What is the value of information in a centralized structure if people behave like

What is the value of information in a centralized structure if people behave like “yes-men?”

by Hans O. Melberg

Introduction
Long time ago I had a summer job at a campground. One of my tasks was to measure the temperature in the water. I then went to the manager and he, in turn, called the Radio station which broadcasted the water temperature from all the large campgrounds in that part of the country. Those of us who knew the area and the process behind smiled every time we heard the temperatures on the radio. Many of the campgrounds were very close so there should be very little variation. However, since most campgrounds wanted to have the highest temperature there was a tendency – at least for some – to exaggerate. This created quite a lot of variation between campgrounds that were located next to each other. Moreover, the initial exaggeration was even more exaggerated since the information about temperature passed through several steps. First of all the person who did the measurement often chose the “best” location in the water (shallow, calm waters) and – if in doubt - he tended to round upwards. The manager who made the call to the radio station also sometimes rounded upwards. I do not know if the Radio station knew about this or simply believed the numbers they got. Anyway, the example illustrates what I want to discuss in this paper: The relationship between centralization and the quality of information.

More general
Let me leave the campground and turn to a slightly more abstract example. Imagine that information goes through several chains before it reaches a Central that makes a decision based on the information. Assume, moreover, that at every step in the chain there is an incentive to be a “yes-man” in the sense that for every step in the chain the information is slightly distorted (up or down from the original “truth”). For instance, people at the lower levels might all tend to know what king of information (or estimate) the Central wants and they all add a slight bias in that direction as information passes through their hands. Say, for instance, they all change an estimate by 5%. The relationship between the number of steps in a chain and the quality of the information that reaches the central would look something like this:

In other words, there is a slightly non-linear relationship in the sense that adding more steps reduces the value of information less than the previous step.

The next step is to formulate the relationship between the quality of the information and the quality of the decisions made. Assume you live in a world in which a reduction in information is non-linear. For instance, you are a stock speculator and the reduction from 90% to 80% reduces the quality of your decision by more than a reduction from 20% to 30% (Maybe there is a slightly “winner takes all” structure so once you are below a limit there is little to lose by being even lower; you are not going to win anyway!). Visually, the relationship between the quality of information and the quality of decision, could, for instance be as below:

Putting all this together we have a potential relationship between the quality of decisions and the number of steps in a chain:

Conclusion: So what?
One possible conjecture based on the reasoning above could be that centralization quite rapidly runs into serious problems. This is due both to the fact that the quality of information decreases and that the quality of decisions decreases non-linearly as information gets worse. Of course this conclusion is surrounded by a lot of if’s and the most valuable lesson from this short observation is perhaps that I now have a better knowledge of which if’s that are important to create the conclusion:
- If different steps in the chain have different incentives about whether to go up or down, then the conclusion is weakened (because they to some extent cancel each other out)
- If the relationship between the quality of information and the quality of the decision is linear (or – perversely - negative) then the conclusion is weakened (even turned on its head if the value of information is negative).
- It may be wrong to simply assume that centralization is the same as “many steps.” Maybe it is decentralization that creates “many steps?”
More self-criticism could be that:
- It may be that the focus is slightly wrong since the problem of centralization and information need not be mainly deliberate distortion of information, but more distortion due to incomplete knowledge of local affairs.
And a suggestion for further study would be:
- A more formal representation of the problem might use a principal agent model in which the principal himself is an agent to another principal (and so on). I would then be interested in how the degree of inefficiency in the optimal (final) contract changed as the number of steps in the chain increased.

And, lastly, the observation illustrates the importance of always keeping your eyes open to potential interesting phenomena even when you work at a camp-ground!