dark side of the nudge

Month: August, 2013

The Price of Gambling

My high street in south London recently featured in a Channel 4 documentary on gambling (12.06, see video). In a short space of road there are six bookmakers: two branches of William Hill, two branches of Betfred, a Paddy Power, a Coral and a Ladbrokes. Placed conveniently nearby are a number of payday lenders and pawn shops.

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The documentary points out that bookmakers cluster in this way partly because of the regulations over “fixed odds betting terminals”, high-speed betting machines where large sums can be gambled frighteningly quickly. Law restricts these machines to four per betting shop. But since they are such high-earners for the bookmakers, they simply open extra branches, usually in relatively deprived areas (9.30, see video).

Gambling is, clearly enough, a high-revenue industry. Although there are around 450,000 problem gamblers in the UK (19.50, see video) – a scary number – the gambling industry must always find new ways of increasing revenue. And if creating new gamblers is too difficult, then the only other way to increase revenue is to put up the “price” of gambling.

The price of gambling is hidden over time. Gamblers do not feel the price on every trial, since sometimes they will win and hence pay a negative “price”. Everyone knows the joy of getting something for free – at a price of zero. Perhaps the thrill of gambling is a souped up version of the same reward process.

But most gamblers do pay the price over time. Especially in mechanical games such as roulette, with no skill element, the house will always win in the long run. The industry is currently exploring two main ways to increase the price of gambling., decomposed as follows:

Price of gambling = expected loss per bet * amount wagered per hour

You can either get people to accept bets that are more statistically unfair, or you can get them betting higher amounts per hour. And if you can’t get them betting more per bet (because of loss aversion), you can increase the number of bets per hour. The online gambling industry was the first instance of how modern technology could exploit this latter point, but it is now moving into mobile devices and the high street with fixed odds betting terminals. The terminals are an issue the government is aware about, but there are some other features of the price of gambling that are less well known.

If the speed and stakes of gambling are already maxed out, then the only other way to increase the price of gambling is to get gamblers accepting bets that are more statistically unfair. This is an especially new and sophisticated way of increasing the price of gambling. Traditionally, bookmakers strove to have an “even book”, where the odds are initially set, and then adjusted so that a roughly equal amount is wagered on each outcome of a sporting event. In American football the main bet is whether a team can “beat the spread”, a bet with two mutually exclusive outcomes (beat the spread/not beat the spread) that should be equally likely. The spread is used to adjust for skill differentials between teams, so if team A is a marginal favourite, beating the spread might see them winning by a margin of more than three points. If an equal amount is bet on each side, then the bookmaker earns a risk-free profit of 5% of the total book, since they only offer odds of of 10-to-11 on each event with p=0.5 (bet 11 to win 10). This is pretty good, since it requires little knowledge of the psychology of gambling and probability, or the event being bet on (some sophistication is required to set the initial odds on a skill/luck domain such as a sporting event).

But bookmakers are starting to realise that a little more savviness can can produce bigger, although riskier, profits by exploiting biases in judgement and decision making. The football season started today with the community shield between Manchester United and Wigan. Almost all bookmakers promote football bets in their windows, although only three of the shops on my street were geared up this early in the calender. These bets follow a simple and almost universal pattern. They pay-off only if two or more events occur (a conjunction), and these are usually likely events (the best team winning, or a famous player scoring).

So in the match today, Manchester United are clearly the favourite as Premier League champions against a newly relegated side, and Robin van Persie is the most famous goalscorer, with 30 club goals last season. Here are the bets I found most highly promoted:

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Notice how the bets follow the same pattern. Manchester United need to win, and a scoreline of 3-0 wouldn’t flatter them in many people’s minds given the skill difference. And Robin van Persie has to score the first goal. In the last bet Manchester United have to win by the specific scoreline 3-2. In actual fact, they won 2-0, with van Persie getting both goals. Notice how this creates the sense of a near miss, with individual events that are quite likely to happen, there’s a good chance of at least one occurring. When an event occurs, but other events of the necessary conjunction for the bet do not, this creates the sense of a “near miss”. The gambler did not lose; she “nearly won”. But in order to win these bets, a number of events must co-occur. Probabilities of all events happening quickly shrink as more events are added to the conjunction. If the events were independent (not the case here), two 0.5 probabilities would co-occur with 25% of the time, three events 12.5% and four 6.25%. Large conjunctions create many near wins, without a lot of actual ones. This is perhaps why accumulator bets, which offer seemingly high odds if a large number of specific teams win, are so popular.

But there is something even sneakier with the promoted bets. There is a large literature in judgement and decision making on the psychology of probabilistic reasoning, with conjunctions being a key topic of interest. This paper by Tversky and Kahneman (1983) kicked things off, with the finding of a “conjunction fallacy”: where, contrary to the axioms of probability, participants rated the probability of a conjunction (P(AandB)) being higher than one of the constituent parts (P(A)). This can’t, of course, happen, even if B happens with certainty. Of particular relevance here, they found this effect in a sporting context (p.10). Bjorn Borg was at the time the reigning Wimbledon champion, and participants rated the probability of him “losing the first set and winning the match”, as being higher than the probability of him “losing the first set”. The high perceived likelihood of him winning the match, an event that most participants had strong memories of, led to the conjunction fallacy.

This paper led to a large debate in the field, much of which isn’t especially relevant here. A recent paper by Khemlani, Lotstein & Johnson-Laird shows, however, that you can be irrational about conjunctions without committing the fallacy. Asking participants to estimate P(A), P(B), P(AandB), is enough to fix the “joint probability distribution”. Probability estimates can still be irrational, even if they do not commit the conjunction fallacy, if the joint probability distribution implies a negative probability for one event or more. And this happened frequently in their experiments (although it was not in a sporting context), especially if the probability of the conjunction was estimated before the individual event probabilities.

Bookmakers are clearly exploiting our poor ability to comprehend the probability of two or more events co-occuring. Bookmakers are no longer striving to earn risk-free profits with an even book. They do not promote, or even offer, bets that are the complements of their highly-advertised bets, such as “Robin van Persie not to score the first goal, and Manchester United not to win 3-0”. Bookmakers would rather risk making a loss when their promoted bets do happen, simply because the likelihood of these events happening is so much worse than the odds they offer.

These bets are a sophisticated way of increasing the price of gambling. Not only do they look attractive on the surface, Robin van Persie scores lots of goals, Manchester United often win, hence attracting more bets, but they are really overpriced compared to a true appraisal of the relevant probabilities. And bookmakers would rather take a risk on these bets not happening, than hope to earn risk-free profits from a balanced book. Exploiting errors in probabilistic reasoning is a clever way to raise the price of gambling.

Now, of course the gambling industry has an answer to every criticism. They are just offering the bets that people like, and they are bringing jobs to areas that need them. But jobs in this industry are only paid by a zero-sum transfer of wealth away from gamblers, something that the industry is becoming more efficient at. Take away the gambling, and consumers will have more money, which they can spend on other things and which in itself can create as many jobs as the gambling industry. Plus consumers can now actually spend their money on things with intrinsic value.

In most industries, consumers happily pay for high-price products that they highly value. A brand new iPhone makes a lot of people very happy. There is little evidence that the same thing works in gambling. Increasing the price of gambling makes most gamblers worse off, since they lose more money and at a faster rate. The price of gambling is hidden, both because it is only paid over time, and because a number of psychological effects are being used to add extra opacity. How much does this latter point add to the price of gambling?

Values and Nudges

“Nudge for good.” – Richard Thaler

 

When signing copies of his book, Richard Thaler tells his followers to “nudge for good”. And of course, most of us do want to do exactly that. Although there are plenty of dark nudgers and nudges out there, most of the ill-intentioned behaviour change out there is likely a result of random trial-and-error and imitation. But what do we even mean by “nudge for good”? Whose version of good do we mean? A key problem that proponents of behaviour change have faced is precisely trying to convince the public, and vocal opponents, that they “know better” than the average Joe. If the nudger (aka “choice architect”) is as systematically biased as the man on the street, then why should we nudge at all?

I believe that a key distinction lies between nudges that are value-free, that improve behaviour, and value-laden nudges, which merely affect it. Behaviour change is being hijacked by those who want to impose their values upon others. In doing so, they not only undermine the movement in many people’s eyes, but they also manage to miss the low-hanging fruit that could be easily reached to make real improvements in our lives.

David Cameron’s recently announced UK porn filter is a perfect case of a heavily value-laden nudge. This is an example of a default option nudge. Currently, the default option is to have free access to online porn. People who don’t want to receive access to porn have to opt-out. The new system flips this around. The default option will be for no access to porn, with people having to actively opt-in to accessing it with their ISP. Since many people are too lazy to question a default rule, the hope is that this change will help many people who do not want access to porn, but who aren’t willing to actively change from the current default. People who do want to access porn will not be prevented from doing so; they merely have to jump through an extra hoop.

The British population is being nudged in a way that flows from David Cameron’s own personal definition of “good”. Put aside for one moment that this is being rolled out without a proper randomised controlled trial – the usual metric for behavioural interventions. The filter is naturally attracting a lot of scathing attention in the press (c.f. Vice), and a lot of the criticisms are being directed at nudge theory. But is the really theory at fault, or just the fact that people are using it to fulfil their own personal goals? And people who question these personal goals will naturally question the theory that comes with their implementation.

But it doesn’t have to be like this. Many things we do – many “mistakes” – do not come with this value-laden baggage. If on the one hand we have a normative model of behaviour, which says how people rationally should act, and on the other hand a systematic bias – an average irrational mistake – then this debate is really superfluous. By nudging people towards the normative model, by reducing the average size of their mistakes, then there really isn’t any debate. Reducing systematic biases is an improvement, no matter your personal beliefs. And there are in fact so many biases in decision making, in financial decisions, probabilistic decisions, matters of health, and life and death, that we really should be budgeting our scarce nudge capital in better ways. There are only a limited number of economists, psychologists, and practitioners who are interested in these things. But there are so many systematic mistakes that are currently being unattended to, or only explored at a very shallow level. Econ 101 teaches us that any scarce resource should be allocated to where its comparative returns are highest.

Constraining choice architects to work within this framework of normative models and systematic biases will help in two ways. It will prevent people from arbitrarily imposing their values and personal beliefs on others. We have a great tool here for making the world a better place. It would be a shame to ruin it because the tool is associated with a whole bunch of extraneous baggage that comes with it in many people’s minds. And, perhaps more importantly, it will ensure that the tool is used in the most efficient way possible.

Here is one example of a value-free nudge; there are plenty more possibilities that could be found by reading around the judgement and decision making literature. Bayesian inference is the normative model for updating prior beliefs in the light of new evidence. A purely rational Bayesian decision maker should, over an indefinite course of time, update their beliefs to perfectly match objective probabilities in the world around them. Medical testing is one example of a Bayesian inference task. There is some prior probability that the patient is ill, a medical test is then performed, and an updated probability of illness can be computed. Crucially, medical testing is not a perfect science: there is some probability of false positives (a healthy person testing positive on the test).

Physicians should, normatively, use this model of decision making when informing patients with positive test results. Most people – physicians and non-physicians included – display systematic biases, however. We tend to not fully appreciate the role of false positives, and so overestimate the chances of having a disease given a positive test result. For example, HIV testing is very reliable, in that the vast majority of people with the disease will test positive. But people tend to make the opposite (and incorrect) inference, that a person who tests positive will almost certainly have the disease. In fact, for people in low-risk groups, the probability of having HIV given a positive test result can be around 50%. This is because the false positive test result is roughly as likely as a person in a low-risk group actually having HIV.

Nudging physicians towards making more accurate diagnostic inferences is one example of a value-free nudge, because it reduces the extent of a systematic bias from a normative model. This is a “good” thing, no matter your political, ethical, or moral beliefs. And in this case, there are nudges that can improve statistical inferences (e.g. by representing probabilistic information in terms of naturally occurring frequencies, or by highlighting causal pathways that can be responsible for false positives).

Given that there are so many potential value-free nudges out there, we should aim for the low-hanging fruit and aim to making improving behaviour our priority, not merely affecting it. Hopefully those in power will realise that there are bigger gains to be made from this tool than just political point scoring. The danger is that such value-based nudges might swing popular opinion so far away from behaviour change that we might lose support for this very valuable tool.