1 - You dial the number of a call center, and the automated system informs you that the estimated waiting time is eight minutes.
2 - You dial the number of a call center, and the automated system tells you that the estimated waiting time has a uncertainty of plus or minus one minute.
Which automated system is providing you with a more informative answer in your opinion ? Could you base on the information provided by the first one your decision to hang the phone and go for a beer or stay on the line ? Or would you be more confident of your decision (not necessarily the same!) based on the information provided by the second statement ?
I would be happy to hear your opinions in the comments thread below. To guide the discussion here are a few things to consider:
- Bayesians will be more comfortable with this problem, since they are accustomed to use a prior for parameters in their problems.
- In the example, the parameter is bounded from below: it cannot be negative (I wish there were negative waiting times!). This has some implications in the case at hand but could be neglected for simplicity.
- Some kind of lex parsimoniae would caution us to be conservative and avoid assuming that the call center is being smart: let us assume that the information they provide is based on the same investment of computational power in the two cases (other assumptions could lead to different conclusions).
- The focus of our discussion should be on the information content, not on the best user strategy (which is a related and interesting topic).
- To answer quantitatively the question, one would need to use Information theory and a underlying model describing the probability density function of the various parameters entering the calculation of the waiting time and uncertainty. Yet some interesting guidelines can be extracted by the analysis of the problem.