During the 2017 presidential campaign, I bled myself dry in a lot of debates on Facebook, because Facebook debates are actually of no interest, which I didn't know at the time (interesting video on that here).
I was trying to convince others (or, in the worst cases, to have the last word).
And then I realized that people on the other side were actually trying to do the same, so it wouldn't lead to anything by definition.
As time went by, I thought that maybe the best I could get out of it was to learn things, and there many questions came up.
How do you believe someone? Do I have to take their opinion into account?
Since then I discovered bayesianism. This philosophy formalizes what I believe is the best way to quantify the credit one gives to someone, or to any theory in general.
In this series of articles I will show how formalizing one's knowledge (at least crudely) allows one to have a better apprehension of the world.
Bayes in a nutshell
The youtuber 'Mental Hygiene' presents Bayesianism very well in this video. Without presenting the mathematical details, the basic idea is that we assign a probability to an event or information. For example, I think there is a 0.1% chance that God exists (Bayesians prefer to write as "odds", so 1 that God exists for 999 that he doesn't, rated 1:999, but which I'll round up to 1:1000 - more info on this rating in this article for our english-speaking readers)). This is what is called a bayesian credence . At the very beginning, this probability is necessarily subjective. Nevertheless, expressing phenomena in the form of probabilities :
- makes it easier to communicate with other people
For example, telling someone that there is a 70% chance that I will come to their party is much more explicit than saying that I will 'probably' come. Liv Boeree explains this concept in a ted conference. ''Probably' can mean a 50% chance for some people, and a 90% chance for others. - makes it easier to anticipate all possible outcomes. When I estimate that one of my friends has a 70% chance of coming, it means that - in the idyllic world where I can replay the evening as many times as I want - he won't come on average 3 times out of 10. If I organize a game night where I would like to have a specific number of players, I can take this information into account in the number of invitations I send out. I'll talk about this later when I come back to the work of Nassim Nicholas Taleb, but in many areas - especially in economics - to consider that something that is very unlikely to happen will not happen is a very serious mistake.
The strength of Bayesianism is that once I start thinking in terms of Bayesian credences, I will be able to combine them with each other and update my credences in the presence of new information (according to Bayes' theorem).
Let's take again the example of God who - in my opinion - has 1:1000 chances to exist. If this year a miracle takes place I will be able to update this credence. If in front of a committee of researchers and certified magicians, a man walks on the water claiming to be the new son of God, then perhaps it is a miracle. Of course it could also be when a swindler manages to fool a multitude of scientists (this has already happened, incredible story but true). If I consider it 2:1 that it is a divine phenomenon, then I have to revise my Bayesian credence. Concretely, with this odds notation it's very simple.
credence a priori × probability of the new data = credence a posteriori ⇔ probability that the observed miracle is divine × previous probability that God exists = New probability that God exists ⇔ 2:1 × 1:1000 = 2 : 1000
In this example, I previously believed that there was very little chance God exists. The miracle has 2 chances for one to be divine in my opinion (2 for 1, that's not much in Bayesian terms). Therefore, the credence that God exists doubled for me. It hasn’t evolved much in absolute terms though – 2 :1000 is still low. Bayes' theorem is a simple formula but with very deep and diverse consequences, and they are better detailed in this awesome book of Lê Nguyên Hoang.
Bayesianism: How to use it in real life?
Obviously, it is not possible to reason like this constantly (but it can be good to try to get closer to it). However, Bayesianism allows us to formalize a way of giving credit to a person or to a given argument.
There are many examples of the pitfalls that Bayesianism can avoid (diagnosing rare diseases is difficult, Monty Hall's problem ...). Another good example was provided by Inria when Emmanuel Valls introduced Internet surveillance to "stop terrorists".
Let's say I have a (almost) perfect algorithm that detects 99% of the messages that terrorists send to each other on the Internet (in this example, the terrorists are not smart, so they do not encrypt their message). Also, this algorithm will have 1% false positives. Note that these 99% and 1% are very optimistic values.
According to Wikipedia, there would be 850 S files for jihadism in France, let's round up to 1000. There are also about 60 million French people (a rounded down number).
The algorithm designed by the government on the 60 million French people, will therefore mark 600,000 of them as "terrorists" (1%). It will also mark 990 of the real terrorists as terrorists. So, in the end, 600 990 people will be considered by the algorithm to be terrorists, and therefore it will be very, very difficult to find the right needles in this haystack, of which 1 in a thousand will be a true positive.
This analogy shows that what I believe about a theory necessarily depends on what I believed before. As we'll see in this blog, you have to rely on what you believed before to update your theories.
In conclusion : How can I believe something?
The important message of this post is:
- that we create (consciously or not) theories about the world, and that it's important to quantify the belief we have in our theories, by at least approximate probabilities.
- that one can combine these credences between themselves, and that to do it formally makes it possible not to fall into certain traps.
In the rest of this blog, we will study which credentials to give to which evidence of a theory, and by extension how to believe someone or not.
PS : Many thanks to David Bagatta for the typos!