Justice 1---Why I disagree with Rawls

As I mentioned in the previous blog, this is a series of blogs that I will discuss about issues related to justice. I dedicate this series of blog to my US history teacher, Mock Trial coach, and mentor when I was an exchange student. He challenged me to read widely, think deeply about important issues.  It was during a discussion with him, when I first invoked a Rawlsian argument, forced to defend it, and think hard about it. Today, however, I intend to tear it down.

Rawls' framework

Rawls had a powerful idea---the veil of ignorance. The idea is that if we debate policy now, our opinion will be influenced by our current positions and status---a rich person might favor small redistribution, an African American might favor Affirmative action, and an healthy person might fight against universal health care. Rawls' idea is that, let us return to the "original position", that is we do not know who we will be, whether we are black or white, rich or poor, healthy or frail. We decide on what kind of policy we will want:

"no one knows his place in society, his class position or social status, nor does anyone know his fortune in the distribution of natural assets and abilities, his intelligence, strength, and the like. I shall even assume that the parties do not know their conceptions of the good or their special psychological propensities. The principles of justice are chosen behind a veil of ignorance."

Under this framework, Rawls reached the conclusion that a just society will maximize the utility of its worst-off citizen (subject to preserving basic liberty, and equality of opportunity):

Social and economic inequalities are to be arranged so that they are to be of the greatest benefit of the least-advantaged members of society.

Rawls' Fallacy:

That I argue is wrong. Yes, we are behind the veil of ignorance, and we are unsure who we will be, but why do you assume we will design the rules so as to make our worst outcome as good as possible. Consider an analogy, when you pick stocks, you do not choose a stock that will give you the best return in the worst case scenario, you will consider the average return and the variation. For an extreme example, one asset will give you 0 return no matter what. Another asset will give you 100% return 90% of the time, but -0.1% return 10% of the time. It will be crazy to think one will just choose the first risk-free asset over the second asset.

Utilitarian Argument:

What should be the conclusion? I argue, it is utilitarian. Choosing the rule under the veil of ignorance is like making ex-ante optimization. I will show that this ex-ante maximization problem is equivalent to an ex-post aggregate utility maximization problem, thus justifying a utilitarian framework. If you see this, you can skip the next two paragraphs.

 Let me formalize this a bit, let $i$ be a random variable of the type of a person. Under the veil of ignorance, we do not observe our type. We choose the rule for the society $\theta$. After we choose the rule, the veil of ignorance is lifted, and we learn our types, and we get a utility depending on both our types and the rule we choose $U_i(\theta)$. The question is ex-ante, how will we choose the rule $\theta$? I think at this point, it is fairly obvious to economics student, what the answer is.  We need to decide on a decision rule and if we impose some axioms of rationality (discussed in appendix), like one can compare two rules under the veil of ignorance, we have only one way of choosing---the Von-Neumann Expected Utility Framework. In other words, we will choose the optimal $\theta$ so as to maximize
\[
\max_{\theta} E ~U(i,\theta)
\]
where the expectation is taken over $i$.

There are dual interpretations to the objective function shown above. It could be interpreted as ex-ante optimization with uncertainty over type, or it could be interpreted as maximizing average ex-post utility of people in the society. This dual interpretation means that an ex-ante expected utility maximization problem is equivalent to an ex-post aggregate utility maximization problem.  So if you accept the veil of ignorance and the rationality assumption, you have to accept that a just society maximized the aggregate welfare of all its people, weighting everyone equally, at least in principle.

Critiques:

I do have some criticisms/cautions.

The link from theory to practice is far from obvious. I briefly discuss three.

In reality, the rule we impose will influence the distribution of the type $i$ for later generations. For example, if rich and poor people have different birth rate, the distribution of types will change. Another channel is genetics, for intelligence and disease. I do not want to get into this, as a truthful discussion makes people uncomfortable. It suffices to say, the theory suggests an overly static framework.

It is impossible to assign utility value to different people in practice, thus, the ex-post maximization problem is ill-defined in practice. We have to assign the utility ex-post, but we are already out of the veil of ignorance, so our assignment could no longer be innocent.

Finally, let us not forget the political economy. People who make the rules ex-post are not angels, why could we trust them to design the rule optimally even if the model is perfect and they can get the utility function?

Of course, there is another possibility, after reaching the natural implication of the veil of ignorance (with the aid of assumptions), we might come to doubt this very assumption/framework to begin with?

Appendix:

Axioms of rationality that will lead to Von-Neunmann framework (from wikipedia)
I need to point out that it is true this framework has been attacked as a model for human decisions, (most prominently by prospect theory). But those attacks point to the irrationality of human beings, not the logical coherence of this framework. It is a perfect model for how decision should be made, though a crappy model for decisions are actually made.

Completeness assumes that an individual has well defined preferences and can always decide between any two alternatives.
Axiom (Completeness): For every A and B either or .


This means that the individual either prefers A to B, or is indifferent between A and B, or prefers B to A.


Transitivity assumes that, as an individual decides according to the completeness axiom, the individual also decides consistently.
Axiom (Transitivity): For every A, B and C with and we must have .


Independence also pertains to well-defined preferences and assumes that two gambles mixed with a third one maintain the same preference order as when the two are presented independently of the third one. The independence axiom is the most controversial one.
Axiom (Independence): Let A, B, and C be three lotteries with , and let ; then .


Continuity assumes that when there are three lotteries (A, B and C) and the individual prefers A to B and B to C, then there should be a possible combination of A and C in which the individual is then indifferent between this mix and the lottery B.
Axiom (Continuity): Let A, B and C be lotteries with ; then there exists a probability p such that B is equally good as
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