What about under Dim Light?

The full-disclosure principle states that if some individuals stand to benefit by revealing a favorable value of some trait, others will be forced to disclose their less favorable values. An example of toads competing for mates was used to demonstrate this principle. Note that the toads need to croak only at night, when vision information is not available; there is no need to croak under bright sunlight as the size of the opponent is clear to each toad. That is fine, but what about under dim light? In this case, the vision is not as clear as under bright sunlight, yet the size of the opponent can still be approximated. Now would the toads still croak? And which of them would croak? I asked my economics professor, and he said he did not know. Half-kidding, he said I can do a research on it.

Well, a serious research do not seems to be possible; however, a little study seems might be a choice. That is what I did.

My argument is that when there is a moderate amount of information (e.g. vision in dim light), those competitors who clearly have the most advantage, as well as those who clearly have the least, would not need to disclose the favorable value (e.g. pitch). However, those in the middle do.

Of course, it is impossible to get a bunch of toads to do an experiment. Yet as the toad example serves to explain the principle, so I can also use other scenarios for solving my doubt. One real world scenario that can demonstrate this “dim light” situation is the standard of colleges. Basic statistical information of the colleges is available, yet it is insufficient for judging the standard of a college. We can approximately tell which of the colleges are among the best, but we cannot do the same for the rest. My hypothesis is that the middle-ranking colleges would put more effort in promoting themselves; one way of doing that is to write more detail description on college guides, which is what I studied. The following is the procedure of my study:

1. A Random sample of size 9 or 11 was taken from each of the ranking categories in U.S. News’ doctoral ranking . The categories are: Top 50, tier 2, tier 3 and tier 4.

2. Peterson’s Guide to Four-Years College allows deans to write a passage to describe each of their own college . The length of the passage is no set (each college has two pages for all their information). I aware points according to the length of the passage a college used to describe itself; 1 points for a quarter page or less, 2 for half page, 3 for half and a quarter, and so on.

3. The mean is taken for each of the sample. Here is the result:
Category Top 50 Tier 2 Tier 3 Tier 4
Sample Size 11 11 9 9
Mean 1.636 2.182 2 1.889
4. 2-sample t-tests are done for each category against others .

The result is simple—the only difference that is statistically significant is the one between Top 50 and tier 2. So the only conclusion that I can firmly made is that tier 2 colleges use more effort (measured in how long they wrote) to describe themselves than top 50 colleges. Ignoring statistical test results however, the mean of each category does seem to indicate that the colleges in the middle use more effort in describing, thus promoting, themselves. The figures also seem to indicate that the colleges ranked the worst use more effort in promoting themselves than the top colleges. This may suggest that even the worst equipped competitors would try every possible way to enhance their competitiveness.

Recall the different situations I put forward in the first paragraph. If all college applicants have perfect information on the standard of the colleges, none of the college will write more to promote itself, because that would be useless. If no information is available, then all colleges will try to write long descriptions, because that description would be the only information the applicants have. The real situation we found, however, is that colleges of moderate standard wrote more. Therefore, despite that evidence is weak, the argument that under moderate information, only moderate competitors would disclose advantageous values seems to make sense.

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