to play Lotto - it has a negative expected value (playing Lotto hundreds of times will lose you money, on average). This point has been made many times (see here for one example from Stats Chat - a simple search on Stats Chat will find you dozens more posts relating to Lotto).

So, if a rational person would never play Lotto, there must be some other explanation for that behaviour. So, I was happy to read this article in The Conversation by Ryan Anderson and David Mitchell (both James Cook University), which used some behavioural economics (among other reasons) to explain why people play Lotto. One reason related to availability bias:

The availability bias/heuristic relates to the idea that people judge the likelihood of something based roughly on how readily examples of it come to mind.

For example, you can probably think of news stories about when a shark has bitten a swimmer. One reason is this kind of a story is sensational, and will likely be highly reported. How often have you seen the headline: “No sharks at the beach today”?

Because you can easily bring to mind examples of shark attacks, you might be tempted to conclude shark attacks are far more common than they actually are. In fact, the chances of being attacked by a shark are somewhere in the neighbourhood of one in 12 million.

You hear and read stories about lottery winners all the time. Jackpot winners always make the news, but the battlers who have been playing for 20 years without winning are relegated to obscurity.

Based on this, it’s at least reasonable to think “jackpotting” can’t be that rare. The net effect is that winning seems possible.

Another related to the sunk cost fallacy:

In economics, a sunk cost is any previous expense that can’t be recovered – like a previous business expenditure on software, education, or advertising. Because this cost has already occurred and can’t be recovered, it should no longer be factored into future decisions. But this is seldom the case.

The sunk-cost fallacy occurs when you make a decision based on the time and resources you have already committed. Research suggests adults are more likely to fall victim to the sunk-cost fallacy than either children or lower-order animals.

In lotto, people will often persevere with what they sometimes know is economically irrational – like buying more lotto tickets – simply because they have already invested so much.

People are susceptible to the sunk cost fallacy because of loss aversion and mental accounting. Loss aversion simply means that we value losses more than we value equivalent gains - we prefer to avoid losses more than we seek to capture gains. This would seem to suggest we should avoid the losses that are inherent in Lotto. However, mental accounting (as the name implies) suggests that we keep 'mental accounts', such as an account for Lotto, and we like to keep those accounts in positive balances. Once we've played Lotto once, we will continue to play because if we stopped when we are behind, then we have to accept the loss from that mental account. As long as we keep playing, there is the chance that we win and the mental account turns positive. Note that this is also an explanation for much gambling behaviour, but also why we stay in jobs we hate, relationships we don't enjoy, investments that are not paying off, and so on. We don't want to acknowledge the loss.

Another behavioural economics explanation that Anderson and Mitchell referenced was our misunderstanding of small probabilities:

Gambling studies professor Robert Williams suggests that although humans have evolved some appreciation for numbers, we don’t really understand big numbers.

We deal with amounts like six, 24 and 120 all the time, but throughout history it’s never really been important to measure out 18 million of something, or count 50 million of something else.

Odds of one in 200 million don’t seem that different to odds of, say, one in 3 million. In both cases success is really unlikely.

Give someone a choice between odds of one in three and one in 200, however, and the difference is really obvious. It’s certainly not that people can’t grasp really big numbers, but that they don’t have much meaning until we stop and think about them.

It's actually worse than Anderson and Mitchell infer. Not only do people not understand probabilities, we have a tendency to overestimate the likelihood of very unlikely events. This is one of the cornerstones of prospect theory, the theory developed by Nobel Prize-winner Daniel Kahneman, along with Amos Tversky. So, if we overestimate small probabilities, we overestimate our chances of winning Lotto, and this makes us more likely to play (compared with if we understood the real probability of winning).

Finally, Anderson and Mitchell also made a point that I have made before, that people facing hard times have less to lose and are more willing to take a punt on Lotto. This isn't behavioural economics at work though - it is people becoming less risk averse. Either way, Lotto is more proof (if any were needed) that our behavioural biases are actively working against us making rational decisions, and the assumption of rationality is dead.