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"One assigns a "cost" to one variable, and a benefit to another, and tries to assess how best to minimize the cost while maximizing the benefit."

I'm sure you intend to say that one tries to maximise the benefit minus the cost, but the wording as it stands asks one to attempt what is typically impossible (and too often demanded).

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by technopolitical on Wed Jan 24th, 2007 at 03:55:13 AM EST
How about looking at the feasible region in "cost/benefit space" and finding the efficient boundary where it is impossible to increase the benefit without also increasing the cost? The mathematical analisys ends there, with a collection of multiple pareto-optimal solutions, and then it becomes a political decision to choose a single solution as a goal.

Anything else is trying to abdicate to mathematics our responsibility to make our own decisions.

"It's the statue, man, The Statue."

by Carrie (migeru at eurotrib dot com) on Wed Jan 24th, 2007 at 04:52:50 AM EST
[ Parent ]
Isn't it typical, though, for most situations of interest to be characterised by costs that increase with benefits?
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If one aims to overall maximise benefit minus cost, one typically faces a political decision regarding how to weight incomparable benefits and costs -- e.g., to different people, or of different kinds. Lives vs. dollars seems often to be the most controversial.

Words and ideas I offer here may be used freely and without attribution.

by technopolitical on Wed Jan 24th, 2007 at 01:45:09 PM EST
[ Parent ]
Well, you're assuming you've already eliminated the suboptimal strategies which, in the case of combinatorial optimisation, is an NP-hard problem.

You can always find an exchange rate of, say, lives vs. money that will make your preferred solution globally optimal, but that's a posteriori. The choice of which  of multiple unimproveable strategies to adopt is political.

"It's the statue, man, The Statue."

by Carrie (migeru at eurotrib dot com) on Wed Jan 24th, 2007 at 02:08:41 PM EST
[ Parent ]
Hmmm... Yes, there's a lot of policy-space in which multiple metrics that are thought to be trade-offs can in fact be simultaneously improved.

For example, it is generally thought that increasing security by means of more effective surveillance and control must necessarily decrease freedom, when these could, in fact, be used to maintain or increase security while increasing freedom.

Words and ideas I offer here may be used freely and without attribution.

by technopolitical on Thu Jan 25th, 2007 at 12:23:27 AM EST
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