Comment author: Andreas_Giger 08 October 2013 04:24:19AM 1 point [-]

There used to be a thread on LW that dealt with interesting ways to make small sums of money and ways to reduce expenditure. I think among other things going to Australia for a year was discussed. Does anyone know which thread I'm talking about and can provide me with the link? I can't seem to find it.

Comment author: Coscott 02 October 2013 06:01:22AM 0 points [-]

We did not discuss Cesàro sums.

I have no need for the new continuous question, if you are happy with saying that a per day analysis is no less arbitrary than a coin flip analysis.

The math is proving to be too much work to write up, so ill just tell you why I think there is a difference between per day and per coin flip. In the per coin flip, you take each of the possible coin flip sequences with equal weight when you are taking the averages of the partial sums in the Cesàro sums. In the per day analysis, you are putting much much more weight on the coin flip sequences which have more flips, because there are many more days which include them.

Comment author: Andreas_Giger 02 October 2013 08:54:59AM *  0 points [-]

The "many more days that include them" is the 3^n part in my expression that is missing from any per day series. This 3^n is the sum of all interviews in that coin flip sequence ("coin flip sequence" = "all the interviews that are done because one coin flip showed up tails", right?) and in the per day (aka per interview) series the exact same sum exists, just as 3^n summands.

In both cases, the weight of the later coin flip sequences increases, because the number of interviews (3^n) increases faster than the probabilistic weight of the coin flip (1/2^n) decreases.

However, this doesn't mean that there exists no Cesàro sum. In fact the existence of such a sum can be proven for my original expression because the quotient of the last two numerators (if we include both odd and even coin flips) of the isomorphic series is always 3:1, regardless of wether the last coin flip was even or odd. (The same thing can be said for the quotient of the last 3^n and 3^(n-1) summands of your series. Basically, the per day series is just a dragged out per coin flip series.)

The reason why my estimation for the Cesàro sum is 0.5 is that if we express that quotient in a way that one coin state is written first, then it alternates between 3:1 and 1:3, which results in 1:1 which is 0.5. Obviously this is not exact maths, but it's a good way for a quick estimation. (Alternatively, you could intuitively infer that if there exists a Cesàro sum it must be 0.5, because whether you look for even or odd coin flips gets increasingly irrelevant as the series approaches infinity.)

Also, since I haven't previously touched upon the subject of the isomorphic series: If we call my original expression f, then we can construct a function g where g(n) = f(n)-f(n-1) with f(-1) = 0, and a series a = g(0) + g(1) + g(2) + ...

Does that all make sense?

Comment author: Andreas_Giger 01 October 2013 11:07:48AM 0 points [-]

I saw this post from EY a while ago and felt kind of repulsed by it:

I no longer feel much of a need to engage with the hypothesis that rational agents mutually defect in the oneshot or iterated PD. Perhaps you meant to analyze causal-decision-theory agents?

Never mind the factual shortcomings, I'm mostly interested in the rejection of CDT as rational. I've been away from LW for a while and wasn't keeping up on the currently popular beliefs on this site, and I'm considering learning a bit more about TDT (or UDT or whatever the current iteration is called). I have a feeling this might be a huge waste of time though, so before I dive into the subject I would like to confirm that TDT has objectively been proven to be clearly superior to CDT, by which I (intuitively) mean:

  • There exist no problems shown to be possible in real life for which CDT yields superior results.
  • There exists at least one problem shown to be possible in real life for which TDT yields superior results.

"Shown to be possible in real life" excludes Omega, many-worlds, or anything of similar dubiousness. So has this been proven? Also, is there any kind of reaction from the scientific community in regards to TDT/UDT?

Comment author: Andreas_Giger 02 October 2013 01:42:02AM *  -1 points [-]

I think people have slightly misunderstood what I was referring to with this:

  • There exist no problems shown to be possible in real life for which CDT yields superior results.
  • There exists at least one problem shown to be possible in real life for which TDT yields superior results.

My question was whether there is a conclusive, formal proof for this, not whether this is widely accepted on this site (I already realized TDT is popular). If someone thinks such a proof is given somewhere in an article (this one?) then please direct me to the point in the article where I can find that proof. I'm very suspicious about this though, since the wiki makes blatantly false claims, e.g. that TDT performs better in one-shot PD than CDT, while in fact it can only perform better if access to source coude is given. So the wiki article feels more like promotion than anything.

Also, I would be very interested to hear about what kind of reaction from the scientific community TDT has received. Like, very very interested.

Comment author: Coscott 01 October 2013 10:27:56PM *  0 points [-]

I haven't actually done the math yet, but I don't believe you. I think that if your terms are "per interview" then the more recent chunk of 100% even will overpower all the older stuff because there are so many of them, and the series of averages will oscillate.

Comment author: Andreas_Giger 02 October 2013 12:15:10AM 0 points [-]

I take it that my approach was not discussed in the heated debate you had? Because it seems a good exercise for grad students.

Also, I don't understand why you think a per interview series would net fundamentally different results than a per coin toss series. I'd be interested in your reports after you (or your colleagues) have done the math.

Comment author: Coscott 01 October 2013 09:55:32PM 0 points [-]

That is wrong. Sorry. floor(3^x) doesn't work because sqrt(3)<2. Try floor(5^x).

Comment author: Andreas_Giger 01 October 2013 10:04:54PM 0 points [-]

I could have said that the beauty was simulated floor(5^x) times where x is a random real between 0 and n

Ah, I see now what you mean. Disregarding this new problem for the moment, you can still formulate my original expression on a per-interview basis, and it will still have the same Cesàro sum because it still diverges in the same manner; it just does so more continuously. If you envision a graph of an isomorphic series of my original expression, it will have "saw teeth" where it alternates between even and odd coin flips, and if you formulate that series on a per-interview basis, those saw teeth just get increasingly longer, which has no impact on the Cesàro sum (because the series alternates between those saw teeth).

Concerning your new problem, it can still be expressed as a series with a Cesàro sum, it's just a lot more complicated. If I were you, I'd first try to find the simplest variant of that problem with the same properties. Still, the fact that this is solvable in an analogous way should be clear, because you can essentially solve the "floor(5^x) times where x is a random real between 0 and n" part with a series for x (similar to the one for the original problem) and then have a series of those series for n. Basically you're adding another dimension (or recursion level), but not doing anything fundamentally different.

Comment author: Coscott 01 October 2013 08:51:17PM 0 points [-]

You are taking a Cesàro sum by treating each possible series of coinflips as a summand. This is arbitrary. If you instead took a series over time, it would not have a Cesàro sum. (i.e. for the partial sum at time t, you only count Beauties that might exist in the first t days)

Comment author: Andreas_Giger 01 October 2013 09:00:46PM *  0 points [-]

What do you mean by "time" in this case? It sounds like you want to interrupt the interviews at an arbitrary point even though Beauty knows that interviews are quantised in a 3^n fashion.

Comment author: Andreas_Giger 01 October 2013 08:40:52PM *  0 points [-]

(1/2 * 3^0 + 1/8 * 3^2 + ...) / (1/2 * 3^0 + 1/4 * 3^1 + 1/8 * 3^2 + ...)

... which can be transformed into an infinite series with a Cesàro sum of 0.5, so that's my answer.

Comment author: IlyaShpitser 01 October 2013 01:15:14PM *  10 points [-]

The question "which decision theory is superior?" has this flavor of "can my dad beat up your dad?"

CDT is what you use when you want to make decisions from observational data or RCTs (in medicine, and so on).

TDT is what you use when "for some reason" your decisions are linked to what counterfactual versions/copies of yourself decided. Standard CDT doesn't deal with this problem, because it lacks the language/notation to talk about these issues. I argue this is similar to how EDT doesn't handle confounding properly because it lacks the language to describe what confounding even means. (Although I know a few people who prefer a decision algorithm that is in all respects isomophic to CDT, but which they prefer to call EDT for I guess reasons having to do with the formal epistemology they adopted. To me, this is a powerful argument for not adopting a formal epistemology too quickly :) )

I think it's more fruitful to think about the zoo of decision theories out there in terms of what they handle and what they break on, rather than in terms of anointing some of them with the label "rational" and others with the label "irrational." These labels carry no information. There is probably no total ordering from "best to worst" (for example people claim EDT correctly one boxes on Newcomb, whereas CDT does not. This does not prevent EDT from being generally terrible on the kinds of problems CDT handles with ease due to a worked out theory of causal inference).

Comment author: Andreas_Giger 01 October 2013 07:43:17PM 1 point [-]

I don't like the notion of using different decision theories depending on the situation, because the very idea of a decision theory is that it is consistent and comprehensive. Now if TDT were formulated as a plugin that seamlessly integrated into CDT in such a way that the resulting decision theory could be applied to any and all problems and would always yield optimal results, then that would be reason for me to learn about TDT. However, from what I gathered this doesn't seem to be the case?

Comment author: Andreas_Giger 01 October 2013 11:07:48AM 0 points [-]

I saw this post from EY a while ago and felt kind of repulsed by it:

I no longer feel much of a need to engage with the hypothesis that rational agents mutually defect in the oneshot or iterated PD. Perhaps you meant to analyze causal-decision-theory agents?

Never mind the factual shortcomings, I'm mostly interested in the rejection of CDT as rational. I've been away from LW for a while and wasn't keeping up on the currently popular beliefs on this site, and I'm considering learning a bit more about TDT (or UDT or whatever the current iteration is called). I have a feeling this might be a huge waste of time though, so before I dive into the subject I would like to confirm that TDT has objectively been proven to be clearly superior to CDT, by which I (intuitively) mean:

  • There exist no problems shown to be possible in real life for which CDT yields superior results.
  • There exists at least one problem shown to be possible in real life for which TDT yields superior results.

"Shown to be possible in real life" excludes Omega, many-worlds, or anything of similar dubiousness. So has this been proven? Also, is there any kind of reaction from the scientific community in regards to TDT/UDT?

Comment author: John_Maxwell_IV 28 September 2013 04:25:30AM *  2 points [-]

How many people actually did the exercises katydee suggested? I know I didn't.

katydee, perhaps you could take a semi-random sample of things in relevant reference classes (politicians/organizations) and demonstrate how easy it is to make fun of them? Otherwise I suspect many people will take you for your word that things are easy to make fun of.

Here's my semi-random sample of organizations and politicians. I'll take the most recent 3 Daily Show guests I recognize the names of and the largest 3 charities I recognize the names of.

  • Richard Dawkins

  • Chelsea Clinton

  • Robert Reich

  • Salvation Army

  • American National Red Cross

  • American Cancer Society

Here are my brief attempts to make fun of them.

  • Richard Dawkins: He wasn't satisfied with being an eminent biologist, he just had to stir up controversy by provoking religious people. And his arguments apparently aren't even very philosophically sound. Stick to biology next time, Dawkins.

  • Chelsea Clinton: Good luck finding a man who's higher status than you to marry.

  • Robert Reich: Is he liberal because he's short or is he short because he's liberal?

  • Salvation Army: Ineffective charity that spreads religious lies. Chumps.

  • American National Red Cross: We're all going to die eventually anyway. Organizations like the Red Cross just prolong our misery.

  • American Cancer Society: Clearly cancer is just a side effect of aging and your money is better sent to SENS. Also, just how much money have we poured in to cancer research without finding a cure yet? They should call it the "American Cancer Researcher Welfare Program".

It seems to me that the things I can make fun of the most easily are the ones that have legitimate arguments that reflect poorly on them (e.g. the Salvation Army and American Cancer Society). But maybe I'm just bad at making fun of things.

Comment author: Andreas_Giger 28 September 2013 07:32:51PM 0 points [-]

How many people actually did the exercises katydee suggested? I know I didn't.

I did, but I don't think people realised it.

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