All assisted search, irrespective of the manner in which they are assisted, can be modeled as a probably distribution biased towards selecting elements in the target.Marks and Dembski claim that the average active information is a measure of search performance - at least they write in their remark:
If no information about a search exists, so that the underlying measure is uniform, then, on average, any other assumed measure will result in negative active information, thereby rendering the search performance worse than random search.Their erratum seems indeed to proof the remark in a slightly modified way:
Given a uniform distribution over targets of cardinality k, and baseline uniform distribution, the average active information will be non-positive(The proof of this statement in the erratum is correct - at least as far as I can see...)
So, lets play a game: From a deck of cards one is chosen at random. If you want to play, you have to pay 1\$, and you get 10\$ if you are able to guess the card correctly. But you are not alone, there are three other people A, B and (surprisingly) C who'll announce their guesses first. They use the following search strategies:
- A: he will announce a card according to the uniform distribution
- B: he will always announce ♦2
- C: He has access to a very powerful oracle, which gives him the right card. Unfortunately - due to an old superstition - he is unable to say ♦2, so every time this card appears he will announce another one at random
But what would Marks, Dembski or Ewert do? They calculate the average active information according to the formula given in the erratum. This E[I+] is 0 for player A, but -∞ for B and C. As negative active information on average renders the search performance worse than random search, they have to stick with player A.
So, either average active information is not a good measure of search performance, or not every assisted search, irrespective of the manner in which they are assisted can be modeled as a probably distribution. Or it is a bit of both...