Let us begin with an apparent paradox: egalitarians don't believe in equality. Quite rightly, as equality is, in itself, of no value. This is obvious, when you think about it. Produce two equally large (or small) meals; then put them in front of a coalminer and a baby. Now pat yourself on the back for acting on your egalitarian commitments. It is obviously silly - one of them needs much more food than the other, and the other needs something different, as well as less of it. Equality here is pointless.
To say that what you really mean by equality is "equal treatment, according to need" is an evasion. When you give each of them the right food in the right amount, what matters is that it's right: that it is right for each. Saying "equally right" doesn't show that there's any magic in equality.
So what do egalitarians believe in, if not in equality? They really believe in such things as justice, efficiency, social solidarity and a bare decency of treatment for the disadvantaged. Inequalities of wealth, power and social esteem allow the rich, powerful or well-regarded to protect themselves against the demands of justice and efficiency and, in the process, to diminish social solidarity.
Giving people a vote, for instance, is a (small) step towards equalising power, and a long step towards ensuring that the powerful have to take notice of the needs of the less powerful. Legal aid helps the hard-up to defend themselves in court. Taking healthcare out of the market place reduces the chances that the demands of the better-off will exclude the poor from treatment. Free public education reduces the risk that the children of the poor will be poor and illiterate for ever. These are steps towards greater justice, greater efficiency, and perhaps greater social solidarity.
You can see why we call ourselves egalitarians. It's much more effective as a matter of rhetoric to emblazon "Liberte, Egalite, Fraternite" on your banner than "Let us reduce injustice, inefficiency, class division and callousness to whatever degree a prudent use of resources permits". One sustained a revolution; the other sounds like the Liberal Democrats in alliance with Gordon Brown. Although we are not currently on the barricades, we are in a state of some confusion, and new Labour's professed "anti-elitism" and glibly imprecise talk of "access" do little to clarify matters.
The question is how to distribute the benefits that society creates for its members. "Equally" sounds like an answer only until you probe it. Take healthcare. Nobody thinks that everyone should wear glasses just because some people need them. What is the underlying principle? It is more the principle of efficiency than any other: that is, meeting people's needs without waste and according to the urgency of the need. Negatively, we know what the implications are: if Mrs Jones and Mrs Smith both have malignant tumours that need treating quickly, Mrs Jones ought not to be able to buy her way in front of Mrs Smith. Equal need gives you an equal claim on resources. But what if there is only one bed, one surgeon and three nurses rather than six? Who goes first? Does equality help at all in deciding positive priorities?
Intuitive reactions vary a lot. If you take seriously the idea that the NHS distributes care "according to need", you will try very hard to find a tie-breaker between Mrs Jones and Mrs Smith that is based on their needs. The sceptically minded think that you won't find it. One will live and one will die; and neither wishes to be the one who dies. If their needs are identical, you will then look for the next nearest needs: you may find that one has two children, and the other has only one, and think that there's your tie-breaker. You may then discover that the one child is likely to be rendered permanently depressed by the death of her mother, while the other two are wonderfully resilient . . . and so on. Textbooks on medical ethics drive students mad by running them through such hypothetical decisions.
And should we think only of the needs of the patient? What about the needs of the wider society? Another great device for tormenting medical students on ethics courses is to play "productivity" against "need", until everyone begs for mercy. Imagine Mrs Jones is employed by Kleinwort Benson on £300,000 a year, while Mrs Smith stays home with her four difficult children. Mrs Smith scores high on need and Mrs Jones on productivity. Now what?
I suspect that most people, when it comes to health, would put need ahead of productivity. But education is mostly an instance of the opposite. What is "equal opportunity"? It is not that children who are all thumbs should be recruited to medical school in the same numbers as the dexterous and neat. It is that students should be selected on merit, and merit in this case is a matter of being likely to be a good doctor, surgeon or whatever. We may disagree about whether future brain surgeons need five A grades at A level, but nobody doubts that they should have steady hands and a glacial capacity to stay calm when their patients are 15 seconds away from death. What is equal about equal opportunity is that, if you have those unusual and desirable qualities, you should get into medical school no matter what your parental income, and no matter your family tree, secondary school or postcode. It isn't that the clumsy and awkward have the same right to a place as anyone else.
The reasoning here is simple. Medical education costs society large sums of money; as it is "our" money, we think it should be spent for our well-being. The right people to spend it on are those who will deliver the goods. This is old-fashioned meritocracy, and none the worse for that. Because we know exactly what we want from brain surgeons, nobody seriously challenges the standards of "merit". Rejected applicants to medical school don't complain that University College Hospital is unwarrantedly hostile to the diagnostic practices of shamans and witchcraft detectors.
Yet, even here, people's views waver about what constitutes merit. Some are satisfied with past performance; others want better evidence of potential future performance. The parents whose children have got five A grades at A level don't hold exactly the same view of merit as the parents whose children haven't, but who might have done if they had gone to different schools.
Things get more complicated close up. If you think that, besides non-lethal brain surgeons, we want benign, tactful, soothing, non-sexist, non-racist GPs, you will also think that merit is a bit more complicated than it looks - predicting who will deliver those outputs is harder than looking up their school records to see how many A* grades they got at GCSE. That allows plenty of room for disappointed candidates (or their teachers) to complain that they weren't rejected on merit, or that they were rejected on the wrong sort of merit, or that the people choosing students weren't much good at detecting the right sort of merit. In subjects such as physics and maths, merit is tightly defined by competence at tasks that everyone agrees are the tasks, and complaints are fewer. The view that we would like nice industrial chemists at the other end of the educational process is not widely canvassed (although perhaps it should be).
But merit does not always override need in education. "Special needs" education is an obvious area where it doesn't. It is clear, too, that the minimal educational provision involved in producing bare literacy and numeracy and a minimum of job skills ought morally to be distributed according to need - which implies more resources for people who have less attentive or less competent parents and who live in less economically robust areas.
Then there are what you might call "higher" needs, of the "man does not live by bread alone" variety. We have become so splendidly obtuse about education in the past decade or so that even when Chris Woodhead, the chief inspector of schools, tries to defend high-quality, liberal education, he doesn't know how to do it other than in vocational, job-oriented terms. Mocking degree courses in golf studies for their vocational ineffectiveness is exactly wrong; observing that they probably don't do a lot for students' cultural development may be nearer the target - although it may be equally irrelevant.
But if we think that young people should study English, physics, philosophy, modern languages, or whatever else, just because it is good for them to have their minds and their imaginations stretched, how do we decide which ones should benefit? Do only dazzlingly clever young people get to do philosophy, on the grounds that only they will produce anything new and interesting? Or do we favour the really muddled and incoherent on the grounds that they need it more than most?
Or should we treat liberal education like a consumer good? People pay to go to the opera and to concerts; why not make them pay to be taught Racine and Homer? Or do we think that high culture is something like fresh air, something that everyone ought to enjoy for free, and which it would be unjust to distribute by price or merit? We may not all need a stiff dose of the later dialogues of Plato, but we all need an equivalent stimulus. If we thought that were true, we would treat the liberal arts departments of universities like libraries or parks, and let everyone in for nothing, provided they behaved themselves.
In all these areas, there is something that the egalitarian wants to say, which is that it should not be left to the market, or not to the market alone, to distribute education, health and culture. One of the young Marx's better jokes was against the rich person with no taste - "Never mind," said Marx. "Send your money to the concert." And the view that healthcare should follow need, that education follow some combination of need and talent, and culture the capacity to appreciate what's on offer picks up the same thought. The welfare state, as well as older varieties of philanthropy - the kind of patronage that used to be practised by sections of the aristocracy or by the Greek city state - amount to an attempt to protect what you might call morally relevant principles of distribution.
But what of really scarce resources, where you cannot satisfy all the legitimate claims on them? Sometimes, there is a shortage of resources because it would be too expensive to satisfy fully the demand. (Cheap tickets for Covent Garden or Glyndebourne; expensive medical operations.) Sometimes, there is a shortage for logical reasons - if one person gets whatever it is, others can't. (A ticket for the Wimbledon tennis final; access to Stonehenge on midsummer morning; a seat in parliament.)
Here is the point where equality, rather than justice or efficiency, might genuinely be what we are after. Tossing a coin equalises chances; the purely arbitrary chance of a prize in a lottery does so, too. What they do not achieve is justice in a positive sense. Nobody deserves to win a prize in a lottery; nobody is entitled to it. It really does seem that, when it comes to handing out undeserved fortune and misfortune, we want equal chances.
If equal need entitles you to equal treatment, but equal treatment cannot be had, then you can at least have an equal chance of treatment. It is not a way of achieving justice or efficiency, but it does achieve a kind of negative fairness. The law acknowledges this in some extreme conditions; shipwrecked sailors who resort to cannibalism to survive will escape the charge of murder if they select the victims by lot, but not if they choose on some other grounds.
The lottery ought to play a more prominent role in politics. The ballot box achieves equality of something absolutely feeble: a few-millionth part of an impact on who gets to govern us. It certainly doesn't give the ordinary voter serious access to power. Why not give everyone an equal chance of exercising real power by choosing all or some of our rulers by lottery? The Athenians understood that the lottery was, as Aristotle observed, the democratic method par excellence of choosing people to hold office.
A lottery could hardly produce a worse House of Lords than the accidents of royal libido and the Prime Minister's whims and fantasies do already, and it would certainly produce a properly representative one. Anyone who tries to argue that a lottery would produce an intolerable outcome must go on to explain why, if that is so, we are happy to have randomly selected juries that can send us down for 25 years. Neither the Commons nor the Lords exercises anything like as much influence over our lives as a jury does in a serious case.
How about university admissions? I was cheered last year by the observation of the retiring head of North London Collegiate School that, once you had a pool of children who were evidently competent to handle the work at Oxford and Cambridge, narrower discriminations, on the basis of teachers' recommendations and interviews, were probably no better than tossing a coin. The same is doubtless true for any oversubscribed college course anywhere. We ought to get as close as we can to ranking students on merit; but once we are stuck, it would be more honest to toss a coin than to invent unpersuasive reasons for choosing one student over another.
And life-or-death operations? We try desperately to find reasons for our choices in such cases, but perhaps we ought not to. It is, after all, sheer luck - good or bad - that we've been dealt the genetic hand we have. It may not be luck that we have eaten, drunk and smoked too much in the past 50 years - but once we are numbered among the unwise, it is sheer luck as to whether or not we get whatever ailment we have exposed ourselves to. Ought we not to acknowledge that, once we have explored all the good reasons for prioritising Tom over Dick and Dick over Harry and found nothing decisive, we should just toss a coin?
It may seem unsatisfactory that all we can say on behalf of equality - the value that is supposed to be at the heart of the politics of old and new Labour alike - is that we really want justice, efficiency, social solidarity and acknowledgment of need, and that where these don't tell us what to do, we'll toss a coin. On the other hand, it may be that the best defence of equality lies in just that thought. We know, deep down, just how far good and ill fortune dictate our fates. The more decisions bear the thumbprints of individual people, the more we fear that we have been treated unfairly. Fate is something we just put up with. Perhaps the last and best argument for choosing juries, handing out scarce school places and selecting people for treatment by lottery is that such procedures reduce the resentment of the unlucky in ways that no rational argument could ever do.
Alan Ryan is warden of New College, Oxford