Brexiteers and Risk

Here's a quick post about a story that caught my eye.  Apparently Nigel Farage has placed a £1,000 bet on Britain voting to leave the European Union.  Let's assume that Nigel Farage wants the UK to leave the EU, then this tells us something about the man and his attitude to risk.

Suppose I offered you the following two options.  Option 1: I toss a fair coin, if it comes up Heads, you pay me £10,000; but if it comes up Tails, I pay you £11,000.  Option 2, I just give you £450.  Most people, if they are honest, would probably choose option 2.  But on average, Option 1 is worth £500.  If you are honest with yourself and choose option 2, then you are risk averse.

Economists usually assume that individual agents are risk averse.  In other words we don't like risk, and, where possible, we would pay someone else to take on our risks for us.  That's why there are companies that sell insurance.  Insurance policies pay out sums of money in states of the world where certain events have happened, such as our house being robbed, or our car being damaged in an accident.  In that way, betting markets, which bet on events happening or not happening are actually a lot like insurance policies.

So how would a risk averse individual approach betting on the EU referendum given that they have a preference the result should go one way or the other.  If someone really wants to see the UK vote to leave the EU, they should actually bet on the UK voting to stay in.  That way, they narrow the set of possible outcomes in terms of how happy they are at the result.  Their elation at Britain voting to leave would be a little muted by having lost a bit of money, but their disappointment at Britain voting to stay would be compensated by having won some money.

For die hard proponents of either remain or leave, it may well be the case that even bets of £1,000 don't provide stakes high enough to provide full insurance (ensuring they are just as happy in either event), but they must be able to use betting markets to provide some insurance.

So what does it tell us about an individual if they bet £1,000 on their preferred outcome, thus widening the outcomes and exposing themselves to more risk.  It could be that they perceive the odds are very favourable, and so they take on more risk for what they perceive as a much higher expected level of wealth.  However an individual should be aware of and correct for their own optimism bias.

The other possibility, and this seems somewhat more likely, is that they are not risk averse as most people are believed to be, but risk loving.  They enjoy risk and the shot of adrenaline they get as they wait to see if their horse crosses the line first.  The wider the risk, the greater the adrenaline hit and the more fun it all seems to be!

I'll be the first to admit that people like this can be fun to hang around, but I just have one more question for you: How much of your money are you willing to trust them with?  Because a vote for Brexit is a vote to trust some highly risk loving people with all of our money and all of our futures for generations to come.

A Brexit Thought Experiment...

Let me introduce Nigel.  Nigel is a very wealthy family man who lives in a very wealthy region of the country.  He is in fact the 5th wealthiest man in the country.  He's rather proud of this and mentions it quite a lot.

One day, Nigel is looking through his monthly expenditures and wondering where he can make some savings.  Although he is very wealthy, this is a prudent thing to be doing.  After all, as his mother always said: “look after the pennies, and the pounds will look after themselves.”  Looking through his expenses, Nigel spots that family membership of his golf club looks a bit high.  He pauses to consider this fact.  He doesn’t actually much like the officials who run the golf club.  They have a habit of being a bit officious and petty in enforcing the club's rules.  Is this club membership really worth the money?

Nigel broaches the idea of resigning their family membership with his wife and children over dinner that evening.  To his utter amazement, they look at him as though he’s gone mad, even after he mentions the amount of money they’d save.

They point out that the club's facilities are brilliant. They go there and have a great time every week.  Furthermore, Nigel uses it very effectively to network with clients and potential clients.  His family point out that the commission he earns on business won at the club more than covers the cost of membership.

Nigel tries to calmly rebut all their points.

Just because they are resigning their membership of the golf club doesn’t mean they’ll lose access to any of its facilities.  They’ll still be able to use the driving range; the 18 hole course; the restaurant and the bar.  So they’ll still get all the networking advantages too.  The weekly family trips aren’t going to stop.

Nigel’s family seem strangely skeptical about this argument.  How will they get access to the facilities if they are not members.  There is the possibility for non members to use the facilities - for a daily fee.  But the daily fee is large enough that, given the number of times in a year they visit the club, they’d be better off just paying the annual membership fee.  Visitors paying the daily fee still have to abide by all the niggling little club rules when they are at the club.

Nigel is absolutely amazed to hear this rebuttal.  Don’t his family realise how business works.  Once he is no longer a member, he’ll be able to negotiate his own special rate.  After all, he’s the 5th wealthiest man in the country, the golf club will want his business, and will bend rules in order to get it.  So he’ll be able to negotiate terms that wouldn’t necessarily be available to others.

His family are still sceptical.  Will they want our business that much they ask?  They might be a bit hesitant to give us special terms, wouldn’t they think it was dangerous to set that kind of a precedent?

At this point Nigel gets frustrated and and a bit angry: "of course they won’t mind about setting the precedent!" he exclaims.  Afterall, we buy a hell of a lot more from them than they buy from us!

At this point, his family look at each other and just say “yes dear”.  They know from bitter experience that it is better not to argue the point when Nigel has become this animated.  Besides this vocal argument is happening inside the club's restaurant, and people are starting to stare.  It is all a bit embarrassing.

If you are reading and are a British citizen and a member of a golf club or tennis club, or even a tiddlywinks club, then I implore you: before 23rd June, try this:  

• Go to your club, tell them you are resigning your membership, but insist to them that this means you will still have every right to continue using the club’s facilities.   
• If they put up a fight, try to negotiate your own special rate.   
• See how far you get…

 

Bayes' Rule and Political Inference

Consider a question such as: Would politician A be a good leader or not?  Now consider some information that might arrive that might inform our answer to that question in the form of the recommendation of an opinion former, maybe a newspaper makes a decision as to whether to endorse A or not.

Suppose an individual’s prior belief that A is a good leader is p, and their prior belief that the newspaper endorses a politician who is a good leader is q.  Once the news arrives, the newspaper will either endorse A or not.  If they do not endorse A, then the individual’s posterior probability that A is a good leader will be:

p'= p(1-q)/[p(1-q)+q(1-p)]

But the posterior belief about the accuracy of the newspaper’s endorsements will also have changed, and will indeed be the complement of the probability above:

q'= q(1-p)/[p(1-q)+q(1-p)]

Afterall, once the newspaper does not endorse A, either A is not a good leader or the newspaper does not make good endorsements. 

Suppose that the newspaper is a source that we would normally trust reasonably well, q=0.75.  It might, for example, be The Economist. But suppose that we are convinced on a level approaching religious fervour that politician A would be a good leader, and p=0.99.  Then as a result of the newspaper’s lack of endorsement for A, a bit of doubt will creep in, and  p'=0.97, but by far the biggest movement is in the probability that the newspaper endorses good candidates and doesn’t endorse bad ones as q'=0.03.

What if the newspaper endorses the politician?  Then the posterior probabilities in this case will be:

p''= pq/[pq+(1-p)(1-q)]

q''= pq/[pq+(1-p)(1-q)]

Similar results obtain if the individual detests the politician in question, and believes, with semi-religious fervour, that they are not a good leader.  Suppose that q=0.75, and p=0.01, and the newspaper endorses the politician.  Then the posterior probabilities will be p''= q''= 0.03.  So, once again, by far the biggest update  from the news of the recommendation is on the reliability of the recommender, rather than the subject of the recommendation.

The lesson?  When a group of people are absolutely convinced that a politician is the right/wrong person to lead, endorsements, or failures to endorse will be treated more as evidence of the accuracy of the person giving the endorsements rather than as evidence about the potential leader in question.  This offers some explanation as to why "marmite politicians" people who are either really liked or really hated, are able to maintain their core support in the face of such ferocious attacks as they frequently receive.  To their supporters, the attacks contain more information about the attackers than about their target.  To their detractors, any defence of them contains more information about the defenders than about the subject of  the defence.