I wrote an article about the quantum immortality which, I know, is a controversial topic, and I would like to get comments on it. The interesting twist, suggested in the article, is the idea of measure increase which could compensate declining measure in quantum immortality. (There are other topics in the article, like the history of QM, its relation to the multiverse immortality, the utility of cryonics, impossibility of euthanasia and the relation of QI to different decision theories.)
The standard argument against quantum immortality in MWI runs as following. One should calculate the expected utility by multiplying the expected gain on the measure of existence (roughly equal to the one's share of the world’s timelines). In that case, if someone expects to win 10.000 USD in the Quantum suicide lottery with 0.01 chance of survival, her actual expected utility is 100 USD (ignoring negutility of death). So, the rule of thumb is that the measure declines very quickly after series of quantum suicide experiments, and thus this improbable timeline should be ignored. The following equation could be used for U(total) = mU, where m is measure and U is expected win in the lottery.
However, if everything possible exists in the multiverse, there are many my pseudo-copies, which differ from me in a few bits, for example, they have a different phone number or different random child memory. The difference is small but just enough for not regard them as my copies.
Imagine that this different child memory is 1kb (if compressed) size. Now, one morning both me and all my pseudo-copies forget this memory, and all we become exactly the same copies. In some sense, our timelines merged. This could be interpreted as a jump in my measure, which will as high as 2power1024 = (roughly) 10E300. If I use the equation U(total) = mU I can get an extreme jump of my utility. For example, I have 100 USD and now my measure increased trillion of trillion of times, I supposedly get the same utility as if I become mega-multi-trillioner.
As a result of this absurd conclusion, I can spend the evening hitting my head with a stone and thus losing more and more memories, and getting higher and higher measure, which is obviously absurd behaviour for a human being - but could be a failure mode for an AI, which uses the equation to calculate the expected utility.
In case of the Quantum suicide experiment, I can add to the bomb, which kills me with 0.5 probability, also a laser, which kills just one neuron in my brain (if I survive), which - let's assume it - is equal to forgetting 1 bit of information. In that case, QS reduces my measure in half, but forgetting one bit increases it in half. Obviously, if I play the game for too long, I will damage my brain by the laser, but anyway, brain cells are dying so often in aging brain (millions a day), that it will be completely non-observable.
BTW, Pereira suggested the similar idea as an anthropic argument against existence of any superintelligence https://arxiv.org/abs/1705.03078