Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

In response to Priors Are Useless
Comment author: WalterL 21 June 2017 01:38:11PM 6 points [-]

I definitely agree that after we become omniscient it won't matter where we started...but going from there to priors 'are useless' seems like a stretch. Like, shoes will be useless once my feet are replaced with hover engines, but I still own them now.

In response to comment by WalterL on Priors Are Useless
Comment author: DragonGod 21 June 2017 02:10:23PM 0 points [-]

But this isn't all there is to it.
@Alex. also, take a set of rationalists with different priors. Let this set of priors be S.
Let the standard deviation of S after i trials be d_i.

d_{i+1} <= d_i for all i: i is in N. The more experiments are conducted the greater the precision of the probabilities of the rationalists.

In response to Priors Are Useless
Comment author: Akhenator 21 June 2017 12:21:10PM 0 points [-]

I might be a bit blind but what are Priz1 and Priz2? Because here it looks like Priz1=Priz2. And what the priors do? What are your hypothesis?

I am sorry if I didn't get it (and I'm maybe looking like a fool right now).

Comment author: DragonGod 21 June 2017 02:07:29PM *  0 points [-]

The priors are the probabilities you assign to hypotheses before you receive any evidence for or against that/those hypothesis/hypotheses.
[;Pr_{i_{z1}};] and [;Pr_{i_{z2}};] are the posterior probabilities on [;Pr_{i_1};] and [;Pr_{i_2};] respectively.

In response to Priors Are Useless
Comment author: CronoDAS 21 June 2017 12:01:34PM 5 points [-]

It can take an awfully long time for N to get big enough.

Comment author: DragonGod 21 June 2017 02:03:10PM 0 points [-]

True. I don't disagree with that.

Priors Are Useless

1 DragonGod 21 June 2017 11:42AM

NOTE.

This post contains Latex. Please install Tex the World for Chromium or other similar Tex typesetting extensions to view this post properly.
 

Priors are Useless.

Priors are irrelevant. Given two different prior probabilities [;Pr_{i_1};], and [;Pr_{i_2};] for some hypothesis [;H_i;].
Let their respective posterior probabilities be [;Pr_{i_{z1}};] and [;Pr_{i_{z2};].
After sufficient number of experiments, the posterior probability [;Pr_{i_{z1}} \approx [;Pr_{i_{z2};].
Or More formally:
[;\lim_{n \to \infty} \frac{ Pr_{i_{z1}}}{Pr_{i_{z2}}} = 1 ;].
Where [;n;] is the number of experiments.
Therefore, priors are useless.
The above is true, because as we carry out subsequent experiments, the posterior probability [;Pr_{i_{z1_j}};] gets closer and closer to the true probability of the hypothesis [;Pr_i;]. The same holds true for [;Pr_{i_{z2_j}};]. As such, if you have access to a sufficient number of experiments the initial prior hypothesis you assigned the experiment is irrelevant.
 
To demonstrate.
http://i.prntscr.com/hj56iDxlQSW2x9Jpt4Sxhg.png
This is the graph of the above table:
http://i.prntscr.com/pcXHKqDAS\_C2aInqzqblnA.png
 
In the example above, the true probability of Hypothesis [;H_i;] [;(P_i);] is [;0.5;] and as we see, after sufficient number of trials, the different [;Pr_{i_{z1_j}};]s get closer to [;0.5;].
 
To generalize from my above argument:

If you have enough information, your initial beliefs are irrelevant—you will arrive at the same final beliefs.
 
Because I can’t resist, a corollary to Aumann’s agreement theorem.
Given sufficient information, two rationalists will always arrive at the same final beliefs irrespective of their initial beliefs.

The above can be generalized to what I call the “Universal Agreement Theorem”:

Given sufficient evidence, all rationalists will arrive at the same set of beliefs regarding a phenomenon irrespective of their initial set of beliefs regarding said phenomenon.

 

Exercise For the Reader

Prove [;\lim_{n \to \infty} \frac{ Pr_{i_{z1}}}{Pr_{i_{z2}}} = 1 ;].

Comment author: DragonGod 13 June 2017 12:43:42PM *  1 point [-]

I’m a 19-year-old Nigerian male. I am strictly heterosexual and an atheist. I am a strong narcissist, and I may have Narcissist Personality Disorder (though I am cognizant of this vulnerability and do work against it which would lower the probability of me suffering from NPD). I am ambitious, and my goal in life is to plant my flag on the sand of time; engrave my emblem in history; immortalise myself in the memory of humanity. I desire to be the greatest man of the 21st century. I am a transhumanist, and intend to live indefinitely, but failing that being the greatest man of the 21st century would suffice. I fear death.

I'm an insatiably curious person. My interests are broad; rationality, science, mathematics, philosophy, economics, computing, literature.

My hobbies include discourse and debate, writing, reading, anime and manga, strategy games, problem solving and learning new things.

I find intelligence the most attractive quality in a potential partner—ambition and drive form a close second.

Mathematical System For Calibration

0 DragonGod 13 June 2017 12:01PM

I am working on an article titled "You Can Gain Information Through Psychoanalysing Others", with the central thesis being with knowledge of the probability someone assigns a proposition, and their calibration, you can calculate a Bayesian probability estimate for the truthhood of that proposition.                      

                  

For the article, I would need a rigorously mathematically defined system for calculating calibration given someone's past prediction history. I thought of developing one myself, but realised it would be more prudent to inquire if one has already been invented to avoid reinventing the wheel.           

              

Thanks in advance for your cooperation. :)             

             

#Disclaimer                        

 

I am chronically afflicted with a serious and invariably fatal epistemic disease known as narcissist bias (this is a misnomer as it refers a broad family of biases). No cure is known yet for narcissist bias, and I’m currently working on cataloguing and documenting the disease in full using myself as a test case. This disease affects how I present and articulate my points—especially in written text—such that I assign a Pr of > 0.8 that a somebody would find this post condescending, self-aggrandising, grandiose or otherwise deluded. This seems to be a problem with all my writing, and a cost of living with the condition I guess. I apologise in advance for any offence received, and inform that I do not intend to offend anyone or otherwise hurt their sensibilities.                  

In response to Any Christians Here?
Comment author: myra 13 June 2017 05:57:06AM 0 points [-]

I never believed in Love Spells or Magics until I met this special spell caster when i went to Africa to Execute some business.. He is really powerful..My husband divorce me with no reason for almost 4 years and i tried all i could to have him back cos i really love him so much but all my effort did not work out.. we met at our early age at the college and we both have feelings for each other and we got married happily for 5 years with no kid and he woke up one morning and he told me he’s going on a divorce.. i thought it was a joke and when he came back from work he tender to me a divorce letter and he packed all his loads from my house.. i ran mad and i tried all i could to have him back but all did not work out.. i was lonely for almost 4 years… So when i told the spell caster what happened he said he will help me and he asked for him full name and him picture..i gave him that.. At first i was skeptical but i gave it a try cos have tried so many spell casters and there is no solution… so when this spell caster finished with the readings, he got back to me that he’s with a woman and that woman is the reason why he left me…The spell caster said he will help me with a spell that will surely bring him back. but i never believe all this… he told me i will see a positive result within 3 days.. 3 days later, he called me himself and he came to me apologizing and he told me he will come back home.. I cant believe this, it was like a dream cos i never believe this will work out after trying many spell casters and there was no solution..The spell caster is so powerful and after that he helped me with a pregnancy spell and i got pregnant a month later.. we are now happy been together again and with lovely kid.. This spell caster has really changed my life and i will forever thankful to him.. he has helped many of my friends too with similar problem too and they are happy and thankful to him..This man is indeed the most powerful spell caster have ever experienced in life.. Am Posting this to the Forum in case there is anyone who has similar problem and still looking for a way out..you can reach him here:Please contact Dr okoko for help he is a trustworthy man EMAIL drokokosolutionhome@gmail.com or visit his web http://drokokospellhome.webs.com/
and be blessed you will also testify the good work.

In response to comment by myra on Any Christians Here?
Comment author: DragonGod 13 June 2017 09:17:33AM 0 points [-]

Well this is interesting....

Comment author: entirelyuseless 06 June 2017 01:08:24PM 1 point [-]

I don't see a convincing argument here. In fact, I don't see any argument at all, convincing or otherwise.

Comment author: DragonGod 13 June 2017 08:58:27AM 0 points [-]

Do you think the argument from infinity is in fact a valuable heuristic?

Comment author: entirelyuseless 08 June 2017 02:49:20AM 1 point [-]

More scattering of information, presumably.

Comment author: DragonGod 13 June 2017 08:57:23AM 0 points [-]

The second law of thermodynamics I see...

In response to Any Christians Here?
Comment author: Lumifer 13 June 2017 01:40:48AM 6 points [-]

You might be interested in Leah Libresco who used to hang around the rationalist sphere and now runs a blog of her own.

Comment author: DragonGod 13 June 2017 01:47:20AM 0 points [-]

Thanks, I'll take a look at the link,

View more: Next