“Weight of evidence”, or why internally consistent theories that explain more are more likely to be true

This post is dedicated to Edenist Whackjob because he’s having trouble with this idea and I haven’t been able to keep up with all his comments. Also he is the best example of “massive lateral thinking” that I’ve ever seen :-P

For example, a detective may have two distinct theories about a murder. 1) The butler did it, 2) somebody else did it. His job is to craft an internally cohesive narrative which fits all the facts together with perfect certainty. Not one fact may be out of place. If it can be proven that the butler has a solid alibi, then it doesn’t matter how much of the rest of the evidence points his way.

The question of what is a “fact” is a perceptual matter of induction and belief. Whether we believe that the butler’s alibi is “solid” (sound, in logical parlance) is a matter of perception. It can But if we accept it as truth, then the detective cannot also accuse the butler of the murder.

The narrative (theory) does not have to describe everything that has ever happened, from the solubility of salt to the Warsaw pact, in perfect causal detail. However, it must explain as many facts as possible, with emphasis on those we consider relevant to the case. With this in mind, I am approaching a logical definition for the phrase “weight of evidence”.

Given a set of facts A = {a, b, c, d…} where the values are weighted by “relevance”, then a theory’s “weight of evidence” is the sum of the weighted facts it explains, divided by the total weight of all possible theories. Remember, we are assuming all “theories” are internally consistent. If a theory is not internally consistent, then it has a 0% probability.

For example, there are two competing theories “Butler” and “Not-butler” which are internally consistent. Butler explains a, b, c but d is unaccounted for. Not-butler explains c and d. If all evidence is weighted equally, then the total weight T is (a + b + c) + (c + d). Then the weight of evidence for the butler theory is (a + b + c)/T.

If they’re weighted equally (a = b = c = d), then T = (a + b + c) + (c + d) = (a + a + a) + (a + a) = 5a. And “Butler” = (a + b + c)/5a = (a + a + a)/5a = 3a/5a = 60%. That is, we can say there is a 60% chance that the butler did it. Not enough to convict, but enough to continue the investigation. (Because the other theory is mutually exclusive, “not butler” has a 40% chance, or 1 – P(“Butler”).)

If the probability is high enough, then in court terms we would say it is “proven beyond a reasonable doubt”.

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40 Responses to “Weight of evidence”, or why internally consistent theories that explain more are more likely to be true

  1. Edenist whackjob says:

    Nicely explained. Do I have a problem with this? :)

    • Aeoli Pera says:

      No, I don’t think so. I have merely formalized the source of your uncertainty.

      • Edenist whackjob says:

        Example where I’ve given voice to that? Just trying to get it.

      • Edenist whackjob says:

        “Here, particularly,”

        I don’t think I’m using your mode of deduction, though. This needs clarified.

      • Edenist whackjob says:

        “I may not be able to keep up anymore with my intent to reply to every comment, but reading and considering them all is the least I can do.”

        Should I stop posting every random thought I have here? Put down your ground rules. No need to abuse your ingenopathy (ie need to consider everything worthy of a reply).

        • Aeoli Pera says:

          Of course not, you produce an extraordinary amount of good ideas! You really ought to have a blog, but I’m fine with you writing one in my comments if that’s easiest for you. And I enjoy interacting with you too.

      • Edenist whackjob says:

        “I was pointing out where you expressed anxiety over the uncertainty of this method. But maybe I misunderstood your question.”

        I don’t think my situation is analogous to your whodunnit example. It’s not like I’m stringing together two internally coherent explanations for comparison. My trouble is more with what is actually relevant. Ie pattern-matching more than deduction.

      • Edenist whackjob says:

        “Of course not, you produce an extraordinary amount of good ideas!”

        That’s great to hear. I often doubt myself (not a humble-brag, it’s the truth).

        Maybe you should go through all of my comments and create some compilations, like you did with Game. Post it on the blog and see what people say. Maybe I’ll start a blog then.

        Main problem with starting a blog: I sometimes suspect I am mentally ill (I *know* I have an anxiety disorder and a generally depressive/anhedonic outlook on life, but I don’t really know if I am eg paranoid schizophrenic too). Having a blog would reinforce those delusions that I maybe-have.

  2. Edenist whackjob says:

    Problem: how do you weight objectively? In your example you just assume equigravity of all links.

    • Aeoli Pera says:

      You can’t. There is no such thing as an objective perception.

    • Edenist whackjob says:

      Does that mean that your theory needs another paradigm where relevance is the key factor, or am I asking the wrong question here?

      • Aeoli Pera says:

        Yeah, a complete theory would have to explain how to decide what is relevant. The fact that ordinary people do this very well is just another miraculous property of the supercomputer upstairs.

      • Edenist whackjob says:

        “The fact that ordinary people do this very well ”

        Can you explain a bit further? Not trying to be a dick, I just can’t relate to that statement.

        • Aeoli Pera says:

          If there’s been a murder, and there’s a gun on the floor, even a dull person will assign a high relevance to the gun.

          If you don’t think that’s downright miraculous, then try to write a program to tell a computer how to do that in any situation.

      • Edenist whackjob says:

        “If there’s been a murder, and there’s a gun on the floor, even a dull person will assign a high relevance to the gun.”

        It’s certainly the most salient thing, yes.

        I just don’t see how that mode of reasoning is analogous to what I do.

        I think a better analogy would be finding a room with a gun, a naked lady (alive), Donald Duck, and a bro from a frat, and then being asked “what genre is the movie?”

        “If you don’t think that’s downright miraculous, then try to write a program to tell a computer how to do that in any situation.”

        Well if you give it a corpus of text and ask it to pick out the most salient facts, then I think it would be within reason to expect an expert-system AI to pick out “gun” given the parameters “seek for relevant associations to ‘murder'”.

  3. Edenist whackjob says:

    https://heartiste.wordpress.com/2015/09/12/comment-of-the-week-the-microjizzome/

    This makes think about Rocco Siffredi. He’s licked the buttholes of thousands of women. Maybe he wants to gobble up their feminine essence.

    I’ve liked a few cracks myself. Maybe not so wise.

    • Aeoli Pera says:

      Lol, bro that is disgusting. But as you said, I guess this is the blog for that sort of thing.

      Lol, now I’m thinking about what decisions brought me here. I’m cracking up.

      • Edenist whackjob says:

        “Lol, now I’m thinking about what decisions brought me here. I’m cracking up.”

        What are you coming up with?

        Also, I’m on Phenibut right now. I notice that my verbal intelligence seems to be a bit impaired. Normally I can just write off a sentence on the first try, now I find myself re-typing a bit.

      • Aeoli Pera says:

        Sounds like choice paralysis more than anything.

      • Edenist whackjob says:

        “Sounds like choice paralysis more than anything.”

        Yeah. I usually have a mechanism saying “yes, this is the correct choice of words”. Now it seems somewhat muddled. Could be navel-gazing, though.

        Ugh, that didn’t come out right :p

      • Edenist whackjob says:

        “Goodnight and God bless.”

        Thanks, bro. It’s actually 4am here so maybe I should do the same.

  4. Edenist whackjob says:

    “Also he is the best example of “massive lateral thinking” that I’ve ever seen :-P”

    Care to expand that a bit? I’m flattered :)

  5. Edenist whackjob says:

    Black mating patterns have become the norm in the West.

    Romantic love is dead.

    Compare movies of today to 20 years ago.

    Where are the people in love?

    People are hooking up, not kissing passionately.

    Look at people in general. People are not falling madly in love, writing poems. Such things are seen as silly. People just wanna fuck :)

    This is an example of one those fuzzy EW-patterns that I’ve been talking about. I see it, yet I can’t fully believe it. How would you use your formal logic to prove it, Aeoli? (Not a dick, I desperately want to know).

    • Edenist whackjob says:

      The “beta” concept of love (idealizing the woman, writing her poems, having oneitis, stuff like that) is actually the highest one!

      The “alpha” concept (degrading the woman, treating her like a stuffed toy, Go Fuck Then Other Girls, stuff like that) is actually r-selected baboonery!

      Damn, wish I had realized that before letting PUA corrupt over the last 10 years. The damage is done now, though. Hard to let something go that brings you cheap pussy.

    • Edenist whackjob says:

      How did I arrive at this chain of thought? I heard a sappy pop song on the radio.

      Then, I typed the song lyrics into Google, and it suggested the correct ones. Then I got the AI thought below.

  6. Edenist whackjob says:

    That experience when you type something mistyped into google and it suggests the correct version? Imagine if you did what with a fully formed argument, and it spat back something equally well-formed? That’s what AI is going to be like. We are all going to have a personal teddybear AI in the cloud who helps us with our schemes. Imagine what Koanic would be like with someone of massive computational power, with access to all the world’s information, ready at his beck and call?

    It actually wouldn’t change the relative power-levels that much, because everyone would have the tech. The rising tide, and all that. It would just mean that the world got more powerful as a whole. But Koanic would still be smarter than Joe Random, even if both of them had an AI assistant.

    Actually, scratch that. Koanic would get WAY more powerful in relative terms also. Reason: growth isn’t linear. Joe Random keeps using his AI-assistant for looking up chicks and curry recipes.

    Now, off to watch that movie with Scarlett Johansen and AIs…

    • Edenist whackjob says:

      “Imagine if you did what with a fully formed argument, and it spat back something equally well-formed? That’s what AI is going to be like. We are all going to have a personal teddybear AI in the cloud who helps us with our schemes. ”

      I have a few friends like this. It’s spooky. The only problem is they don’t wanna help me with my schemes :)

      • Edenist whackjob says:

        Just realized that if I am as smart as I like to believe, I should be out there building that AI.

        Ever since I started wanting pussy, my drives in life have been more mundane, though.

        Heuristic: if you want pussy a lot, you can’t be a genius. For the simple reason that you don’t have a strong enough drive to make it happen.

  7. Edenist whackjob says:

    AH, psychoticism and endogenous personality are actually all aspects of the same thing. Being reality-oriented rather than social-orientented. (I feel really odd saying *I*, with my mental problems, am reality-oriented, but in the abstract sense of being more interested in mental maps than people’s feelz I certainly am).

    AH: Truth – recognizing the vastness of information, seeing the falseness of the boxes that society allows
    Endogenous: Love – being strongly attracted to finding out information, hating falseness
    Psychoticism: Power – having the drive and locomotory/sensorylimbic ooomph to go out there and find the truth, feeling a barrier between oneself and the other when sucking up to social graces

    (Reference: Steve Pavlina’s “Truth, Love and Power” model).

  8. Probability isn’t taken into consideration. Bayes’ Theorem is banned in courtrooms.

    http://www.theguardian.com/law/2011/oct/02/formula-justice-bayes-theorem-miscarriage

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