Dear RG-community
Why is it said, that value functions need to monotonic in multi criteria evaluations (i.e. multi attribute analysis)? E.g. Belton and Stewart state in their book (Multiple Criteria Decision Analysis: An Integrated Approach), that value functions which are not monotonic probably represent two conflicting criteria (link attached). However, why is that bad? Does it invalidate the decision procedure? By disentangling all the non-monotonic value functions into monotonic ones, I would require much more input by the experts and I doubt whether I'll gain better insights, as their thinking is non-monotonic.
Example: Experts state that a slope between 20 and 45% is best for grape production, which indicates a non-monotic function. Behind such a statement, there are underlying criteria, e.g. a slope of less than 45% is best for mechanical working of the grapes and a slope bigger than 20% is best in terms of insolation and microclimate. If I disentangle the initial non-monotonic value function, which relates:
- slope -> grape production value
into
- slope -> microclimate value
- slope -> insolation value
- slope -> mechanical work value
I would need to add another set of comparison and 2 value functions more. What is the additional benefit I'll get out of such an exercise? Of course, the bi-section technique does not work on non-monotonic value function, so I'll loose the ability to do that, but would I need to do so?
Many thanks for help on that and providing references.
https://books.google.ch/books?id=mxNsRnNkL1AC&lpg=PA124&ots=DKJmPREyJz&dq=why%20need%20value%20functions%20to%20be%20monotonic&hl=de&pg=PA124#v=onepage&q&f=false
One of the advantages is that by disentangling it the decision-maker gets to know better what are the fundamental objectives of his or her decision problem. Keeney in his Value-Focused Thinking (1992) includes it as an example of uncovering hidden objectives.
Another reason is that many theorems of economics rely on such an assumption, but that's another field with aims distinct from what you are doing.
In sum, modeling is both an art and a science. So if the decision maker is confortable with it, go ahead. I understand your point of view and believe that there is no problem in modeling that way.
I think you raised a very interesting question. However, you assume that it is always possible to disentangle all the non-monotonic value functions into monotonic ones. I think that for the example you provided this may be true (although I know nothing about the conditions that influence grape production), but for other types of phenomena, it may be impossible to separate individual effects from combined effects. For example, if you assume that human interactions influence grape production in some way, it may be more difficult to separate effects of different variables, like social class or some intra- or inter-group conflict (just to give an example from the top of my head). However, if you do not need to think about this, then my guess is that your assumption could work.
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