No, I would NOT be willing to give 2-1 odds in making a bet that the coin will
land tails. IT'S A FAIR COIN! If you ever have yourself saying that a coin
has a 2/3 chance of *landing* tails, not just of having *landed* tails, you
have left the realms of sanity!
Besides, the experimenter makes a bet with one person, in each case. If the
coin lands tails, he makes a bet with the uncloned. If it lands heads, he
makes a bet with the original. In either case he makes one bet. From his
point of view, he should bet at 1/2 odds. If I'm told that I am not the
clone, then I should also bet at 1/2 odds. Therein lies the paradox: When I
am told that I am not cloned, have I learned information about the coin-flip
or only about myself?
And if I'm not told that I'm the clone, what should I bet that I was cloned?
>From the experimenter's view, he should gain $200 from the uncloned and lose
$100 to each of the cloned, so I should bet $200 against $100 that the coin
landed heads. But I haven't gained any additional information!
One of the problems with this scenario is the existence of a clone. This
confuses everything. My situation:
I agree to be part of a research experiment. I am told that a coin was
flipped. If it came up heads, only I, Person A, was selected to take part in
the experiment. If it came up tails, two people were selected to take part in
the experiment, one of them being "Person B".
What is the probability that the coin came up heads?
What is the probability that I am person B?
If I am not person B, what is the probability the coin came up heads?
> In effect, cloning makes it a non-zero-sum game. The changes introduced
> by cloning in potential future earnings cause the gains or losses of the
> bet to be evaluated differently. The result is that it may be rational
> to take a bet which gives an expected profit to the other player.
I think the cloning is a side issue.
But: In the scenario above, there was the possibility that I would not be
person A. If cloned, someone is always a person A. Either my selection
provides me with information I did not have (I might not have been selected),
or being person A provides me with information I did not have (I might have
been person B). Only with cloning, perhaps, can I - or one of me - always be
told "You exist and are not person B".
--
sentience@pobox.com Eliezer S. Yudkowsky
http://tezcat.com/~eliezer/singularity.html
http://tezcat.com/~eliezer/algernon.html
Disclaimer: Unless otherwise specified, I'm not telling you
everything I think I know.