Can the proposals satisfy more parents?

Introduction

Gil Sweetenham's remarks at the Stringer open meeting on Monday 28 November made explicit what was strongly suggested in the Consultation Document, pp1-2. We can fairly put it this way:

Change will only be contemplated if it can be shown that it will raise the percentage of children allocated to their first preference school.

Gil claimed that work at the Council had suggested that such a rise would be the consequence of the adoption of a dual node for Stringer, assuming that 'first preference first' was retained.

However Gil's claim, properly interpreted, is necessarily false as a matter of simple arithmetic, given one uncontroversial assumption. Whatever number-crunching may be going on at the Council cannot affect this conclusion.

Argument

We must distinguish true preference from expressed preference. People are often forced to behave strategically. Obviously only true preferences really matter, although we can observe only expressed preferences. Assume that people's true preferences over schools are fixed (why this matters will be made clear later). It then follows, arithmetically, that:

Under 'first preference first', the percentage of children allocated to their (true) first preference school is independent of how places at oversubscribed schools are rationed

To see this, consider a simple example. We have four schools and 100 places at each school. Suppose that adding up the true first preferences would produce totals for the schools of, say, 130, 110, 90, 70. Then there are going to be 40 dissatisfied applicants in any case and the other 360 – 90% – of applicants will get their truly preferred school. Different rationing methods (eg moving nodes around) can only affect which 10% of applicants are dissatisfied. It is in this sense that Gil's claim cannot be correct.

Expressed preference versus true preference

The above argument does not carry over to expressed preferences. Changes to the rationing method can affect the extent to which parents are forced to misrepresent their true preferences. To take a pertinent example, if (parts of) Stringer and Blatchington Mill are 'moved away' from the Withdean area, then – under 'first preference first' rational parents may be induced to place Patcham first, even if it is third or lower in their true rankings.

So Gil's claim can be right in terms of expressed preferences. But what this means is that we can manipulate the figures up by forcing parents to misrepresent what they really want – more than they did before. In the limit, if there is effectively no choice, so that parents more or less have to put a particular school first (for fear of some very unpopular alternative), you might get quite close to 100%.

Is it right to assume that true preferences are fixed?

The answer is: 'no' in general, but 'yes' in the present case.

The rationing method can feed back to change true preferences if it alters the relative popularity of schools. The banding proposals in the White Paper could have this effect. If the ability mix were forced to be the same in all schools, one reason for preferring one school over another would be eliminated, so that the numerical imbalance illustrated earlier might be reduced. This recalls Mr Hawker's accurate observation (report to CFS, 5/9/05) that the solution to the oversubscription problem must involve achieving 'parity of esteem' across schools.

The proposals currently under consideration for Brighton and Hove do not have any such motivation and there is no reason whatsoever to expect them to have such an effect. As we learned at the Stringer meeting, when one parent asked at an Information Event whether there has been a Social Impact Assessment of the proposals, he was told that this was not what the proposals were about.

Conclusions

1. The proposed changes to the distance measurement method can indeed only move around a fixed burden of discontent, as stated in the recent Deputation to Council
   
   
2. Notwithstanding this, the changes could raise the percentage of expressed preferences met. But no policymaker could possibly regard this as an 'improvement', as it would signal only a rise in the extent to which parents had been forced to misrepresent their true preferences.

Annex: equal preference versus first-preference-first

The simple arithmetic becomes a little less simple under equal preference. What can be said? Retain the assumption that true preferences are fixed.

1. An equal preference system can at most satisfy the same number of true preferences as a first-preference-first system, and will usually satisfy fewer (by perhaps as much as 10%). This will happen if some of the places at oversubscribed schools go to people for whom the school was only, say, the true second preference. In the numerical example, for instance, the 90% you get under first-preference-first is the absolute maximum available.
   
   
2. What happens if we 'first' introduce equal preference and 'then' vary the rationing method? The percentage might go either way at the second stage, but it can never rise above the first-preference-first 'ceiling' – 90% in the example.