mathematics


Legal costs used to be based upon hours but this does not provide an incentive for lawyers to be time-efficient. Costs escalated. Managing legal costs involved squeezing down the scale of the work or the hourly rate of pay. Hence, purchasers of legal services shifted to alternative remuneration models with contracts for fixed or formula-based fees.

One of the enabling factors for this shift has been the availability of legal cost databases. Using statistical techniques, thousands of individual legal transactions can be summarised into a formula. Packets of work are identified: a law case is assigned standard amount of time. If the volume of cases is large enough then a “swings and roundabouts” argument can be made. Losses on one case can be made up by gains on another case. This is an economy of scale and leading to the demise of smaller legal practices.

Packetisation is suitable for transactional activities such as conveyancing. However, when it extends into the criminal justice system there is disquiet. As crime, and expenditure on crime has risen, publicly funded lawyers have to work within tighter case budgets. The UK already spends more per capita on criminal defence than any other country in the world and there is no political appetite to increase expenditure. The scope of criminal legal aid has been progressively reduced. Soon those facing jury trials will be subject to a means test.

Quality inevitably suffers when the time spent per case is limited. Less time is spent with the client. Elaborate case preparation is precluded. Clients may feel pressured to accept a solution that they do not really want. The delivery of justice is changing to be more affordable. The question is whether this changes the nature of justice – a question to which I will return.

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The reports on school mathematics drop bleakly one on top of the other. Each arrives at the same recommendation: a child needs a teacher to sit down with them and explain it in understandable terms; in other words, individualised learning. The drawback is the cost. Mathematics teachers are in demand elsewhere. The downsizing of the maths-savvy financial sector may have led to a temporary improvement in recruitment but a radical solution is required.

Many parents opt for private tuition, particularly for examination preparation. This is mainly provided by private tutors, often working within a franchise. Tuition centres, which, by aggregating students, could provide a more efficient service, are comparatively few. This is the direct result of government education policy which is biased against private education. Although about 7% of British children attend “private” schools, these are not actually private schools – they are charitable foundations. A private school seeks to make a profit which is frowned upon.

The financial obstacles to private educational providers are considerable. They have to charge parents VAT. They incur corporation tax as well as income tax. They do not qualify for relief on the local tax. By contrast, a charitable school avoids these fiscal burdens. Furthermore, a private tutor does not charge VAT, may not declare the income to the tax collector, and works without premises. Thus the UK has a fragmented private tuition sector. The outcome is confused and expensive access to individualised mathematics support.

The government has high expectations of the nation’s schools. Yet, it does not have the wherewithal to fund them to the extent required. It needs to encourage more investment in the education sector. There are numerous projects involving some sort of public-private partnership, but these have not transformed educational attainment. Dismantling the barriers to private schooling would unlock a swathe of private capital which would enhance the education sector.

There is a fear that private schooling may widen social divisions. However, society is not riven by mathematics nor, indeed, by differential knowledge of any particular subject. Improving the subject knowledge of children brings obvious personal and social benefits. We need to give children every opportunity to learn in the best way for themselves.

Suppose you had to get some work done on your bathroom. You meet with the potential plumbers, discuss the job and get quotes. You have all the information you need, you just have to decide. Let’s say that you want to be able to explain the decision to someone else so you want to make it objective. You devise a neat table setting out the important criteria and then score the plumbers. You might have cost, track record, customer service and so on. Give them marks out of 10. You might place greater weight on cost. Whichever gets the highest overall score should get the job, right? Wrong.

The weakness of the scoring matrix approach is found in the weightings given to the criteria. These should depict the relative importance of the criteria. Unfortunately they rarely do so because they are set too early. Objectivity requires that we should not know in advance what the scores are going to be. For example, one could end up with quotations from the plumbers within a relatively narrow price range. Let’s say that the price difference is miniscule. It is a mistake to give more weight to the price than to the track record of the plumber. The risk associated with poor workmanship would outweigh the cost savings. Weightings should come after scoring. It is only then that we are in a position to judge the relative importance of the criteria – given the range under consideration.
Using a “scientific” method makes a favourable impression. It is one of the most widely used methods of decision making. It is prevalent in business and the public sector, in recruitment and supplier selection. Some organisations make it mandatory. Unfortunately, it is grossly misunderstood. As a result, faulty decisions are commonplace. The next time you wonder how an unsuitable somebody managed to get a position in your organisation do not be surprised to learn that they ticked all the right boxes. It is just that some boxes should have been more important than others.