It's actually an impossible solution, since Kolmogorov complexity is uncomputable. However, there are some related complexity measures which are computable, so that they are merely impractical rather than impossible to apply: http://www.scholarpedia.org/article/Algorithmic_complexity#O...
Of course, you can bet that the writers of the test did not use anything related to algorithmic complexity when deciding the correct answers to these questions. We can't show the exact complexity of the different hypotheses, but we can sometimes compare hypotheses. Imagine programs that generate answers according to the different hypotheses. Between the program that answers according to taxonomy, and the program that answers according to word length, which one requires a look-up table of animals and their classes?
1. Someone named "mistercow" is obviously biased on this question.
2. Another item to factor in, beyond lookup table size, is that questions are written in English, and the medium (spelled words) should not be snuck in as part of the content, except where sometimes it is done intentionally :)
Also, in classification problems like these, one should also consider not just how efficiently a solution chooses an answer from the set, but also how cleanly it isolates the cluster of items in question from the unnamed items. That is, since [cow,hen,pig,sheep] are all animals, more so than a random word is, animality should be part of the rule used to choose among them.
3. As blauwbilgorgel notes, Google's very successful solution to model picking is to slurp of everything published publicly online (and with Books, also many things published offline) and sample over the combined output of humanity. This is still biased towards written text, published text, and loquaciousness, but it's pretty good.
>Another item to factor in, beyond lookup table size, is that questions are written in English, and the medium (spelled words) should not be snuck in as part of the content, except where sometimes it is done intentionally :)
That just strengthens my point. The word-length hypothesis doesn't require any information about English. If we change our assumptions to say that the program is being fed the raw visual stimuli (as a human is), then the word-length hypothesis gets even stronger, since it merely involves comparing the widths of the stimuli.
But most of the information about the medium can be ignored when comparing hypotheses because it is constant across them.
>Of course, you can bet that the writers of the test did not use anything related to algorithmic complexity when deciding the correct answers to these questions.
Allow yourself to entertain the thought that they did. Imagine programs in our brain. Things that are easy to decode/(de)compress and require little energy/instruction are of low algorithmic complexity to them.
Start writing down farm animals in your mind. How long before you get to "hen"? You may have written down "chicken", but that would be too easy for a Mensa question, so you'd have to substitute that one :P
Wrong or obscure "answers" to a test question take more energy to produce, they are more complex, more random, less orderly. For me, "Cow" is the shortest program that gets executed first when I think of farm animals. It was likely one of the first programs for the test writer too.
Of course, you can bet that the writers of the test did not use anything related to algorithmic complexity when deciding the correct answers to these questions. We can't show the exact complexity of the different hypotheses, but we can sometimes compare hypotheses. Imagine programs that generate answers according to the different hypotheses. Between the program that answers according to taxonomy, and the program that answers according to word length, which one requires a look-up table of animals and their classes?