Re: Quantum Suicide without suicide

From: George Levy <GLevy.domain.name.hidden>
Date: Thu, 09 Jan 2003 20:22:30 -0800

Tim May wrote:

> From: Tim May <tcmay.domain.name.hidden>
> Date: Thu Jan 9, 2003 1:22:32 PM US/Pacific
> To: cypherpunks.domain.name.hidden
> Subject: Re: Quantum suicide without suicide
>
>
> On Thursday, January 9, 2003, at 12:32 PM, George Levy wrote:
>
>> As you can see, suicide is not necessary. One could be on death row -
>> in other words have a high probability of dying - and make decisions
>> based on the probability of remaining alive.
>>
>> Being on death row, dying of cancer, travelling on an airline, or
>> sleeping in our bed involve different probability of death... These
>> situations only differ in degrees. We are all in the same boat so to
>> speak. We are all likely to die sooner or later. The closer the
>> probability of death, the more important QS decision becomes.
>>
>> The guy on death row must include in his QS decision making the
>> factor that will save his life: probably a successful appeal or a
>> reprieve by the state governor.
>
>
>
> No, this is the "good news" fallacy of evidential decision theory, as
> discussed by Joyce in his book on "Causal Decision Theory." The "good
> news" fallacy is noncausally hoping for good news, e.g., standing in a
> long line to vote when the expected benefit of voting is nearly nil.
> ("But if everyone thought that way, imagine what would happen!" Indeed.)
>
> The guy on death row should be looking for ways to causally influence
> his own survival, not consoling himself with good news fallacy notions
> that he will be alive in other realities in which the governor issues
> a reprieve. The quantum suicide strategy is without content.
>
>> As you see, suicide is not necessary for QS decisions.
>>
>
> No, I don't see this. I don't see _any_ of this. Whether one supports
> Savage or Jefferys or Joyce or Pearl, I see no particular importance
> of "quantum suicide" to the theory of decision-making.
>
> It would help if you gave some concrete examples of what a belief in
> quantum suicide means for several obvious examples:
>
> -- the death row case you cited
>
> -- the airplane example you also cited
>
> -- Newcomb's Paradox (discussed in Pearl, Joyce, Nozick, etc.)
>
> -- stock market investments/speculations



OK. Let's consider the case of the guy dying of cancer and playing the
stock market simultaneously.. In real life, the hard part is to get
meaningful probability data. For the sake of the argument let's assume
the following scenario:

Given:
1) Alice is dying of cancer. The probability that she dies after six
months but within the year is 80%. According to data compiled by
doctors, she is highly unlikely to die outside this time window. Before
the six monts, she is not sick enough and after the six months she is
highly likely to get into remission. Alice has no family that she may
worry about if she dies. In other words, she does not care about
branches in the manyworld where she does not exist.

2) Bob is perfectly healthy. The probability he dies of cancer is 0.

3) Charles is a young biologist fresh out of school but who has lots of
ideas. He has just started a company, Oncocure, and has declared to the
press that he intends to come up with a cure for cancer within six
months. He is about to make his company public through an IPO offering.

4) A reputable market analysis firm has declared that the Oncocure stock
will increase in value by a factor of 1000 if the cure that Charles is
promising is working, and Charles is a genius. Otherwise, the stock will
drop to zero and Charles is a quack.

5) A reputable academic has declared that the probability of Charles
coming up with a cure is 0.1%.

6) If Charles has a medicine that works, then Alice intends to take it
and she will be cured.

Question:
Assuming that the market analysis data and that the probabilistic
evaluation by the academic are correct
1) should Alice buy the stock from company? What is her expected rate of
return?
2) should Bob buy the stock from the compay? What is his expected rate
of return?

Solution:
There are four scenarios:
A) Charles does not come up with a cure, AND Alice lives.
       Probability = (1-0.001) x ( 1- 0.8) = 0.1998

B) Charles does not come up with a cure AND Alice dies.
       Probability = (1-0.001) x (0.8) = 0.7992

C) Charles does come up with a cure AND Alice lives using the cure.
       Probability = (0.001) x (1) = 0.001

D) Charles does come up with a cure AND Alice dies. This scenario is
impossible since Alice intends to take the medicine.
       Probability = (0.001) x (0) = 0

The third person (as seen by Bob) probabilities must add to 1 which
they do: P(A) + P(B) + P(C) + P(D) = 1
The following step is important and is probably the most controversial:
The events that Alice can perceive are only A and C. Hence the
probability distribution which is applicable to her must be normalized
to make her probabilities add up to one.
   P'(A) = P(A) /(P(A) + P(C)) = 0.1998 / (0.1998 + 0.001) = 0.99502
   P'(C) = P(B) /(P(A) + P(C)) = 0.001 / (0.1998 + 0.001) = 0.00498

Where the prime indicate the probabilities seen through Alice's eyes.
This normalization is just an application of Bayes theorem:

P'(A) = P(a|b) = P(b|a)P(a) / (P(b|a)P(a) + P(b|not a) P(not a)) =
P(a AND b) / (P(a AND b) + P(not a AND b))

where a = cure works and b = Alice lives

In our case P(A) = P(No Cure AND Alice lives)
                P(B) = P(No Cure AND Alice dies)
                P(C) = P(Cure AND Alice lives)
                P(D) = P(Cures AND Alice dies)

Notice that as expected P'(A) + P'(B) = 1

Now let's calculate the expected value for $100 par value of stock for
Alice and Bob after the medicine is tested:
1) Alice. If Alice buys the stock, the rate of return that she will
perceive will be controlled by scenarios A and C.
       Expected value of the stock = P'(A) x (value of stock with no
cure) + P'(C) x (value of stock with working cure)
                                                   = 0.9952 x 0 +
0.00498 x (100 x 1000) = 498

2) Bob. Since Bob is not affected by Alice's health, the controlling
scenarios are A,B,C,D. Hence
       Expected value of the stock for Bob = P(A) x (value of stock with
no cure) + P(B) x (value of stock with no cure) + P(C) x (value of stock
with working cure) + P(D) x (value of stock with working cure)
       = 0.1998 x 0 + 0.7992 x 0 + 0.001 x (100 x 1000) + 0 x (100 x
1000) = 100

As we can see, the rate of return for Alice is 4.8 times that of Bob.
Alice will make a profit, but not Bob.

Conclusions:
All this involves really basic probability theory.
The first person perspective probability is identical to the probability
conditional to the person staying alive.
The probability of the event in question (stock going up) must be tied
to the person staying alive ( a cure for cancer). In the case of a
"conventional" QS suicide to world conditions matching the requested
state: ie. winning one million dollars. In the deathrow case one could
imagine a scenario in which the event in question (DNA test discovery)
is tied to a reprieve from the governor coming because of a DNA test
exhonerating the prisoner. The prisoner could bet on DNA testing as a
good investment. The airline case is similar. The hard part is figuring
the probability of very unlikely saving events such as a scientific
discovery, ET landing on earth or the coming of the messiah :-)

I have discussed the Newcomb paradox on a previous post (one or two
years ago) arguing that consciousness is "relative" to the (subjective
or mental) frame of reference of the observer in a Turing-type test.


George
 
Received on Thu Jan 09 2003 - 23:24:31 PST