12y5

In my experience, the process of research does not correspond to what you're describing. First, you find something interesting which could be made into a paper. The first thing you do at this point is speaking about it to other researchers, more or less formally (face-to-face discussion, email, formal presentation). Only after having got some feedback, you begin to write a draft. Then, you publish this draft on your personal website at the same time you send it to a journal for review. You get feedback both from the official reviewers and readers of your s...

You forgot to correct an instance of this :

The joint system (X,Y,Z) only has 16 possible states - since Z is just the question "Are X+Y even or odd?" - so H(X,Y,Z) = 4 bits.

I find it particularly disturbing because in this instance, X+Y is always even...

Why is it important that there is a deterministic breaking rule ? When you would like random numbers, isn't it always better to have a distribution as close as random as possible, even if it is pseudo-random ?

That question is perhaps stupid, I have the impression that I am missing something important...

212y

Remember it is Omega implementing the tie-breaker rule, since it defines the problem.
The consequence of the tie-breaker is that the choosing agent knows that Omega's box-choice was a simple deterministic function of a mathematical calculation (or a proof). So the agent's uncertainty about which box contains the money is pure logical uncertainty.

12y-1

I don't understand the special role of box 1 in Problem 2. It seems to me that if Omega just makes different choices for the box in which to put the money, all decision theories will say "pick one at random" and will be equal.

In fact, the only reason I can see why Omega picks box 1 seems to be that the "pick at random" process of your TDT is exactly "pick the first one". Just replace it with something dependant on its internal clock (or any parameter not known at the time when Omega asks its question) and the problem disappears.

212y

Omega's choice of box depends on its assessment of the simulated agent's choosing probabilities. The tie-breaking rule (if there are several boxes with equal lowest choosing probability, then select the one with the lowest label) is to an extent arbitrary, but it is important that there is some deterministic tie-breaking rule.
I also agree this is entirely a maths problem for Omega or for anyone whose decisions aren't entangled with the problem (with a proof that Box 1 will contain the $1 million). The difficulty is that a TDT agent can't treat it as a straight maths problem which is unlinked to its own decisions.

12y0

This is a strategy that I sometimes implement and I think it should be used more often, be it only because it allows friends of friends to meet or get to know one another better and that makes nicer social networks.

However, I wonder if it can be taken too far. If everybody routinely makes this sort of demands, won't people stop to answer them ? Is this technique successful partly because it is not widely used ?

012y

I may have to edit the text for clarification. In fact, I'm going to do so right now.

This is what has been attempted by the Ferry laws in France. The high rates of atheists and agnostics in France are a consequence of these laws, which made education mandatory and reduced the influence of the Catholic church on education.

However, I do not think it raised the sanity line in other domains, and it had bizarre effects, such as an important part of the population which say they belong to a religion but do not believe in any god.