Boole and his Booby Traps

A mathematician called George Boole was born two hundred years ago this week. He was the first to reduce parts of mathematics to yes/no switches, leading to many advances in probability. Then the same logic became the grounding for all modern computers, with its reliance on zeros and ones.

I owe George at least one small gift. In my O level mathematics course, I recall Boolean algebra as an optional subject, one where there was an exam question in a section where you needed to answer only some of the questions. This was a nice example of how systems favour the privileged. Most schools presumably did not have the teachers trained for optional subjects, and many struggled to complete even the regular curriculum. Mine had no such constraints and those of us in the top classes were duly taught Boolean algebra. Now, I suppose guessing that many students would not have had much opportunity for classes, they always made the Boolean question ridiculously easy. For me it was a gimme every time, the first question I turned to, one I could do in five minutes and could always get right. So, much like modern taxes, those with advantages were handed out more. The world is not a fair place.

Key to most of Boole’s logic was that it required variables to be independent of each other. Therein lies the rub, for in the real world less is independent than we like to assume. In the last century, game theory and other advances came along to try to understand what happens when variables depend upon each other. The most common mistake with Boole type logic is to assume either that switches are fixed at zero or one and cannot change, or that two switches are independent when they are not.

I have three examples to demonstrate this, two from business and one from today’s politics. I hope they are useful cautionary tales for people who tend to oversimplify life.

My first example recalls a piece of market research we did in Shell UK in the early 1990’s. Someone came up with a beautiful simple pie chart dividing consumers of motor fuels in price conscious ones to whom price was a major component of buying choice, and those that bought relying on factors other than price.

Lo and behold the first version of the pie chart was split almost 50/50. Ah ha, said our Boolean managers, let us focus on the second group. They are half the market, they offer higher margins, they are amenable to our splendid marketing offers, and the other group probably doesn’t buy from us already. And a fair share of 50% is plenty to maintain or even grow our market share.

What a tragic mistake this was. This occurred just as Tesco and other hypermarkets were starting to put fuel stations in their car parks and pricing well below everybody else.

There were many mistakes in our logic. First, we were used to a segmented market where the only discounters tended to be dirty places where consumers couldn’t trust in fuel quality. We made the mistake that consumers were lured by our positive marketing rather than buying habitually with us out of convenience and because there was no realistic choice, at least for the “good” 50%. Tesco and the others changed all that. Their marketing and convenience was as good as ours, so consumers flocked to them, and not just the price conscious ones.

The next time we did the same research the pie chart segments had moved, maybe to 60/40 in favour of price. Not a disaster yet, but a story foretelling disaster. Our own pricing behaviour relative to the hypermarkets had educated consumers to change their buying criteria, and this accelerated as the hypermarkets built out their networks and were allowed to maintain ever-greater price discounts, and in the end even make more money than us because of their high sales volumes (and low buying costs, because our own colleagues were selling to them more cheaply than they were supplying us, which is another story). There are many factors in this disaster, but it all started with that blissfully simple Boolean pie chart.

The second example is similar and also centres on market research. In the early 1980’s, just when I was a new bank account holder, the banks did some research that produced a pie chart between consumers who switched banks and those that did not. Lo and behold, more than 90% of consumers never changed bank, most of them remaining lifelong customers of their first bank.

Once again, the brilliant managers drew a sweeping conclusion. If only we could lure college kids to bank with us, we’d have them for life! All of a sudden the market was flooded with adverts and special offers aimed at people like me. There was a brilliant one for NatWest by a punk Adrian Edmonson that I still remember.

At college, when we had time between flirting and getting drunk, we all compared the offers and chose the best one. Then three months later many of us would receive another promotion from someone else and switched. We then repeated our switching behaviour throughout our banking lives: I have been at various times with all the UK majors and many of the minors – not chasing offers, but usually responding to some crass disrespectful behaviour.

Of course the marketing geniuses at the banks had let a terrible genie out of the bottle. They had assumed that their research indicated fixed behaviour, and then their own behaviour invalidated their assumption. They created a generation of switchers, and every generation since has been the same.

The third example comes from today’s politics, and concerns Western and especially US attitudes to refugees, especially Arab Muslim ones. The US has a reasonable record for accepting refugees, but in the current case they are very concerned about letting in terrorist infiltrators who will then attack the homeland.

This is fair enough, and some screening makes sense. But the practical outcome is a degree of screening that takes more than a year to complete and means the US cannot do enough to clear the terrible backlog of displaced people from Iraq and Syria, who end up in transit camps or trying to get into Europe.

Can you spot the Boolean error? The US divides potential refugees into terrorists and non-terrorists, and considers the split to be permanent. Then its own behaviour changes the ratios.

At any moment in time, I guess most potential asylum seekers either have an intent to do damage to the US homeland or don’t. Probably the percent of potential terrorists is very small. But what does the US behaviour achieve? While waiting in the poor conditions of a transit camp being subjected to all sorts of interviews and background checks, some of the non-terrorists might change sides. If meanwhile they hear of family members killed by US drones or perishing in the Mediterranean their attitudes might become more hardened still.

Indeed the whole US policy towards the Middle East suffers from the delusion that opinions and positions of others are fixed. Nothing created more terrorists than the invasion of Iraq. The only way to really defeat IS, and all the other groups, is to deal with their grievances. This is tough to achieve, sometimes impossible, but at least policy could focus on avoiding making things worse.

George Boole left a wonderful legacy. It is just a shame that so many of us fall into his booby traps.