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### Be careful in debating lawyers and philosophers

Thus here is an economic argument against legalizing torture: if it is legal, despite the limited circumstances under which it is legal, then – in practice – there will be far too much torture. By the way – the evidence is overwhelming – in every instance in which a government has bureaucratized torture it has quickly gotten out of hand. But again the basic point: from an economic point of view the issue is not “will there be torture” or “will there not be torture” but “what will be the impact of making torture legal or illegal on the amount of torture that is practiced.” Hypotheticals about nuclear bombs in cities do not help us answer this quantitative question.I should also add a warning at this point. Be careful in debating lawyers and philosophers. At this point in the argument they will introduce yet another irrelevant hypothetical “suppose that torture can be made legal without leading to excessive torture – should it be legal then?” To which the only relevant answer is “don’t …
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### John Quiggin on property rights and opportunity cost

The following are excerpts from Chapter 7, Property Rights and Income Distribution from Economics in Two Lessons by economist John Quiggin holds that opportunity cost is the basic notion distinguishing economic from non-economic thought.

...Before we can trade in markets, we must determine who owns what. This determination is subject to the logic of opportunity cost, but can't be reduced to market transactions.
Social decisions about property rights influence the allocation of opportunities between people in a given generation, and between generations. Again, there is no point at which a "once and for all" fair allocation can be settled, leaving everything to market exchange from then on. ... Decisions made today supersede the wishes of the departed and constrain the opportunities of the young and of those yet to be born.
But such decisions must be made all the time, implicitly and explicitly, and the logic of opportunity cost applies to them. Rights allocated to on…

### Invisible hand games

Here are two generalizations of the $$N$$-player normal form game from Cooperation from self-interest in one shot. In the games below, it is irrational for all players to cooperate, though it is rational for them to join coalitions in which at least one of them cooperates and at least one defects. They might collude for larger payoffs than they would obtain if they all defect or if they all cooperate. If all of the players defect, they receive the same payoff they would have received had they all cooperated.Notation. Let $$n$$ be a positive integer with $$n\ge2$$, and let $$f_j:\mathbb{R}^n\rightarrow \mathbb{R}$$ be a family of maps (payoff functions) for $$1\le j\le n$$. In the games considered here, an element $$y\in\mathbb{R}$$ is a strategy (the strategy sets of the players is the same), and the set $$\mathbb{R}^n$$ is the set of strategy profiles. If $$x\in \mathbb{R}^n$$ is a strategy profile, if $$1\le i\le n$$, and if $$y\in\mathbb{R}$$ is a strategy (for player iii), then th…

### Game theory of property rights, opportunity cost and power relations

As I have been unable to locate a unified game-theoretic account of property rights, opportunity costs and power relations in the literature, I have devised my own. Now that my colleagues and comrades have an example, perhaps their competitive instincts, if not a taste for the epistemic values, will compel them to surpass my efforts. (I'm joking of course--the mathematics is trivial.) There are $$N$$ players. Each player $$j$$ has a tree $$T_j$$ of positions. (As in real life, we each have our own trees.) The position of player $$j$$ is a node of $$T_j$$. A strategy $$M_j^r(P)$$ of rank $$r$$ for player $$j$$ at position $$P$$ is an $$(N+1)$$-tuple $\left(P'; S_{j,1}^r,\ldots,S_{j,N}^r\right)$ consisting of a child node $$P'$$ of $$P$$ in $$T_j$$ and a sequence $$S_{j,k}^r\subseteq T^r_k$$ of subsets of nodes of $$T_k$$ $$1\le k \le N$$ of rank greater than or equal to the rank $$r=\mathrm{rank}(P)$$ of position $$P$$ in $$T_j$$. We call the child node $$P'$$ o…

### Read Robert Paul Wolff on Marx

As long as I am slogging through an account of the Temporal Single-System Interpretation of Marx, it would be a tremendous oversight not to read Wolff, Robert Paul. "A Critique and Reinterpretation of Marx's Labor Theory of Value." Philosophy & Public Affairs 10, no. 2 (1981): 89-120. http://www.jstor.org/stable/2264974. Prof Wolff is an engaging writer-- even when he does linear algebra--and an important Marxist scholar.

### Notes on Marx on exchange value and value, versus opportunity cost

Chapter 1, section 1 of Capital is titled, "THE TWO FACTORS OF THE COMMODITY: USE-VALUE AND VALUE (SUBSTANCE OF VALUE, MAGNITUDE OF VALUE)." I will attempt to translate Marx's remarks into contemporary mathematical notation and offer some comments. Marx writes,
Let us now take two commodities, for example corn and iron. Whatever their exchange relation may be, it can always be represented by an equation in which a given quantity of corn is equated to some quantity of iron, for instance 1 quarter of corn = x cwt of iron. What does this equation signify? It signifies that a common element of identical magnitude exists in two different things, in 1 quarter of corn and similarly in x cwt of iron. Both are therefore equal to a third thing, which in itself is neither the one nor the other. Each of them, so far as it is exchange-value, must therefore be reducible to this third thing. -- Marx, Karl. Capital: A Critique of Political Economy (Das Kapital series Book 1) (p. 127…