Another [?] of the Anonymati asks this:
“I'd love to know, Bob, what it is about the zero-sum game
that you find so compelling. You have repeatedly mentioned it over the years. I
am no game theorist, but as an economist I know enough to know that nothing you
say here or in your previous post is at all original - what is it about the
idea that inspires you so? Or is it just to admonish that we should use the
term "correctly"?”
Here is the answer.
For almost sixty years, I have been interested in the ways in which
nuclear deterrence theorists, economists, philosophers, political theorists,
legal theorists and others cloak their partisan arguments in formal garb as a
way of claiming an objectivity that they do not [and could not] have, and to
cow non-technical readers into thinking that something objective, mathematical,
scientific has been said.
I first came upon this phenomenon in the very early Sixties
when I was totally absorbed in the Campaign for Nuclear Disarmament and the
rise of non-military Deterrence Theorists like Herman Kahn arguing for First
Strike nuclear policies. In the summer
of 1962, I wrote a short book, The
Rhetoric of Deterrence, in which I tried to expose these fallacies, a book
I was unable to get published [even though Noam Chomsky, after reading it,
urged me to do so.]
Later on, I published criticisms of Bob Nozick [in an essay
review of Anarchy, State, and Utopia],
Jack Rawls [my book Understanding Rawls]
and Jan Elster [in my review essay “Methodological Individualism and Marx: Some
Remarks on Jon Elster, Game Theory, and Other Things”], all focused on what I
saw as the same failing.
In the mid-Seventies, at UMass, I several times gave a
course entitled “The Use and Abuse of Formal Methods in Political Philosophy”
in which I first taught the students the formal materials and then showed them
how they had been misused by Nozick, Rawls, and others.
Later still, when I turned my attention to Marx, I found the
same phenomenon in the invocation by neo-classical economists of the notion of marginal
product as an ideological justification of capitalist profit.
I freely admit that the wanton and invariably incorrect
invocation of The Prisoners’ Dilemma and Zero-Sum Games bugs me, and since both
phrases are so frequently misused in public discourse, I tend to react
allergically to their appearance. But
the larger issue is the ideological use of formal mathematical arguments to
cloak partisan defenses of powerful interests in the garb of mathematics, to misrepresent
them as science and hence not subject
to political debate.
You might say that all of this work is a fiercely partisan
footnote to C. P. Snow’s famous 1959 lecture, “The Two Cultures.”
Even in the case of the zero-sum game, which was von Neumann's exception to a general statement of Lionel Lord Robbins, in practice powerful interests somehow manage to systematically win zero-sum games against virtually everyone else. Are there uses of mathematics and the social sciences that don't amount to mathematizing partisan support for powerful interests?
ReplyDeleteIndeed there are! A good example is the huge formal literature on Marx's analysis of capitalism.
ReplyDeleteI enjoyed this bit:
ReplyDeleteFor almost sixty years, I have been interested in the ways in which nuclear deterrence theorists, economists, philosophers, political theorists, legal theorists and others cloak their partisan arguments in formal garb as a way of claiming an objectivity that they do not [and could not] have, and to cow non-technical readers into thinking that something objective, mathematical, scientific has been said.
I like the fact that you are a born teacher with the love to explicate material at a level that your audience can absorb. I love the way you personalize your blog post with personal observations.
I'm a fan of anarchist theory but not much for actual anarchists beyond some examples like Peter Kropotkin and Emma Goldman. I enjoy your comments on Marx but I have no taste for him as an actual human being and his manipulations of the International Workingmen's Organization.
I enjoy the fact that over your long career you have "fought the good fight" for nuclear disarmament, for civil rights, for South Africa, etc. While utopia may not be around the corner, and reality tells us that tyrants will always have to be fought, and that freedom and democracy and fairness are fragile things to be protected always, it must give you great pleasure to look back over a life well lived (even if there are the typical human "imperfections" that cropped up from time to time). Life is truly a marvelous thing. And a well-lived life is a thing to marvel over.
RPW wrote:
ReplyDeleteWhat this does is to re-label B's utility assignments so that instead of running from 1 to 0, the run from 0 to -1. This means that A's and B's utilities for any arbitrary lottery L are no longer u and (1-u). Instead, they are now u and -u. And the sum of u and -u is zero.
THIS, AND ONLY THIS, IS WHAT IS MEANT BY SAYING THAT A GAME PLAYED BY A AND B IS A ZERO-SUM GAME."
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How much of a stretch is it to call a game "zero-sum" if the outcome is always that exactly one of the 2 players ends up with something that each is willing to make some effort or incur some expense in order to acquire (or perhaps avoid)? Whether their subjective valuations differ, or even if their subjective evaluations agree but due to differences in wealth they differ in willingness to pay, it seems to me what is key is that if A wins, B loses and vice-versa. A might be willing to pay $100 to be certain of acquiring the prize and B only $50, but in some sense, that is neither here nor there. If A wins the prize, B does not get it.
This meaning of zero-sum/zero-sum game seems clear to me. Is it an abuse of language in any way other than that it does not follow von-Neumann's axiomatic reasoning?