The Sleeping Beauty problem and transformation invariances
I recently read this blog post by Allen Downey in response to a reddit post in response to Julia Galef's video about the Sleeping Beauty problem. Downey's resolution boils down to a conjecture that optimal bets on lotteries should be based on one's expected state of prior information just before the bet's resolution, as opposed to one's state of prior information at the time the bet is made.
I suspect that these two distributions are always identical. In fact, I think I remember reading in one of Jaynes' papers about a requirement that any prior be invariant under the acquisition of new information. That is to say, the prior should be the weighted average of possible posteriors, where the weights are the likelihood that each posterior would be acheived after some measurement. But now I can't find this reference anywhere, and I'm starting to doubt that I understood it correctly when I read it.
So I have two questions:
1) Is there such a thing as this invariance requirement? Does anyone have a reference? It seems intuitive that the prior should be equivalent to the weighted average of posteriors, since it must contain all of our prior knowledge about a system. What is this property actually called?
2) If it exists, is it a corollary that our prior distribution must remain unchanged unless we acquire new information?
On the importance of taking limits: Infinite Spheres of Utility
I had a discussion recently with some Less Wrongers about a decision problem involving infinities, which appears to have a paradoxical solution. We have been warned by Jaynes and others to be careful about taking the proper limits when infinities are involved in a problem, and I thought this would be a good example to show that we can get answers that make sense out of problems that seem not to.
Meetup : Weekly meetup, Champaign IL: Cafe Paradiso
Discussion article for the meetup : Weekly meetup, Champaign IL: Cafe Paradiso
Let's meet at 8pm. We decided last time that we'd like to start talking about Timeless decision theory. It's a big topic, but try to come to the meeting with questions or discussion points. Also, let's talk about doing something social next week.
Discussion article for the meetup : Weekly meetup, Champaign IL: Cafe Paradiso
Meetup : Meetup, Champaign IL,
Discussion article for the meetup : Meetup, Champaign IL,
Let's get together on Wednesday the 14th of November at 7pm at Cafe Paradiso.
Last time we talked about wanting to discuss specific topics at the meetings, and we decided that we're going to start with Consequentialism.
So try to read a little bit about it before next time. Possibilities include:
- Wikipedia
- Check Consequentialism on LessWrong
- Consequentialism FAQ
- Consequentialism Need Not Be Nearsighted
Also, think about any topics you'd be interested in eventually presenting to the rest of us. You don't need to be an expert: just interested. It can be LW related or not.
See you then.
Discussion article for the meetup : Meetup, Champaign IL,
Meetup : Champaign, IL meetup
Discussion article for the meetup : Champaign, IL meetup
Hi all, We're meeting at Paradiso Cafe at 8pm. I'll try to have a little sign. We'd like to talk about 1) How to get the word out and expand the group 2) What kind of structure we'd like to see for the meetings 3) What topics we want to cover in detail 4) When we should regularly meet.
See you then.
Brad
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