Rolf Nelson wrote:
> On Oct 25, 7:59 am, "Wei Dai" <wei....domain.name.hidden> wrote:
>> I don't care
>> about (1) and (3) because those universes are too arbitrary or random,
>> and I
>> can defend that by pointing to their high algorithmic complexities.
>
> In (3) the universe doesn't have a high aIgorithmic complexity.
I should have said that in (3) our decisions don't have any consequences, so
we disregard them even if we do care what happens in them. The end result is
the same: I'll act as if I only live in (2).
>From your post yesterday:
> True. So how would an alternative scheme work, formally? Perhaps
> utility can be formally based on the "Measure" of "Qualia" (observer
> moments).
This is one of the possibilities I had considered and rejected, because it
also leads to counterintuitive consequences. For example, suppose someone
gives your the following offer:
I will throw a fair coin. If the coin lands heads up, you will be
instantaneously vaporized. If it lands tails up, I will exactly double your
measure (say by creating a copy of your brain and continuously keeping it
synchronized).
Given your "measure of qualia"-based formalization of utility, and assuming
that you're selfish so that you're only interested in the measure of the
qualia of your own future selves, you'd have to be indifferent between
accepting this offer and not accepting it.
Instead, here's my current approach for a formalization of decision theory.
Let a set S be the description of an agent's knowledge of the multiverse.
For example, for a Tegmarkian version of the multiverse, elements of S have
the form (s, t) where s is a statement of second-order logic, and t is
either "true" or "false". For simplicity, assume that the decision-making
agent is logically omniscient, which means he knows the truth value of all
statements of second-order logic, except those that depend on his own
decisions. We'll say that he prefers choice A to choice B if and only if he
prefers S U C(E,A) to S U C(E,B), where U is the union operator, C(x,y) is
the logical consequences of everyone having qualia x deciding to do y, and E
consists of all of his own memories and observations.
In this most basic version, there is not even a notion of "how much one
cares about a universe". I'm relatively confident that it doesn't lead to
any counterintuitive implications, but that's mainly because it is too weak
to lead to any kind of implications at all. So how do we explain what
probability is, and why the concept has been so useful?
Well, let's consider an agent who happens to have preferences of a special
form. It so happens that for him, the multiverse can be divided into several
"regions", the descriptions of which will be denoted S_1, S_2, S_3, etc.,
such that S_1 U S_2 U S_3 ... = S and his preferences over the whole
multiverse can be expressed as a linear combination of his preferences over
those "regions". That means, there exists functions P(.) and U(.) such that
he prefers the multiverse S to the multiverse T if and only if
P(S_1)*U(S_1) + P(S_2)*U(S_2) + P(S_3)*U(S_3) + ...
> P(T_1)*U(T_1) + P(T_2)*U(T_2) + P(T_3)*U(T_3) ...
I haven't worked out all of the details of this formalism, but I hope you
can see where I'm going with this...
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Received on Sun Oct 28 2007 - 21:46:03 PDT