Death Note, Anonymity, and Information Theory

Nice analysis! I really like the way you quantified it.

This is off-topic, but I think Death Note is practically begging to be re-written as rationalist fanfiction: Light's manipulation skills could be used to discuss psychology and cognitive biases (much like Draco Malfoy in HP:MOR). L would of course be a Bayesian rationalist, and Soichiro and Izowa could be Traditional Rationalist foils who would allow L to explain the ins and outs of high-level rationality. (As you've shown here, information theory could play a larger role in L's investigation.) The cat-and-mouse games between L and Light could be turned into decision theory problems; the rules related to ownership of the notebook could be used to explore timeless reasoning (much like the film Memento). The story is already brimming with ethical questions, and both L and Light's internal monologues could be used to discuss consequentialism and utilitarianism. I'm not sure what could be done with the rest of the characters or how the supernatural aspect would be handled, but it would probably be an interesting read.

Arguably, the biggest mistake Light made was one of abstract strategy: he started using the Death Note almost immediately after obtaining it. He should have spent many years testing the thing, pondering its implications, studying police work, etc, before putting his plan into action.

Big DN fan, my thoughts:

1) Only a mistake if you consider his goal to be "kill as many people as possible" rather than "reduce crime as much as possible", and for the latter the small loss of anonymity may well be a justified sacrifice for the deterrent effect he could achieve by exposing his own existence. Especially since, as you point out, he might well have been discovered anyway.

2) Yep, pretty big mistake there.

3) I think you slightly under-rate this one, by not considering that L can't always eliminate people with certainty, prior to this it would have been possible that Kira was not Japanese but was timing his kills to make it look like he was to lead the police awry. This test made that hypothesis a lot less likely.

4) Agreed, this is the big screw-up, also probably the one that most of the viewers could have been expected to spot.

5) Bear in mind he was actually quite careful to prevent Penbar from being singled out, although he could have done better by delaying all the killings for a week or so. Misora would have narrowed down his anonymity even more had she not been killed.

For his optimal strategy, might he not have been even better off by deliberately sending misleading information, by timing the killings to indicate he lived somewhere else for example? After all, applying your strategy might well narrow it down to 'people who know information theory' which probably costs quite a few bits.

But... but... Light actually won, didn't he? At least in the short run - he managed to defeat L. I was always under the impression that some of these "mistakes" were committed by Light deliberately in order to lure L.

When you talk about the number of bits of anonymity he has once it's been narrowed down to Kanto, shouldn't that be the male population of Kanto?

Edit: The section about comparing mistakes also seems somewhat contradictory; first you talk about the number of people excluded (and so the first bit is, by definition, the most valuable) and then by the number of bits (and so the 11 bit mistake is more important than the 1.6 bit mistake). It may help to resolve the tension between the two approaches more explicitly.

Have you seen the live-action movie version of Death Note? The pair of two-hour movies cover roughly the first season of the anime, but they have a different ending, one inspired by a popular fan theory...

I like Death Note, but I found "Liar Game" to be more realistic - at least I personally learned more psychology from it. What do you guys think?