Rawlsekianism Reloaded Part IIa: The argument for Maximin (or Leximin)

by Murali

By popular demand, I am back with part 2 where I derive the principles of justice. Unfortunately, part 2 started to take up lots of space and had to be split up. Part 2a will concern itself with the decision criteria parties in the original position will use. In part 1, I justified using the agreement of mutually disinterested rational actors behind the veil of ignorance to derive the principles of justice. Assuming that my reasoning in the previous post was inescapable, we are now forced to accept whichever principles so chosen.

To be clear, the principles of justice do not directly tell us what obligations we have or what constraints we ought to observe. Rather, the system of obligations, constraints privileges, rights and powers make up the basic structure. Choice among alternative basic structures is justified with respect to the principles of justice whatever they may turn out to be. The point of the original position is to choose and thereby justify those principles.

As such, it is a mistake to ask whether the parties in the original position would choose Nozick’s historical principles of acquisition, transfer and rectification. Those are not principles per se, but rules that Nozick claims ought to be followed. What justifies those rules for Nozick is the notion of self-ownership. Self ownership is problematic on a number of counts.

1. It justifies the concept of being able to own other things by appealing to the concept of ownership (owning your own body and the product of its labour)
2. Just because you mix something that you own together with something that is un-owned does not make the mixture yours in its entirety. It could be yours only to the extent that your labour is a component of the product (if it didn’t require much effort, it is yours only a bit?). Being the first to urinate into sea does not give you even partial ownership of the sea. Therefore the justification Nozick gives for acquisition is defective for being ad-hoc.
3. I could go on to give a sweet take down of Nozick, but we are getting far afield.

Regardless, to be charitable, we consider that Nozick’s principle of self-ownership is, at the very least, a possible principle of justice against which the basic structure can be justified. But even more charitably, we may simply say that Nozick’s principle of justice consists of a particular list of negative liberties which includes rights against interference in one’s property, is of over-riding importance. We can perhaps even draw up a whole list of said principles.

In many ways, this site is like a live example of what happens when you have lots of people with very different basic principles. There are some who think that the existence of material inequality is bad. There are some who think that the fact that luck has a lot to do with producing this inequality is bad. Then there are some who think that this concern with inequality is misguided and that we should focus on the least well off. Then of course there are those who want to maximise all or some of the goods in life. Some will say everyone else is wrong headed and that the key thing is negative liberty. Some will think that desert is a good basis of distribution. Others think need is. Others think that whichever of these claims have merit, achieving those distributions should not involve violating certain side constraints. Some others think that we should refer to tradition and Judeo-Christian values. There is a whole gamut of core beliefs here on this site, and as a result when people have disagreements about first principles, apart from some effort to show that other foundational principles would prove a better fit with what we suppose are their other commitments, the conversation stops. In fact, it seems that it stops often because we either believe that there are no reasons we can put forward to those who hold nothing in common with us in terms of political values. Or sometimes, when we see how radically some people differ from us, we just stay silent from pure shock that anyone would believe that! Or we may just be at a loss for words. One of the key ways in which we could actually talk about different principles is to see if they would be agreed to by rational, mutually disinterested actors behind the veil of ignorance.

So, the solution is this: we feed in all these principles into the original position and whichever of the principles is chosen will be the principles of justice. At the very least, we can hope to narrow it to a range of principles.

One quick thing to note is that some of the principles would be quickly ruled out in the veil of ignorance. This is because such principles appeal to a specific conception of the good. Such would include appeals to religious values, appeals to side-constraints (for their own sake) and appeals to goods that fall outside the list of primary goods. This ruling out is not illegitimate; it just happens that those principles do not appeal to anything that would appeal to the parties in the original position.

What we have left, are what Nozick termed end-state principles. Note that this is not problematic at all. We did not assume these principles away. Rather, we have merely brought to the fore that all those other principles depend on a substantive conception of the good. But such a conception cannot be brought into a freestanding conception of justice. At this point, we should be very careful. When all is said and done calling these principles end state principles is fairly accurate: They appeal to how much of a primary good someone has laid claim to throughout his or her lifetime. They do not consider instantaneous distributions the proper subject of enquiry simply because it is impossible to pin down exactly which instant we should care about. More importantly, the parties in the veil of ignorance (as well as us) can surely conceive of a situation where the instantaneous distribution seems horrible (think of earning $3 an hour working at McDonalds) but where things work out fine later (the job providing valuable work experience to a teenager who later starts his own business.). In other words instantaneous disparities in primary goods can merely be a product of different people in different stages on the journey to getting more of the primary goods.

Just to recap: the primary goods are things like the various liberties, wealth, power, opportunities etc, maybe even the social bases of self respect. (The latter can be problematic and it is arguable whether or not it is in fact a primary good or not)

The nature of the end-state principles is that they refer to various criteria that have to be fulfilled by the distribution, whatever it turns out to be. Choosing between various end-state principles, therefore, amounts to choosing between various criteria. One way, to better understand the original position, is to abstract just a bit more. What we will do is look at how one of the parties will choose, and see if it is arbitrary and if so to what extent it is so. Non-arbitrariness means that there is a unique solution and agreement can be wrested from the original position.

One further way of simplifying the situation is to simply for now ignore the issue of primary goods. What we are after for now is a decision procedure with which we may evaluate different principles of justice. To that end, what follows are a few comments on decision theory.

Rawls’s veil of ignorance is often compared and contrasted with Harsanyi’s own version of the veil of ignorance. One distinctive feature of Harsanyi’s set-up is that the parties behind the veil know the details of every single person in society. i.e. while there is complete uncertainty about which particular person you may turn out to be, because the complete details of the society are known, we can estimate the probability with which we could occupy any position in society. However, that is precisely why such information is obscured in Rawls’s original position. The issue of whether or not a particular principle of justice does not depend on the particular position in society we are likely to occupy.

That is why we stipulate that such probabilities are obscured from the parties in the veil of ignorance. To be stringent about this stipulation, we can also rule out using Bayes Rule (Laplace’s principle of insufficient reason) to give all outcomes an equal probability. The reason being, that doing so is unmotivated. Similarly, we can similarly rule out subjective probability distributions simply because the parties lack any reason to choose one probability distribution over another. Without any measure of probability, the parties cannot maximise expected payoff (the summation over all outcomes of the products of the payoff for that outcome and the probability of said outcome).

In order see more clearly what criterion will be used, we can abstract away from the situation and address the situation of choice starkly. A person is choosing from among a number of lotteries. Each lottery has a finite number of known outcomes each with a unique payoff. However the probability of each outcome is not known. Given that the person prefers a larger payoff to a smaller one, what strategy should the person pursue in selecting which lottery to play in?

Some of the strategies to be used are the following:

1. Maximin (and leximin for the lexicographical version):
   This strategy looks at the worst outcome in each lottery and picks the lottery(s) whose worst outcome is the highest [pardon the grammar]. And out of those, selects the lotteries where the next-to-worst outcome is the highest and so on and so forth until there is only one lottery remaining.
2. Maximax (leximax)
   Similar to Maximin (Leximin), but prioritises by maximising the payoff of the best outcome before maximising the payoff of the second highest and so on and so forth
3. Minimax regret
   Minimises the maximum regret. The regret is the difference between the actual outcome and the best outcome.
4. Maxi-mean
   Maximises the average payoff assuming that the average payoff information is provided
   Note that information about the median is not provided as together with knowledge about the payoff for each outcome, too specific information about the population can be extracted.
5. Mixed strategies:
   A combination of 2 or more of the above strategies. More will be said about this later.

We can for now rule out minimax regret as the parties prefer a higher payoff to a lower one. Minimax regret merely minimises the difference between the best and the worst outcome, the difference only being incidental to any absolute measure of payoff.

The argument for choosing between minimax and maximax is a bit more complicated. It is highly intuitive to imagine a type of lottery with five outcomes as a lottery where you buy a ticket which you can scratch to reveal a letter ranging from A to E. A to E refers to an envelop containing the payoff with A having the lowest and E having the highest. What we have to do is choose between different sets of 5 envelopes.

While this is an extremely intuitive way to set the problem up, the problem of finding a solution still seems intractable. Consider an alternative way of setting up the problem. Consider envelopes A’ to E`.

A’ contains the same amount as A

B’ contains the difference in amounts between B and A

C’ contains the difference between C and B

And so on and so forth.

Therefore, for example, when someone scratches a ticket and gets the D outcome, he is given envelopes A’ to D’ inclusive. It is then analytic that the probability of getting at least envelope A’ is 100% and also more than that of getting B’ as well, which is in itself higher than getting C’ as well. i.e. if we were to try to modify the lottery by adding unit pay-offs to the envelopes, adding the marginal unit payoff to envelope A’ would be preferable to adding it to B’ and so on and so forth simply because the probability of receiving at least A’ is the highest while that of receiving E’ is the lowest. Therefore leximin is preferable to leximax.

The problem with Maxi-mean is that it risks the possibility of getting really low pay-offs in order to entertain the possibility of getting higher ones. To see how this is bad, consider that the payoffs are used to pay for a wish-list. (This feature of the matches the way in which primary goods are all purpose means to whatever ends people may have). Assuming the wish list is ordered (again, this is a reasonable assumption because people tend to have concerns which are more immediate. If people did not they would be unable to choose which to pursue), people will prefer satisfying items which are a higher priority than those which are a lower priority. Therefore, each marginal unit of payoff that a person receives will go towards satisfying their highest priority items.

The straightforward implication is that the payoff in envelop A’ has a higher priority than the envelope in B’ which has a higher priority than the payoff in envelop C’ and so on and so forth. Another way of saying this is that a person (assuming they were rational) would rather risk not satisfying items that are lower down in his priority than risk not satisfying items higher up in the priority. i.e. Envelope A has a higher priority than envelope B which in turn has a higher priority than envelope C and so on and so forth.

This straight away again rules out leximax of course, but also rules out maxi-mean. At the same time, mixed strategies of maximin and maxi-mean are also ruled out. Any mixed strategy fails to maximise the payoff for A before maximising the payoff in B and so on and so forth. Therefore leximin is the strategy used by a rational individual when choosing lotteries with known outcomes but not the probabilities of the outcomes.

Since the situation in Rawls’s original position mirrors the situation in the lottery, leximin is the strategy chosen by parties in the original position. Also, since leximin, qua strategy is itself determinate, it would be agreed to behind the veil of ignorance.

Unfortunately, dear readers, we have to end here for now. At more than 2400 words and counting, I decided to split this post up. If we can agree that leximin will be the decision strategy in the original position, then we are all on the same page, and we can move on to Rawlsekianism Reloaded Part IIb: The two principles of justice and their lexical priority.