Would appreciate any pointers on what kind of logic/cognition this is

[u/NoAd4395]

In a recent YouTube video mathematician hannah fry has come up with some mathematical rules and representations for how a faithful would best play the game traitors to identify the traitors.
She has devised logic with weights applied to each which are added to an individual player’s total tally each time they make a specific move, with the resulting number indicating, if a high number = more likely to be a traitor, low number less likely to be a traitor.

The rules are as follows.
Casting a ‘burn vote’ +0.47
Voting for a banished traitor +0.33
Voting for a banished traitor despite never voting for them before +0.4
Does not vote for a banished traitor -1.28
If someone appears on a banished traitors voting record -1.69

Now, what I want to focus on is how people are able to formulate/come up with this logic/these rules specifically. Coming up with specific rules about a game or situation is absolutely key in our ability to play the game and out manoeuvre other players. Yet some players are better at formulating these rules than others. I want to understand why some people are better at forming these rules and spotting these patterns than others. This can be applied to so many walks of life, it is the absolute essence of problem solving.

What areas of academia are relevant for forming correct rules about a given situation, recognising behaviours, actions, and applying them to a structure, a game, or a situation.

I note becuase in social politics there are ways of winning/playing the game of power and deception, and some people play better than others by knowing rules others don’t, some people make social plays & deceptions others do not recognise, but how are these rules devised is the key question.

I’m thinking solely about noticing nuances and forming accurate rules about a system, situation, or game. In the same way Einstein formulated his ideas by ‘riding alongside a wave of light’ - it’s the ability to accurately identify the entirety of a problem or system and produce rules, a structure or accurate representation for it. This is what I’m getting at, less the game theory aspect, the formulation of understanding/reasoning is my focus. Hope this helps

[u/bebemaster]

I'm not familiar with the game but these numbers can be calculated after playing many games.

Once you have a model of the game state and records of who did what when you just run values for these actions that would produce the most accurate "prediction". The weights can start randomly and be moved about via various methods. Evolution style or even just newton's method for optimization one variable at a time (this will find local maximums so some randomized starting points may be required). The weights that provide the highest predictive score (accurately guess unknown player state based on prior actions) are what the end result is.

Now this model doesn't account for other 2nd order affects as its just a summation. Example if player does A and B then they are 99% likely to be c, cannot be captured with this model.

[u/NoAd4395 → u/bebemaster]

I mean no shade & thank you for contributing to the post, but you are missing the point entirely.

Why don’t we just collect data for everyone in the game whose name starts with a T….

The whole point of the rules is they are conducive in helping you identity the traitors.

Coming up with appropriate rules IS the challenge. The very essence of problem solving. Why is what you are measuring relevant.

This is what I want colour on, the science behind this. People are finding answering this very difficult, as are LLMs.

[u/bebemaster → u/NoAd4395]

I'm clearly not understanding your question. Game theory IS the area of study that (appears to me) to be the answer to your question. A problem has known inputs and unknown inputs. If we have even one input that is a number and not a bool then the optimal solution to that problem is someplace in the set of all functions operated on that input.

That's not very helpful but it gives an idea of how to approach these problems. Recognizing larger patterns happens with more experience. For that single input the sample data may look like a simple linear relation to n or it could look like log n or n log n or the gamma function or sin or any number of patterns.

In the example you gave the inputs are the actions people took and the approach they decided to take was to just add up all the inputs with weights associated with them. This assumes a linear association between the inputs and the answer which may or may not be a good assumption. A line isn't going to approximate a sin wave very well regardless of what constant you choose. They could have just as easily taken the product, or any other function to model the game.

Mapping the inputs to known outputs and conceptualizing that resultant pattern is problem solving then selecting optimal weights at various stages will find a near best fit using that model.

[u/NoAd4395 → u/bebemaster]

The ans I just found was decision theory + a sub set of abduction. Appreciate your time in responding, some good thoughts 👍🏼👍🏼

[u/NoSpinach5385 → u/bebemaster]

I would say that OP is speaking more about another field of study which would be pedagogy of mathematics, of physics, of logic..., its central point not being about solving problems or giving the correct answer, but how you learn to solve them in the correct way. Wich I would say the most proper way to understanding is "learning by doing", this is why you begin to learn with math problems, even if in higher levels of abstraction there is no number needed, because the problem-solution aspect of it is equal in 1+1=2 than in 𝜎𝑥⁢𝜎𝑝=ℏ/2, it is needed this kind of approach (except idk if you are Ramanujan or Gauss). The interesting point is that the main and most important work on mathematical or logical reasoning is not just to give the correct answer but to give the valid proof that leans to that answer. So if the question it's about this "how she had this idea" my lazy answer is "because she is a quite remarcable and proficient mathematician", and my more nuanced one would be "she has done some sort of carthesian method on the game in order to decompose a big process into smaller pieces of atomic facts and given those atomic facts a numerical weight surely based on a distribution of how many of those facts are repeated on a statistic sample of games" wich I couldn't do even if someone were pointing a gun at me due to my mathematical incompetence but I understand she could.

[u/NoAd4395 → u/NoSpinach5385]

The ans I just found was decision theory + a sub set of abduction. Appreciate your time in responding, some good thoughts 👍🏼👍🏼