I actually think Schelling does better with this end of the spectrum. Partly this is because I find his "weakness can be good" thread of argument more compelling in this case, oddly (is it odd?). When Schelling suggests that there are "military capabilities we might prefer not to have" this seems intuitively satisfying to me. Though, note, I think it's only true when we're talking absolutes and not relatives; we might prefer not to have nukes, or not invent missile defense, but only if the Russians also don't have nukes or missile defense. I think Schelling would mostly agree with that.
However, on a deeper level, I think the general rationalist/game theory-friendly approach just suits conflict (even limited conflict) better, for psychological reasons. My intuition is that war is not in fact "a continuation of policy by other means"; I think there's actually a qualitative difference in how we think about appropriate behavior and what our expectations are when we're trying to get something by bargaining than when we're trying to get something by war, whether or not it's true that limited wars have tacit "cooperative" aspects. I think the two mindsets have entirely different sets of cognitive biases, and that the set of cognitive biases associated with conflict is much closer to the set of cognitive biases displayed by game theorists than is the set of cognitive biases associated with bargaining.
Anyway, there were some bits that I quite liked in this last chunk. For instance:
The argument of this paper leads to a definition of brinksmanship and a concept of the 'brink of war.' The brink is not, in this view, the sharp edge of a cliff where one can stand firmly, look down, and decide whether or not to plunge. The brink is a curved slope that one can stand on with some risk of slipping, the slope gets [sic] steeper and the risk of slipping greater as one moves toward the chasm. ... One does not, in brinksmanship, frighten the adversary who is roped to him by getting so close to the edge that if one decides to jump one can do so before anyone can stop him. Brinksmanship involves getting onto the slope where one may fall in spite of his own best efforts to save himself, dragging his adversary with him. Brinksmanship is thus the deliberate creation of a recognizable risk of war, a risk that one does not completely control. It is the tactic of deliberately letting the situation get somewhat out of hand, just because its being out of hand may be intolerable to the other party..." (199-200)That seems to me to accurately describe many real situations.
Still, even this section has a fairly high density of Dr. Strangelove-esque "solutions" proposed.
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