An idea for how the agreement of the parties can justify the "place the burden on the party able to bear it at the cheapest cost" rule:

Imagine A and B are bargaining. A is going to perform some activity X with a cost of $50 to A. Doing X also entails running the risk of Y occurring, which would cause some substantial harm to A. A can prevent Y at a cost of $10. So A's total cost to perform X is $60, and that is the minimum he will require from B to perform X. What if B can prevent Y for $5? Now, B can pay $50 to A and spend $5 to prevent Y, lowering the total cost of accomplishing X to $55. The parties can now negotiate the division of this gain - possibly agreeing on an exchange of A does X and B pays A $57.50. Both are better off by following the rule.

I think this generalizes to most situations. The idea is that rational parties will allocate risks to the "low cost bearer" and thus maximize the benefit which can be derived from the bargaining behavior, in much the same way a voluntary agreement allocates goods,promises,etc. to maximize benefit. If the parties wanted to diverge from this rule they could easily make explicit allocations of risk, along the line of the captain who says "This voyage will be one to six months, sign on at your own risk." Otherwise, we can assume they are maximizing benefits/minimizing costs (seeking a Pareto optimal solution) and following the "low cost bearer" rule.

-- Anonymous, September 28, 1998