Weather Forecaster’s Dilemma II
This utility-matrix exercise asks whether a forecaster should predict snow given a stated 1% chance. It illustrates how assigned consequences affect a recommendation, but the excerpt’s solution uses probability figures inconsistent with that setup.
THE IDEA
Exercise 43: Weather Forecaster’s Dilemma II
Pretend you are the weatherperson on a local TV station. There is a 1 percent chance of snow tomorrow, which is a normal midweek workday. Determine, using a utility matrix, which of two predictions—“Snow” or “Not snow”—is in your better all-around interest. Consider only two outcomes: it snows, and it doesn’t snow.
Before continuing, work the problem using a utility matrix.
The source refers to a matrix on page 338, which is not reproduced here.
I gave Predict snow–Snow a utility of 100, because most people work and, though they despise how snow delays their commute or hinders their errands and deliveries, they are relieved at having been given fair warning. This is, I believe, the best cell in the matrix for the forecaster because it boosts his or her credibility and enables people to be prepared for the snow, and for that they are grateful.
The worst cell is Predict not snow–Snow. I gave that cell a utility of zero. What could be worse for a weather forecaster?
I gave Predict snow–Not snow a utility of 80. People will have been prepared for snow and be relieved that there was none. Their relief will offset the forecaster’s loss of credibility, unless the forecaster gets the reputation of crying “wolf.”
I gave Predict not snow–Not snow a utility of 30 because, even though working people are pleased that there’s no snow, it’s a nonhappening.
The solution uses .1 probability for snow and .9 for not snow. These figures do not match the probability in the setup.
I multiplied the utilities by the probabilities to calculate the expected values. I added the expected values and determined the ranking. My assessment ranks “Predict snow” as the strongly preferred option. (This analysis may explain why weather forecasters on TV and radio tend to predict snow at the very first sign. They’re afraid of ending up in the lower left-hand cell.)
Try the “Weather Forecaster’s Dilemma” exercise at a party some time. I guarantee the discussion of what each cell’s utility should be will liven things up.
When to use it
A weather forecaster deciding whether to issue a snow advisory based on low probability.
A project manager deciding whether to announce a potential delay to stakeholders.
A doctor deciding whether to test for a rare disease given the test accuracy and patient anxiety.
FROM THEORY TO EVERYDAY LIFE
In practice
Weather Forecaster’s Dilemma II Exercise
The setup states a 1% chance of snow. The author assigns utilities of 100 for correctly predicting snow, 80 for a false alarm, 0 for missing snow, and 30 for correctly predicting no snow. The supplied calculation instead uses a different probability: predicting snow = (0.1×100) + (0.9×80) = 10 + 72 = 82; predicting no snow = (0.1×0) + (0.9×30) = 27. These calculations illustrate the author’s utility assumptions but do not use the probability stated in the setup.
A MOMENT TO REFLECT
Put it to work.
How might the assigned utilities change if the forecaster’s goal is to maximize public safety rather than credibility?
What other real-world decisions could be modeled with a similar utility matrix (e.g., predicting a market crash)?
Why is the utility for 'Predict snow–Not snow' relatively high (80) despite a false alarm?
CONTINUE THE CONVERSATION
Source texts
- The Thinkers Toolkit by Morgan D Jones