Rationality Quotes June 2013

Thomas

Another month has passed and here is a new rationality quotes thread. The usual rules are:

Please post all quotes separately, so that they can be upvoted or downvoted separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
Do not quote yourself.
Do not quote from Less Wrong itself, Overcoming Bias, or HPMoR.
No more than 5 quotes per person per monthly thread, please.

Another month has passed and here is a new rationality quotes thread. The usual rules are:

Please post all quotes separately, so that they can be upvoted or downvoted separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
Do not quote yourself.
Do not quote from Less Wrong itself, Overcoming Bias, or HPMoR.
No more than 5 quotes per person per monthly thread, please.

The numerical value of the prior itself doesn't tell how much information -- or lack thereof -- is incorporated into the prior.

What's a simple way to state how certain you are about a prior, i.e. how stable it is against large updates based on new information? Error bars or something related don't necessarily do the job -- you might be very sure that the true Pr (EDIT: that was poorly phrased, probability is in the mind etc., what was meant is the eventual Pr you end up with once you've hypothetically parsed all possible information, the limit) is between 0.3 and 0.5, i.e. new information will rarely result in a posterior outside that range, even if the size of the range (wrongly) suggests that the prior is based on little information. Is there something more intuitive than Pr(0.3<Pr(A)<0.5) = high?

Error bars usually indicate a Gaussian distribution, not a flat one. If you said P=0.4 +- 0.03, that indicates that your probability of the final probability estimate ending up outside the 0.3-0.5 range is less than a percent. This seems to meet your requirements.

If that doesn't suffice, it seems that you need a full probability distribution, specifying the probability of every P-value.

1CCC13y

Describing probabilities in terms of a mean and an approximate standard deviation, perhaps? Low standard deviation would translate to high certainty.

7Manfred13y

Part 1: The idea of having a "true probability" can be extremely misleading. If I flip a coin but don't look at it, I may call it a 50% probability of tails, but reality is sitting right there in my hand with probability 100%. The probability is not in the external world - the coin is already heads or tails. The probability is just 50% because I haven't looked at the coin yet. What sometimes confuses people is that there can be things in the world that we often think of as probabilities, and those can have a true value. For example, if I have an urn with 30 black balls and 70 white balls, and I pull a ball from the urn, I'll get a black ball about 30 times out of 100. This isn't "because the true probability is 30%" - that's an explanation that just points to a new fundamental property to explain. It's because the urn is 30% black balls, and I hadn't looked at where all the balls were yet. Using probabilities is an admission of ignorance, of incomplete information. You don't assign the coin a probability because it's magically probabilistic, you use probabilities because you haven't looked at the coin yet. There's no "true probability" sitting out there in the world waiting for you to discover it, there's only a coin that's either heads or tails. And sometimes there are urns with different mixtures of balls, though of course if you can look inside the urn it's easy to pick the ball you want. Part 2: Okay, so there's no "externally objective, realio trulio probability" to compare our priors to, so how about asking how much our probability will move after we get the next bit of information? Let's use some examples. Say I'm taking a poll. And I want to know what the probability is that people will vote for the Purple Party. So I ask 10 people. Now, 10 is a pretty small sample size, but say 3 out of 10 will vote for the purple party. So I estimate that the probability is a little more than 3/10. Now, the next additional person I ask will cause me to change my prob