Equality: the game

Suppose two men, two women, or a man and woman meet as equals, because they are in the same room and convention decrees they cannot use force or consensually recognized symbols of superiority to decide who is boss before either speaks. As we are all perfectly aware, they may or may not end the conversation considering themselves equals. As a matter of fact, equality in such a common situation is rare and difficult; the former fact stemming from the latter. To paraphrase Ben Franklin, we (might) all enter a conversation equals, but we do not all leave it equals.

There are two virtues to starting from this simple situation and build upon it to construct a definition of equality applicable to the human scene rather than analyze its previous uses. First, I thereby rid myself of the historical weight attached to the word and enable myself to think freely. However, I am still performing an analysis of the word as it exists in our language by my sheer use of the letters as they appear on the paper in a fashion that does not set us hunting for what alternate meanings I may be giving it. Like it or not, any analysis changes the meaning of the word it is analyzing just by being an attempted definitory use of it, and we constantly decide whether a word is being 'misused', given new meaning, on a 'know it when you see it' basis. Second, the atomic simplicity is wholly defined in such a fashion that it can be analyzed as a game in the game-theoretical sense. I call it a construction of equality and not a reconstruction because I make no claim that I am going to arrive at the word exactly as it has been used so far, which would be as pointless as trying to engineer a baby within a womb through completely artificial means. I am only trying to come up with a clean definition that passes the 'know it when you see it' litmus. It will however not pass the litmus test of those who use the word as propaganda with pre-fashioned objectives, since, even if their politics agree with mine, propagandists all claim that the meaning of a word is something, that its historical use can be summed up, to arrive at a solid foundation from which to organize fictions. As a social scientist needs the foundations of mathematics more profoundly than a natural scientist, so a propagandist needs essentialism-in-history claims more than an analyst; he doesn't have concrete material to work with.

Returning to the situation, I observe that as a game, equality only means that the definitory rather than strategic rules are the same for everybody. It is a debate as ancient as the hills whether this is 'fair', and that would depend entirely on what you mean. To avoid propaganda, I should disclose the following bias: I find the term 'fairness' to be inapplicable unless the things one is supposed to be fair to are the same in some real sense that includes their history and their likely behavior. Thus there is no fairness among humans, but only among the instruments that they use. For instance, if two men are at a lunch counter and one's dollar is rejected for a purchase while another is accepted, it is technically their dollars that have been treated unfairly. Now, whether the situation is the historically obvious one or not, both you and I, reader, know that there is, in the absence of a further story, an injustice involved. But how do we know this? Only because the two men are only known through their dollars. Instruments create the possibility of fairness. Two people cannot be compared without a situation with respect to which they are to be compared. This consequence follows also from the well-known fact that it is neither humanist nor possible to sum up what a person is, regardless of what evidence one has. What follows more uniquely from the above arguments is that the aspects of context that matter are the very instruments whose sameness the comparison actually rests upon.

But then there is no 'justice as fairness' ala Rawls, and the famed 'veil of ignorance' reproduces certain instrumental situations in our assessment of how people ought to be treated at the expense of others. And this with neither a guarantee nor even a reason to believe that the same instrumental situations are being considered by all; in which case the laws arrived at from Rawls's fair state of nature are an unthought and probably incoherent compromise. I will tackle this contentious point further elsewhere. For now, this sketch of an argument is sufficient to point out why I don't think we can make any simple appeal to what's 'really' fair without dehumanizing ourselves and others by restricting the contexts of possible humanity to certain specific games at the expense of others in a judgement. Fairness is a final condition, fit only for sizing up the dead from what we know of them. For the living, there is an infinity of extant further potential information.

Then we can say nothing at all about the 'meaning' of equality. All we can say is that it is a game theory axiom underlying an infinite class of games which nonetheless stand in a one-to-one 'ratio' to all possible games; from the standpoint of cardinality, there is no difference between the class of games that have the axiom and those that don't. Though the latter set may still be richer in possibilities we can actually think up, which is different from cardinality, the former offers no real limits to our imagination. Furthermore, since transfinite mathematics of this sort is completely paradoxical if we apply it to our numeric intuitions, it would be ludicrous to say that restricting the games of life to games with equality of players with respect to definitory rules be limiting or dehumanizing even if those without it were more 'numerous'.

This equality may or may not be a noble condition to impose upon the games we play. To answer that question, I would begin with the literal meaning of the word 'noble' and ask whether its metaphorical meanings really have complete independence from it. But this is a political philosophy post, so I won't go into that here. For me, what matters is that it is not dehumanizing like 'fairness.' This means that equality as a game-theory axiom is under investigation like anything else, but that fairness is not even a proper term for the picture, and is really only mentioned here because of previous uses of it. I am inclined to accept the virtue of equality under this minimal view as an axiom to other political values I may espouse without knowing what other adjectives apply to it.

This minimal view of equality in which it has an uninterpreted definition but no meaning, by the virtue of the infinite class of games it helps define raises many more questions than it answers. But since I happen to think it is also the best view, I will take on these questions in an abstract fashion.

Now what are the 'games' that exist? Since it does not answer the question to say that this class is also infinite, I must pretend it is finite to show it is out there. The games Gi,...,Gn that exist, I claim, and have an equality condition, are the number of 'ways' in which human beings may interact with like instruments that will be treated similarly. An instrument is anything measurable whose likeness can thus be ascertained. Banned from the best city in speech are the soul, the mind, the heart, knowledge, tradition, and the like. There is, then a reason why people complain in one way or another of the soulessness of the modern democratic state. It's supposed to be that way.

The most obvious instrument is the dollar as in the example above. Some people might say there is nothing equal about a man with 10 dollars having those dollars treated the same way as those of a man with an additional 90 dollars. But I maintain that there is, and that any proof to the contrary has to pass through the idea of fairness. Clearly, if the instruments are the relevant aspects of context, and there is an inequality in available instruments of the same type, there is a context of inequality. But since trying to remedy this inequality in practice involves making a massive judgement concerning fairness, based not on partial and limited facts but on no facts whatever, since establishing point equality in a moment would require ignoring the entirety of the past, it is the duty of the person establishing equal situations to remedy them by different means. These do not currently exist on any significant scale but are not difficult to imagine. Imagine, for instance, a city where every store had a sign on its door stating the maximum amount of money that could be spent there in one go, or situation. Those who did not have this maximum sum could not enter, because they could not there be treated as equals in negotiation. If this was all the public business of the city, it would be an equal one.

Some utopia, you may be thinking, and you would be right. This is not yet a description of a minimal implementable view of equality, but only a particular equal game that cannot sustain a society. I need to discuss also how goods are made, how workers are paid, how money is inherited. I will tackle only the last and probably the most sensitive issue. Money can be legally mandated to be inherited by children, by whoever the doner wishes to stipulate in his or her will, by the state, or by some combination thereof. The presently espoused view of equality as game demands only that there be a fair process to determine who inherits it in the sense described in the previous example. This means competition. There cannot be no-brainer inheritance to a legally stipulated party, and the parties must have like instruments. Clearly, then, either the state or individuals are out unless they can be made to yield like instruments. Therefore, if we must keep the estate tax as an economic necessity, which certainly appears to be the case, the state must somehow be represented by an individual with the same rights as everybody else in this process. His goals, though, are different. He is not acting on his own behalf, and this creates a principal-agent problem that is not so immediately solvable. Furthermore, it would be idiotic to introduce the veil of ignorance rejected above for the overall organization of society into a particular game. Society is here only the sum of games, with some of them determining the shape of future rounds of play.

What this example shows is that, if social interaction is to be composed of minimally equal games, some of these games must help shape the rules of future ones. Constitutions are necessary. The contrast in outcome between a constitutionally mandated outcome for inheritance and a locally decided one requires only the total inequality of wealth at the time of drafting and a putting it to a plebescite to be maximal. I suspect that the local versus global distinction is equally drastic in other games. Therefore, anybody who accepts my equality as a condition on games ought to think seriously and creatively about what the constitution of his or her utopia says. But he or she should do so without a 'veil of ignorance'; there is nothing either noble or necessary for equality about remembering only semantic rather than historical reality in proceeding forth, regardless of what the undefined but meaningful term noble may actually imply.