Tuesday, November 10, 2015

Multi-objective decision making

In optimization we like to provide The Optimal Solution and as an OR person I like to apply the same principles to my daily life. However, any time there are multiple goals, the meaning of The Optimal Solution get fuzzier. Deciding the best nut butter to buy is one example of multi-objective decision making. As a company, we can say that a particular decision is objectively better if it leads to higher profits. But once you have more than one goal (taste and cost in the nut butter example, though you could add others like effort to make your own or nutrition), things get trickier. 

The linked post tries to get at this by having a region of worthwhile choices and a region of not-worthwhile choices. That is more or less what most optimization algorithms do. Generally if you have multiple objectives, you give them all weights and choose the option that maximizes the weighted sum. However, those weights are fundamentally subjective. The Pareto frontier attempts to partially get around this by capturing all possible sets of weights and identifying the set of good solutions. But you still typically have to choose one of those options, which takes us back to a subjective decision.

Making a subjective decision is not a bad thing, and weights are a pretty good way to formalize the subjectivity. But it still helps to recognize that taste and cost aren't truly substitutes for each other.

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