Pareto Optimality, Part I

Image result for pareto optimality graph

Pareto "optimality" (sometimes also called Pareto "efficiency") is an ideal often discussed in decision theory and related branches of the social sciences and philosophy. My understanding is that the two terms are synonymous, although "optimality" seems in broader use.

The idea at heart is that it is wrong to refuse to do something that would make somebody better off, unless that action would make somebody else worse off. So any circumstance in which there is an improvement possible for somebody, that does NOT involve a loss for anybody, is a sub-optimal state. Pareto optimality exists, then, when there are no such moves.

As you might guess, there is somebody named Pareto behind this idea. He is Vilfredo Pareto, an Italian engineer (1848 - 1923) who in midlife turned himself into an economist. Indeed, Benoit Mandelbrot (the famous chaos theorist) has said that it was Pareto more than anyone else who turned economics from a branch of moral philosophy into a "data intensive field of scientific research and mathematical equations."

His idea of optimality doesn't sound at all demanding. Indeed, it sounds like it may well describe a situation that is very much less than optimal by an intuitive understanding of the term. It might, for example, describe a situation in which somebody is starving because he cannot find productive work. After all, taking food from someone else to save our starving man's life would be a loss for that someone else (however small the loss) so Pareto optimality does not require it. This is not to say that Pareto optimality prohibits such a taking (a different question), but in terms of the simple definition of the idea, it is clear that Pareto optimality doesn't REQUIRE that the starving man be saved.

That has been the standard objection to the elevation of Pareto optimality to any normative importance: it is too minimal a goal. But Amartya Sen has introduced another twist to discussion of the idea. There is one respect in which it may be too demanding.

Sen asks us to consider that there exists an obscene book, under whatever definition of "obscene" you wish to use. We'll call it LCL (after the initials of the book involved in some famous litigation). Sen's hypothetical requires that we focus on two individuals, whom he calls Lewd and Prude. Each of these two individuals has two demands to make of their surrounding society, two different things that would each make them happy. It is how these two demands intersect that concerns us.

Lewd kind of wants to possess and read LCL. Level of intensity 7 on a scale of 10.

But what Lewd REALLY wants is to require Prude to read LCL, because Prude deserves to be disgusted and shocked. Level of intensity for this want is 10 out of 10.

Meanwhile, Prude kind of wants to avoid possessing or reading the book. Level of intensity 7.

But what Prude REALLY wants is to keep Lewd from possessing or reading the book. Level of intensity 10!

Now: the intuitively sensible idea is "live and let live." Prude can ignore the book, Lewd can own and read it. This produces utilities at level 14 (7 + 7). Neither side gets its 10 but, hey ... deal with it, guys.

What Sen points out is that Pareto might consistently have criticized this live-and-let-live situation as sub-optimal. Surely when we are AT that situation, Prude doesn't have the book and Lewd does, it is possible for the two parties to agree to trade places. Lewd gives up the book and the possibility of any more enjoyment of LCL: Prude has to take it and read it (as a one time thing or at regular intervals -- to be negotiated.) This way both parties are better off.

Of course this assumes a lot. Among much else it assumes enforceability. Prude would have to be sure that once Lewd gives up his copy, he's not just going to buy or download another one. The whole point for Prude is the pleasure of depriving Lewd of HIS pleasure. Lewd also has to have confidence that Prude really will read through the book, and not just leaf through the pages with his eyes closed or something.

Regardless: if the deal can be arranged to everybody's satisfaction, Prude gets the 10 result and Lewd gets the 10 result. EACH is better off and nobody is worse off. So, live and let live is not Pareto optimal. That, in Sen's view, is an argument against the value of the idea of Pareto optimality, since in such matters he takes the acceptability of live-and-let-live as axiomatic.

More thoughts on this tomorrow.

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