Two professors, a macroeconomist and an econometrician, are driving south to visit their friend in Princeton. Neither of them knows precisely how to get there. They arrive at a
two-way intersection, and they have to decide which of roads A or B to take. Only one of these two roads leads to Princeton, while the other would take them to Pennsylvania (and of
course there is no road signal indicating the direction to Princeton).
If the macroeconomist
was to decide which road to take, he would choose the correct one with probability p.
If the econometrician was to decide, she would choose the correct one with probability q.
Consider two strategies the couple could follow:
(i) Randomly choose one of them (probability 1/2 for each) and let that person decide which road to follow; or
(ii) Have them both think about what road should be taken and then either take the road that they both think is correct if they agree or, if they disagree, ‡flip a fair coin to determine which road to take.
QUESTION: Which of these strategies is better for the professors and why? How does you answer depend on p and q?