# How does it make sense to infer the existence of a group from a sequence of events?

Just read an interesting section in The Drunkard's Walk - L. Mlodinow and this section made me think:

[people]... confuse[ing] the probability that a series of events would happen if it were the product of a huge conspiracy with the probability that a huge conspiracy exists if a series of events occurs

My thoughts/questions are:

1. Why is the aforementioned thinking wrong? If there existed some group, wouldn't it be correct to consider the more outrageous coincidences a result of a plan to do something

It makes sense that a group would want a few specific things to happen in order to have any meaning, thus they would actively try to make such specific things happen, and given a group's motivations, you can narrow down what it is they would want to do

1. How does it make sense to infer the existence of a group from a sequence of events? And does the second line of thinking suggest the first is wrong?

A tree moves a bit and a few leaves fall from it, thus a squirrel should exist? If I know it's possible that a squirrel is here because of a tree's location, then I can say it's likely a squirrel shaking a few tree branches

Am I missing something obvious?

• Did you mean "Causal probability" or "Casual probability" – Developer63 Dec 15 '15 at 2:48
• Hahaha definitely the former... or it's a big conspiracy on SE – myTotoro Dec 15 '15 at 16:23
• One question per question please :) – Joseph Weissman Dec 24 '15 at 19:39

The point is that we should use bayesian reasoning to infer a cause from its consequences. The probability that an hypothesis is true given the evidence is not the same as the probability of the evidence given the hypothesis.

For example: the probability that the floor is wet if it has rained is 1 but the probability that it has rained given that the floor is wet is not 1 (because there could be other causes: someone washed his car).

If a serie of events is unlikely, this warrants a specfic hypothesis (for example a conspiracy) only once we analyse all alternative hypothesis and their respective prior probabilities. If a conspiracy is very unlikely, it should weight less than alternative hypothesis even if it explains better the serie. But people tend to stick to one hypothesis only because it would explain the serie.

EDIT: as an example of why unlikely hypothesis should weight less, imagine that the floor is wet in a very dry country. Then the hypothesis that someone washed his car is more plausible. Even if in the absolute the fact that it rained would be a better explanation (the probability that the floor is wet if it rained is higher than the probability that the floor is wet if someone washed his car), the fact that it never rains in this country make it less plausible. Similarly, the fact that a conspiracy is very unlikely for independent reasons makes it a less plausible explanation for a serie of events even if it predicts this serie perfectly. This translate formally in Bayes's theorem with prior probabilities. See https://en.m.wikipedia.org/wiki/Bayes%27_theorem

• Indeed. This is sometimes called confusion of the inverse and is related to the base rate fallacy. – Bumble Dec 15 '15 at 1:40
• This is a very good answer and more or less settles it. Still, I am wondering about the complexities entailed in actual "conspiracy theory" scenarios. The information converging upon the prior probabilities is mediated. A certain "dramatic" value accrues to the "less likely" possibility. (As Hume noted, reports of miracles do "attract" attention and interest.) It seems to me that in the actual social setting of mediated "news" a certain bias tips towards an accumulating, self-confirming consensus around "less likely." This is sociology, not philosophy, but your assumptions may be off... – Nelson Alexander Dec 15 '15 at 3:11
• @NelsonAlexander - Conspiracy theories, as you say, are psychologically attractive. This is for two main reasons: one is that we like to believe that what happens is part of some bigger purpose, not just random s**t; the other is that it feels nice to think we have access to some secret knowledge that others don't have - we are among the circle of the cognoscenti who are in the know. – Bumble Dec 15 '15 at 4:23
• @NelsonAlexander yes this is a complex social and psychological phenomena. I only tried to explain the quote in the question. – Quentin Ruyant Dec 15 '15 at 12:27
• @quen_tin Can you add more clarification to "If a conspiracy is very unlikely, it should weight less than alternative hypothesis even if it explains better the serie." Do you mean satisfying in terms of sounding appealing – myTotoro Dec 15 '15 at 16:26

well the first line of thinking says

"Event A is very unlikely. But if we suppose that there exists an entity Z whose purpose is to make event A happen, then the likelihood of event A happening is higher"

Which is true, given that entity Z actually has the possibility to influence the happening of A or not. Note that this is nothing more than a truism.

"How does it make sense to infer the existence of a group from a sequence of events?"

Well now the question becomes

"Suppose we have a series of events A,B,C,D. All of them unlikely. They all happen though; this is very weird. It can be explained by assuming that there exists and entity Z that is increasing the probability of A,B,C,D of happening"

Now this is one line of thinking. But this "probabilistic approach" fails for several reasons:

First, nobody assures you that the entity Z is "likely" to exists. I mean if for explaining an event that only happens one time in a thousand you claim that there exists and organization whose "probability to exists" is one in a billion, you didn't gain much, did you?

Second, who decides what events needs explaining and what not? This is a delicate point and actually makes most of this kind of arguments fail. Go to your favourite cinema, and look at plaque of a car; let's say it's AB292ZXZ. Amazing isn't it? From all the billions of combinations possible, that is the one that appears right in front of you! Surely can't be just chance, can it? There must exist an entity to explain this very unlikely event!

The point of the last example is that the last event is unlikely if you say "Today I'll go at a random cinema and I'll see the plaque number AB292ZXZ". It's not unlikely if you just look at a random plaque at the cinema and wonder how incredible it is that you observed that one. There is a big difference between a priori prediction and a posteriori explanation.

The conspiracy theories usually try to explain the world a posteriori; they select some events in a purely arbitrary manner and make up imaginative explanations that "connect all the dots" and explain everything. Well this amounts to nothing, as the plaque example shows; you have to make some accurate predictions. At this they usually fail.

To sum up, you could try to explain events by making up secretive organizations that influence our world, but as long as you can't make meaningful predictions about the future it all amounts to nothing.

• Hmmm, that's a very concise answer, though it didn't address everything I had in mind. "you could try to explain events ... but as long as you can't make meaningful predictions about the future it all amounts to nothing" I'm curious what you would say about people claiming the CIA and their regime switching plans? I doubt there were many people that could've predicted which regime the CIA would have targeted next -or you don't believe the CIA had any involvement and those remain purely conjectures – myTotoro Dec 14 '15 at 19:40
• @myTotoro I don't know if the CIA had any involvement but that's beside the point. I was specifically attacking those kind of "probabilistic" arguments. If you can't predict what the CIA will do next but you find hard evidence that something happened in the past, that's good enough. Evidence though needs to be something directly related to the fact, not some a posteriori events that you hand picked and connected to the CIA. – Ant Dec 14 '15 at 19:50
• @myTotoro Of course maybe the CIA really was involved. If you don't have hard evidence of it, you think "maybe happened, maybe not, I don't know". Sometimes one has to guess because the evidence is not present. So you say "I can't prove it happened, but according to my theory this is what's going to happen next" and it really happens, then you can be more confident that your theory is correct. Making correct predictions is the best test for a theory. As long as those really are predictions and not after-the-fact explanations – Ant Dec 14 '15 at 19:53
• Why do people assume the "visible" CIA would be the organization behind regime change? How do you know the "visible" CIA isn't simply a front? How do you know who is giving orders to the visible+invisible CIA+other covert ops organizations? None of us really do. On occasion, insiders write books or otherwise share information, that, if true, would be the closest us mere mortals will get, though with a high probability of having it contain a level of disinformation. One example worth considering is L. Fletcher Prouty's "The Secret Team", preferably the uncensored edition. – Developer63 Dec 14 '15 at 23:03
• @Developer63 I fail to see how that is relevant to the discussion – Ant Dec 14 '15 at 23:21

While @quen_tin has give a fully adequate answer I would like to address the question, since I happen to be a friendly interlocutor with some very intelligent conspiracy theorists.

First, you have "evidence" (E) of some sort, which reason then attempts to place within a causal or rational construct. This might entail predicting consequences or "effects" of (E) and/or retrodicting causes of (E). Both are problematic, but we have a tendency to think prediction is validating and retrodiction is obvious.

In fact, any evidential event (E) can be "overdetermined." There may be many "efficient" or direct causes and an almost infinite number of events that might be causally necessary. It is like the "butterfly effect" in reverse.

So, even in physical systems, "causality" is hardly as straightforward as we imagine. Now enters the idea of "conspiracy." This means human intentionality, causal efficacy, and social organization. For any event (E) there may be any number of people who might have wanted it... and given this overdetermination, one can readily map out the interested "reasons" if not the direct efficacious causes.

One cannot "disprove" a conspiracy theory or any other source of possible causation. One can only rank the likelihood. Conspiracy theory tend to be "unphilosophical" because it assumes two incommensurable levels of human reason, a dualism. First, there are people capable of organizing with superior predictive and causal capacities... and, second,a majority of people who cannot, while still entering into the assumptions of the former.

I would appeal to science as the contrary case. It is very difficult to imagine "secret science" since part of the efficacy of science is its "public" nature, the appeal to transparency and repeatable "experiments" theoretically open to "common sense." Conspiracy theory tends to conflate scientific efficacy with esoteric knowledge.

However, conspiracy theory has a point. More and more of what might have been effects of "nature" of now products of human intentions. And such intentions are always related to "interests" and motives. Yet a "scientific" explanation cannot rest upon ascription of motives. That is theology. The causal connection between malevolent minority "interests" and global "effects" is usually far too remote and fanciful.

The author's statement sounds catchy, but in practice will be of very limited use in dealing with covert groups. Many "Conspiracy Theories" involve covert group(s) who are seen as secretly manipulating events to their advantage, while deceiving casual observers. Bayesian approaches will be of very limited use in analyzing events that potentially involve organizations whose very purpose (and core competencies) involve secrecy and deception, including the activities of false flag events, planting dead-end "clues", and manipulating the public media. Simply sorting out "actual facts" vs. "asserted facts" becomes extremely difficult.

• Solid response, very pragmatic - going to read that story now – myTotoro Dec 15 '15 at 16:21