[extropy-chat] what is probability?
Jef Allbright
jef at jefallbright.net
Sun Jan 14 18:21:02 UTC 2007
Gordon -
There's nothing amazing or paradoxical here. Do you find it equally perplexing when someone asks the average of some set of numbers, and another person responds mean, median, arithmetic or geometric average?
Also, I wasn't "wondering" any such thing as you describe below. Rather, I was challenging you to be more coherent.
- Jef
________________________________
From: extropy-chat-bounces at lists.extropy.org on behalf of gts
Sent: Sun 1/14/2007 9:39 AM
To: ExI chat list
Subject: Re: [extropy-chat] what is probability?
On the subjective theory of probability, two rational agents with the same
background knowledge may hold different judgemental probabilities on the
same outcome, at least in certain situations.
Though I don't necessarily endorse this view, I think I can defend it. Jef
wants to know for example how two rational machine intelligences might
offer different outputs given the same inputs.
Drawing on the cube conundrum, imagine this scenario:
Unbeknownst to each other, two rational agents (machine intelligences,
AI's, whatever) are each given a box containing a cube.
The cubes in the two boxes are identical. The agents know only that their
side-lengths are between 3 and 5 centimeters, their surface areas are
between 54 and 150 cm^2, and their volumes are between 27 and 125 cm^3.
Note there is nothing challenging about these ranges; lots of real cubes
could meet these constraints.
For some practical unspecified reason, each agent must use the information
given to make a best-guess of the probable dimensions of the actual cube
in his respective box. (As often happens in the real world, our agents are
being forced to make decisions under conditions of high uncertainty.)
They make their decisions, then come together to compare their conclusions
and their reasoning. Is it possible that our agents will have reached
different conclusions?
I think so. In fact I'd be surprised if they didn't.
Our agents were forced to decide arbitrarily between 'side-length',
'surface area' and 'volume' as the parameter to use for estimating the
over-all dimensions of the cube. Each of these three methods leads to a
different but perfectly rational judgemental probability. As we've seen,
judgements based on all three parameters are paradoxical.
-gts
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