The Conservatives are proposing a form of free market education, based largely according to them on the Swedish (and also American and Canadian) model of the last 20 years. The problem is, there's no convincing argument what they're doing is constructive.

They want to allow parents to effectively choose which school they want their portion of the schools' budget to go to, in essence forcing schools to compete for students.

There are two main problems with the Conservatives' position, perhaps symbolic of the current trends in politics - firstly, their policy is not right-wing enough, because it fails to allows schools to turn a profit (as Swedish schools can) and hence will likely lead to charitable institutions and small collabratives setting up minor that have little impact on the system; and secondly, it is far, far too right-wing, because it totally fails to promote equality and fairness in the educational system.

If you know me, you'll not be massively surprised to hear that the second issue is where my personal bone of contention is to be found. Newsnight recently found the Swedish model to be unimpressive as a piece of pioneering social organization, noting that in recent years "not only are standards generally down, there are strong indications that the new schools have increased social segregation".

It seems to me blindingly obvious that this is precisely what you would expect from such a crude attempt to make the school system more dynamic.

Obviously, you won't hear me disagreeing with the Conservatives' statement that giving

many more children access to the kind of education that is currently only available to the well-off: safe classrooms, talented and specialist teachers, access to the best curriculum and exams, and smaller schools run by teachers who know the children’s names

is a good thing (although I might well dispute, based on personal experience and the teachers who I know, the claim that one only gets such attention in the public and private school system). And it's trivially true that opening more schools will improve class sizes and, assuming that their budget is not effectively reduced during this process, also improve teaching quality and time (we could look here to up-and-coming countries like China, where 7AM-6PM state-funded schooling is reality for many people, as Ken Livingstone pointed out earlier this week).

Of course,

The Swedish people generally approve of the new system. About 10% of all students of compulsory school age now attend the new schools, and in the upper secondary level it is about 20%.

In fact, the Conservatives' draft schools' manifesto has much in the way of increased spending recommendations and increased powers, intervention and supervision: they will

• allocate increased pay budget control for headteachers (allowing them to "pay good teachers more", rather than the converse, it seems implied);
• "pay the student loan repayments for top maths and science graduates for as long as they remain teachers";
• "legislate so that teachers can ban any items that cause disruption in the classroom";
• "reinforce powers of discipline";
• "set up technical Academies across England, starting in at least the twelve biggest cities";
• "fund 400,000 new apprenticeship, preapprenticeship, college and other training places over two years"

and so on. Hardly the anti-nanny state, fund-cutting image we're used to, is it? The point is the Conservatives are basically in favour of creating more schools and educational institutions and allocating more funds to the school sector. Sure, the usual pro-discipline measures are there, but what's that really but increasing how heavily then government intervenes in day-to-day life? (I'm not against it, but many Conservatives seem to claim to be.)

But really, the basic principle of allocating funds in an essentially market-controlled manner is going to do exactly what it does in every other market - create some really huge, bloated organisations (Tesco, Whitehall, I could go on), crows out many smaller specialist instutitions, and result in bizarre competitions that end up not being beneficial to student, or (more likely) teachers. Put in this light, the apparently reasonable approach of having

more unannounced inspections, and failing schools will be inspected more often – with the best schools visited less frequently [and] any school that is in special measures for more than a year will be taken over immediately by a successful Academy provider.

seems somewhat more likely to result in the rapid construction of very large, monocultured schools, with presumably the same old problems with discipline, management, class sizes, and inefficiency.

Surely this will result in 'good' schools (presumably judged by the local media as much as anyone more qualified) receiving far too many applications to cope with, and hence either taking in too many pupils to manage adequately, or turning away vast swathes of candidates (based on what, one wonders) who would be forced to turn to 'worse' schools, creating significantly more inequality in the educational system, in the short and medium term at least.

Impressively, the Conservatives appear intent on doing this without even offering a monetary incentives to the people owning the schools. Regardless, having schools compete for students might also make for a considerably more high-pressured environment, both for students and teachers.

And even the other celebrated Conservative goals (particularly of 'liberating' schools from the tyranny of the 'politicised' national curriculum) seem thin when you consider even their idols Sweden enforce their curriculum.

Also, an interesting comment is to be found in this draft manifesto - the Conservatives will

end the bias towards the inclusion of children with special needs in mainstream schools.

I don't know what everyone else makes of this, but it sounds fascinatingly dangerous to me.

I went to see Ken Livingstone today.

Ken Livingstone is an interesting man. He is variously described as outspoken, "bold and imaginative", a disgrace, and Trotskyist. Whatever you think of him, I believe that more politicians like him could be a good thing.

I don't mean more left-leaning, or more environmentalist, or more liberal (well, actually, I do think these are good things, but that's really not what I'm getting at) - what I mean is forthright, open and frank. I like Vince Cable. I also have massively more respect for people on the right, like maybe Boris Johnson, and hell, even John Bolton, who state their (frequently wrong...) views openly and, yes, divisively, than those who studiously avoid the controversial in what they have to say, even when it is massively important to the electorate.

Yes, this is heavily directed at Cameron and Osborne and their ilk, people who leave you confused about their long-term vision, and their commitment to their policies.

But it is equally heavily directed to the Blairite school (although I certainly feel Cameron and Osborne - and Clegg, come to that) and the whole culture of 'professional' politicians (I use the word in the same way one describes 'professional fouls' in football) who exist, publically, as sort of ethereal ghosts in the machine, who do not represent with any confidence any values or schools of thought, but rather just give glimpses into an unknowable Whitehall existence.

Perhaps the world would be a better place if politicians (in fact, this is largely directed at higher-ranking ministers and their shadow counterparts) could step away from not just party line, but from the strange brand of modern political pseudo-realism which permeates all attempts at political debate. It is endlessly refreshing to hear people talking coherently about their own personal views, and putting forward reasoned, historical or just plain true arguments about important stuff.

Just my two cents.

Ken Livingstone was speaking at the Cambridge Union on Wednesday 17^th February 2010. He was mayor of London from 2000 to 2008, winning his first election as an independent candidate, and returning as a Labout party candidate in 2004. His achievements include introducing the first same-sex civil partnership register, before the government followed suit 3 years later, overhauling the public transport system, and introducing the congestion charge and other environmental measures. He was succeeded by Boris Johnson, but plans to run again for the role next term. Previously, he had served from 1981 as Leader of the greater London Council until the post was abolished by Margaret Thatcher in 1986. He is currently an adviser on urban planning in Venezuela, where we works with Hugo Chávez who he says is "just like me".

How sure are you?

Oddly, even though it's apparently one of the most fundamental questions to ask, we are often not very good at accurately judging and reporting our certainty of our own knowledge of the world.

I just got back from a stimulating and entertaining talk by the excellent Professor David Spiegelhalter entitled Quantifying Epistemic Uncertainty at the Trinity Mathematical Society.

He talked variously about the vagaries of different ways of interpreting probabilities (particularly the frequentist, Bayesian and 'metaphysical' interpretations, of which more below) and how they relate to our understanding of information in crucial areas like healthcare. He then went on to illustrate (with an excellent practical example in which he involved the whole group) exactly how our understanding of certainty can be quantified (or at least put in a useful frame) and used for the training and adjustment of accurate forecasts.

Metaphysical Understanding

The 'metaphysical' interpretation involves conceiving of possible futures, in an attempt to personalize risk. The article linked to above references this interactive demonstration which you might like to play around with, and maybe even use as the basis for a little experiment of your own. His argument is that the best way of getting people to understand the risks involved in individual lifestyle choices (like the purchase and use of statins) is to phrase it in terms of what could happen to them over 'multiple lives'.

If I am told there is a 10% chance I will suffer a heart attack or stroke in the next 10 years, lowered to 8% by taking statins, then my understanding of this changes according to whether I think of this in terms of, say, a 20% cut in the chance I suffer such an event; or for every 50 people taking statins, one 1 avoid a heart attack.

It is always clear that the mode of presentation of statistical information is of prime importance, and juxtaposition of statistics allows intuitive understanding of relative magnitudes to dominate over any attempt at a full understanding of, say, the worth of a treatment.

He contests that thinking in terms of 'future mes' is the most natural and valuable way to present what are by their very nature subjective statistics and risks. In 2 out of every 100 lives I lead, I would avoid a heart attack because I took statins.

Scoring Rules

The main body of the talk, however, was devoted to understanding the concept of a scoring rule. The idea is that, given some questions, and a subject who is answering them and providing an estimate of their own confidence in the result, you want to know how to reward (or penalise) the subject in order to get the most reliable information out of them about their own confidence.

For example, consider a meteoriologist forecasting the weather - if they are predicting weather with some stated percentage of confidence, how do you give them the incentive to be truthful and accurate and assess their accuracy?

The basic idea, stripped down to the simplest case of a binary event (e.g. will it rain tomorrow?), is to allocate some score S to every a probabilitistic forecast (or set of forecasts). In fact, we always assume we have several foecasts. Then the overall score should be higher when the forecaster is most reliably accurate at declaring uncertainty, and lowest when the forecaster routinely makes incorrect forecasts with high confidence.

Specifically, we call a scoring rule a proper scoring rule if the expected score is maximised (or more generally optimised) if and only if the actual probability of the event is exactly equal to the forecast probability.

For example, take a test with a quadratic (Brier, after the man who created the score around 1950) score, , where x is 0 or 1 according to whether or not the event occurs and q is the estimated probability it does. Then if the forecaster believes that there is a probability p that it does occur, the expected score (from his point of view) is which is equal to . So clearly, the forecaster maximizes his expected payoff by setting his projected likelihood q to exactly what he truly believes it to be, p.

Note that not all scoring rules are proper - not even all likely seeming candidates are. For example, you can check encourages forecasters to exaggerate (i.e. to pick q to be always either 0 or 1).

You can easily conduct an experiment using a scoring rule with any group of people - give them a multiple-choice test (two options each time for these simple rules) and get them to write down a 'confidence' probability for their answer - say 5/10 for a total guess and 10/10 if they are entirely certain. Then give them the corresponding score according to whether their answer was correct and their stated confidence, and you are left with a set of overall scores indicating who was the most honest and reliable answerer. This works very well (especially with punishing negative scores for high-confidence mistakes) as both a party game and statistical exercise.

A sample (quadratic) set of numbers are (listed as confidence, score given correct, score given incorrect):

• 5: +0, -0
• 6: +9, -11
• 7: +16, -24
• 8: +21, -39
• 9: 24, -56
• 10: 25, -75

A few different scoring rules are illustrated here.

In the long run, i.e. over several forecasts and experiments, we can 'decompose' (see this article also) the sum of the Brier score above into three components: Uncertainty, Reliability and Resolution. (Note the linked article uses a Brier score which is lower for better forecasts - this corresponds to dropping the leading 1 term in the above definition and making the remaining expression positive.)

1. Uncertainty provides a measure of how naturally diverse the events are (maximised when the event occurs 1/2 of the time for a binary event like we are considering). The Brier score is higher (worse) when the uncertainty is naturally larger, reflecting the fact that it is more difficult to give accurate predictions in this case.
2. Reliability shows how far from the truth the forecasts were, on average; so a figure of 0 indicates perfect accuracy, whilst larger values show more deviation.
3. Resolution shows how much the forecasts differ from the overall average score - note that one can achieve very high levels of reliability simply by constantly predicting the climatic average; resolution is higher when the forecasts are 'more definite' than this, and so is substracted from the score to improve it for higher resolution. It precisely equals (and hence cancels out) the uncertainty in the score when the predictions are always definite (0 or 1).

Spiegelhalter also noted that one can actually justify the construction of a semi-frequentist, semi-Bayesian theory of probability - and in fact derive the standard axioms of probability as theorems in this alternative, 'deeper' formulation of the subject.

It's possibly worth considering the slightly more fickle aspects of this method - encroaching on the field of game theory, in fact, as one considers less local tactics and maybe even psychological aspects to the situation. Most notably, it may be the case that maximizing expected score leads to non-optimal behaviours, and with human error and tendency to bias confidence included the situation becomes a lot less clear. Scoring rules are fairly heavily used (as suggested by the terminology and examples) in meteorology and similar areas, but the field seems to be studied rather less than one might hope. Still, something to do over the holidays...

David Spiegelhalter is the Winton Professor of the Public Understanding of Risk here at the University of Cambridge. He works largely with public-sector outreach and educational projects and the media, but also teaches an advanced course in Applied Bayesian Statistics, and retains a research interest in several practical areas of statistics, especially healthcare. He also runs the website Understanding Uncertainty, a resource for easy to read statistical treatments of various topics. He was talking at the Trinity Mathematical Society (TMS) on Monday 15^th of February 2010.