As a utilitarian, the kind of equality I care about is equal consideration.* When Jeremy Bentham first suggested that the pains and pleasures of an African should count as much as the happiness of an English person, this view had radical implications, for slavery was still legal in the British colonies. Today, the suggestion that the pain of a nonhuman animal might count as much as the pain of a member of our own species is still radical. That is why this sense of equality remains important.
To care about equal consideration, we don’t need to think that pleasure or happiness is the ultimate end. I’m a preference utilitarian, not a hedonistic utilitarian, so on my view, we ought, roughly speaking, to be trying to increase the extent to which people’s preferences are satisfied and reduce the extent to which they are thwarted. But as far as equality is concerned, the point remains: we should give equal consideration to all preferences, irrespective of whose preferences they are.
This fundamental principle of equal consideration is compatible with a great deal of inequality. Economists have long maintained that allowing the market to provide incentives for people to produce cheaper and better goods and services is the best way to raise the welfare of all, including the poor. If that is correct, and if the poor want a reasonable level of prosperity more than they want to have an income that is no less than anyone else’s, then giving equal consideration to the interests of the poor will require us to allow the talented to become rich.
Against that, the law of diminishing marginal utility pulls utilitarians towards a more egalitarian outcome. To Joe Rich, the loss of $1000 will have no perceptible welfare impact. To Jane Poor, the gain of $1000 will make a significant difference. Other things being equal, therefore, we should redistribute from the rich to the poor until the marginal welfare loss to the rich equals the marginal welfare gain to the poor. But of course, if humans need incentives to make them productive, other things are not equal. So when we plan social policies, we must take account of human nature as it is, not as we might wish it to be. (What we do for ourselves, in terms of our charitable donations, is another matter: I have discussed it elsewhere.) 
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The principle of equal consideration of interests is also compatible with a more fundamental kind of inequality. Suppose that the world consists of two kinds of people. The plebians are capable of having only a limited range of preferences which are not difficult to satisfy, whereas the patricians are capable of a wider range of preferences, which they care about passionately, and which are more difficult to satisfy. (Let’s suppose, too, that these differences are genetic in origin, and unalterable.) Then equal consideration of interests will tell us—other things being equal —to spend more of our limited resources on satisfying the preferences of the patricians than on satisfying those of the plebeians. We should do so, not because we care less about the plebians, but simply because that is the way to do the most in terms of satisfying preferences.
This example may seem fanciful. The world is not divided into two different kinds of people, and even if there are biological differences in people’s capacities to have a wide range of preferences, or to care intensely about the satisfaction of their preferences, these are not things we can measure. Since we have no reliable way of comparing the intensity with which people prefer different things, it seems reasonable to base public policies on the assumption that all human beings—except, perhaps, those in a persistent vegetative state, or with similarly serious cognitive deficiencies—have equal capacities in this respect. But a division reappears when we consider the differences between species. There is no reason why animals should be excluded from the scope of consideration. The principle of equal consideration of interests extends to every being who has interests, which means every being who is capable of conscious preferences, or likes or dislikes. The limit of consciousness, rather than the limit of species, is the point beyond which equal consideration of interests cannot go, simply because beyond that limit there are no interests to consider.
In respect of pain or physical suffering, other mammals, birds, and perhaps all vertebrates, appear to have capacities that are broadly similar to our own—or at least, we cannot assert with any confidence that they are generally less sensitive to pain than we are. For that reason, many of our current practices with regard to animals seem indefensible. Confining hens in small wire cages for their entire productive lives causes great misery to them, and produces eggs that are only a few cents less expensive than eggs produced by hens not so confined. We can do this only because we do not give any consideration at all to the interests of hens to stretch their wings, lay their eggs in a nest, and be able to walk around freely. We are sacrificing their major interests for the sake of very minor interests of our own.
In regard to other preferences, however, the distinction between normal humans and nonhuman animals resembles the imaginary distinction between plebians and patricians. I have argued elsewhere, for example, that normal humans, once they are beyond infancy, are aware of their existence over time in a manner that nonhuman animals are not.  Therefore they can have preferences for what they will do next week, next summer, or over the course of their lives, that nonhuman animals cannot have. This may justify us in taking the killing of a normal human being much more seriously than we take the killing of an animal. That, of course, is consistent with our common moral convictions on that point. The implications of this view for the killing of human beings who lack the cognitive capacities of normal humans, however, are very much at odds with those same common convictions. So here we have a real-world example of how applying a basic principle of equal consideration of interests can, on the one hand, lead to a vast improvement in the situation of those who previously were not recognized as entitled to any form of equality; and yet at the same time, this principle is compatible with significant differences in how we should actually treat those to whom we give equal consideration.
* This essay is not exactly a reply, because I didn’t disagree with Schmidtz all that much—though maybe in the further discussion, some differences will emerge, now that our different frameworks have been laid out.
 “Famine, Affluence and Morality,” Philosophy and Public Affairs, vol. 1 (Spring 1972), pp. 229-43; Practical Ethics, 2nd ed., Cambridge University Press, Cambridge, 1993, ch. XX; One World, Yale University Press, New Haven, 2002.
 Practical Ethics, 2nd ed., Cambridge University Press, Cambridge, 1993, ch XX; Rethinking Life and Death, St Martin’s Press, New York, 1995.