In a message dated Mon, 3 Jun 2002 4:12:40 PM Eastern Daylight Time,

carlw4514@... writes:

> I must be dense, because it seems to me arithmetic

> produces equality of exchange, cheating being another

> issue. Calls for higher math ? [g]

No, not at all. Suppose I have a 100,000 man army, and

you have a 60,000 man army. We fight a battle, and in this

battle we both take 1,000 men prisoners, with 6,000 K&W.

If we exchange prisoners, after the battle I have 94,000

men and you have 54,000 men. If we don't exchange, I

have 93,000 and you have 53,000. 93/53 is (very slightly)

higher than 94/54, thus the superior force is better off

not exchanging.

Actually, there is some higher math involved, because

one can show that, when making equal deductions from

two forces, the smaller force is reduced by the greater

fraction. This means an equal exchange policy is always

a disadvantage (numerically) to the stronger force.

JFE