Why should risk never be weighted?

In engineering and in life, level of risk often differs between solution alternatives, so we need to factor risk into evaluation of, and decision between, alternatives. So far, so good. 

Defining evaluation criteria, weighting the criteria (actually, weighting improvements in the criteria, each over a defined range) and producing a total score for each alternative is common practice. So we define risk as a criterion and assign a weight to it. So far, not so good! In fact, absolutely, totally the wrong thing to do, logically indefensible, likely to lead to major errors in evaluation. Let me illustrate.

Let’s say we weight risk 20% and other, valued outcomes at 80%.

Take two solution alternatives:

A: is very low risk, so scores 20 for risk, but is not so great in other respects, and scores 40 for the rest. So total score for A is 60 out of a possible score of 100.

B: is very high risk, only 1% chance of delivering, so B scores 0 for risk. But if B succeeds the result will be great, the full 80 units. So total score for B is 80 out of a possible score of 100.

So go with B!!! No way!

The real comparison is based on expected value (value times the probability of that value being delivered), which is:

A: 40 units x 100% = 40

B: 80 units x 1% = 0.8

A is a 50 times better solution than B, and we are wrong in our evaluation by a factor of 75 (60/0.8).

If we make our decisions on expected value comparisons, we will deliver, averaged over time, more value from our engineering/receive more value in life than if we make our decisions on any other basis. If risk aversion exists, exactly the same comments apply but we need to perform the comparisons factoring in the aversion to risk. Multiple Attribute Utility Theory (MAUT) provides the tools for doing so rigorously, for use when the importance of the decision justifies the rigor.

Bottom line: always include risk in evaluation of alternatives (we see above how to do that for a simple case), but never weight risk. 

Do you have any questions through to violent disagreement (preferably well argued!)?