Ron Johnston, dissects the no-win rules of the Research Assessment Exercise. With less than a year to go to the submission date for the next Research Assessment Exercise (RAE), there is frenzied activity in British universities.

New appointments are being made, with the individuals to be in place well before March 31 next year; editors are being pressed to ensure that books and journal articles appear before that date; calculations are being made to evaluate which staff to enter and their likely impact on the grade; and efforts are being redoubled to recruit as many research students and assistants as possible for the start of the next academic year.

It may all be to no avail. A department could grow quite significantly; it might even increase its grade by a point: but in either case it may nevertheless earn less money for its institution - and perhaps have to employ fewer staff supervising more students and researchers as a consequence.

A number of factors point to this conclusion, not least the ÖйúAƬ Funding Council for England's decision to impose an "efficiency gain" on research funding alongside that inflicted on the teaching function for several years. But it would almost certainly happen in any case.

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A metaphor which helps appreciate the situation is that of the "tragedy of the commons", long used by those interested in environmental issues to demonstrate why we abuse nature and take decisions which lead inexorably towards a life which Thomas Hobbes characterised as "poor, nasty, brutish and short". It has considerable relevance to the HEFCE's current research funding formula for English universities.

In the "tragedy of the commons" there is an area of common land, on which herders graze cattle. Each will graze as many as possible, until the optimum carrying capacity is reached. No more should be added, but individuals continue to increase their herd size to maximise their returns.

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Since the income from an additional animal goes to its owner, whereas the negative costs are felt by all herders, the result is a net gain to the individual who increases herd size, and so herd sizes continue to grow until eventually the land is exhausted.

Assume that when the land is at its carrying capacity, each animal produces a return of 100. An additional animal reduces the average return to only 99, because the quality of the grazing land declines slightly. If one herder adds an animal above the carrying capacity, therefore, increasing her herd size from 20 to 21, her extra income is 99.

She also loses 20 (i.e. 1 each) because of the reduced value of the other 20, but the net outcome is that her income grows from 2,000 to 2,079; it is clearly in her interest to add that 21st animal. If the other herders do not increase their herd size also, they will lose 1 for every animal owned. So they will respond by adding further animals too, accelerating the rate of deterioration of the commons.

Exactly the same is happening with the operation of the HEFCE's selective funding mechanism. The first table, above, shows an entirely hypothetical example of a discipline with ten university departments. The block recurrent grant research money distributed among those departments is Pounds 3,200,000 which, applying the HEFCE's 1993/94 formula, gives a unit of resource for research (URR - the amount received per staff-member equivalent in a grade 2 department) of Pounds 6,104. Each department's income is determined as: (Grade - 1) x ((number of research-active staff) + 0.10 x (number of research assistants) + 0.15 x (number of research students) + 0.05 x (value of grants from charities/25,000)) This gives the distribution of money across departments shown in the final column.

Each department wants to increase its income. If we assume that the total will not be increased, this can only be at the expense of the others. How? One way, and the one that most hope for, is to increase the grade achieved, because this brings prestige, too.

The outcome of the last RAE showed that it may not bring more money, however, depending on the extent of the overall grade drift in the discipline (and retaining the same grade can mean even less). And how can the grade 5 departments improve? Next time they can strive for a grade 5*, though as yet we do not know if that will bring extra cash, as well as charisma.

So we put grade changes to one side, and look at the only other way to increase income - increase your volume measure (the second term in the equation) - which is exactly the same as the herder adding another animal to the common.

Most departments are doing this, appointing additional staff (which costs money), recruiting more research students (who have to be taught and supervised and whose fees - which some are waiving in order to increase numbers - are small), and seeking more research grants on which RAs can be employed.

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Department 1, for example, may appoint a further staff member, increasing its volume by 4.0 (because its grade is 5). The URR falls to Pounds 6,052, so applying the formula each department except 1 loses 52 for each volume unit, whilst department 1 increases income by Pounds 19,195.

As long as the new lecturer is paid near the bottom of the scale, the strategy works. But others will be doing similar calculations and devising their own strategies.

The second table shows the financial gains and losses from seven strategies:

A: department 2 recruits 10 more research students; B: all grade 4 and 5 departments double their research student numbers; C: all departments increase their research student numbers by 10, multiplied by their grade less 4 points (i.e. a grade 5 department recruits 10 more, a grade 4 department recruits 20, etc.);

D: each grade 5 department recruits a further staff member; E:each grade 4 and grade 5 department recruits a further staff member; F: each grade 4 and grade 5 department increases its staff complement by 10 per cent; G: each grade 4 and grade 5 department increases its staff by 10 per cent and each grade 2 and grade 3 department doubles its research student numbers.

In each strategy, any department which does not grow loses money. But growth does not necessarily bring additional income; expansion must be substantial enough to offset the losses resulting from depreciation in the URR - as in strategy B, where two of the five expanding departments lose income despite some growth in RS numbers.

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Interestingly, although strategies E and F produce extra income for the higher-graded departments, this is insufficient to cover the costs of the additional staff.

Strategy C is the only one in which the lower-graded departments gain, but they have to recruit large numbers of additional students to do so (40 each in departments 5 and 7, which may not be feasible and, in terms of the student load, probably not very productive). Department 5, which has a relatively large number of research students for its grade, also benefits under G.

The general conclusions to draw from these characteristic growth strategies, include:

1: The higher-graded departments are most likely to benefit, because of the operation of the grade multiplier (the first term in the formula) - they are also probably best able to recruit more students and attract more grants.

2: Among the higher-graded departments, the smaller ones tend to benefit more than the larger, because they lose less from the overall deterioration in the URR.

3: Lower-graded departments have to grow very rapidly just to stand still, and thus are at a substantial disadvantage.

4: Appointing more staff is unlikely to produce more financial benefits than costs - unless a higher grade is a very strong possibility as well.

5: If a department does not grow, it is bound to suffer if any other does, hence all feel impelled to grow.

6: Despite this growth impulse, some departments are bound to lose money, which will undoubtedly mean losing staff. Consequently. . .

7: Whatever form the growth takes, the result will be more work for (at best) the same number of staff. Or the necessary consequence of the research funding formula is that academic life will be poorer, nastier and more brutish - and perhaps shorter too?

The lesson that environmentalists and others draw from the "tragedy of the commons" is that sustainable development requires collective action through the state. Unless people are prevented from adding more animals to the commons by an external authority, the tragedy will occur - people acting alone will not take decisions that are in their own and everybody else's long-term best interests.

The Government is not likely to tell universities to stop increasing their research activity, however, and no cartel of universities is going to get binding agreements to end such growth.

Competition will continue; the strong will feel impelled to drive the weaker to the wall - with long-term consequences inimical to the future of research in this country.

There will be fewer research centres, operating at ever-lower unit costs.

Only the HEFCE can act, by changing its funding mechanism so that universities no longer have to grow even to stand still financially.

If that does not happen, the pace of growth will become ever more frenetic (and the strategies employed to achieve it more devious) - and life will become nastier, poorer and more brutish that much sooner.

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Ron Johnston is vice chancellor of the University of Essex. Tables and an illustration of applying the formula can be accessed on the THES Internet service at gopher.timeshigher. newsint.co.uk