> We were given the criteria to use.
> We were told to evaluate each of those criteria, and give it a
> rating from 0 to 10.
> ...
A Congressional staff person once posed this problem: "Find a set
of coefficients for indicators like population, poverty level,
miles of roads, etc etc for a formula to allocate federal revenue
sharing money to congressional districts. And here is the list of
amounts your formula is to allocate, by district."
Clearly that is easily approached by simply doing a linear regression
of amount to allocate against the various indicators. But sometimes
the resulting coefficients will be embarrasingly bizarre (negative,
huge, etc). It is interesting, and educational, in such cases to
present the requestor with the coefficients implied by their desires.
The problem described is more complex, but in the same vein. If 'L'
was in fact worse on all counts, you would need negative coefficients
to make it come out ahead. If it was better on only a few dimensions,
they might have such bizarre large coefficients that it would be an
obvious joke to use those coefficients.
