I posted this question on LessWrong.com where it was suggested i come here. I also posted there about an open source decision making web site I am working on called WikiLogic. The site has a 2 minute explanatory animation if you are interested. I wont repeat myself but the tl;dr is that it will follow the Wikipedia model of allowing everyone to collaborate on a giant connected database of arguments where previously established claims can be used as supporting evidence for new claims.
The raw deduction element of it works fine and would be great in a perfect world where such a thing as absolute truths existed, however in reality we normally have to deal with claims that are just the most probable. My program allows opposing claims to be connected and then evidence to be gathered for each. The evidence will create a probability of it being correct and which ever is highest, gets marked as best answer. Principles such as Occams Razor are applied automatically as long list of claims used as evidence will be less likely as each claim will have its own likelihood which will dilute its strength.
However, my only qualification in this area is my passion and I am hitting a wall with some basic questions. I am not sure if this is the correct place to get help with these. If not, please direct me somewhere else and I will remove the post.
The arbitrarily chosen example claim I am working with is whether “Alexander the Great existed”. This has the useful properties of 1: an expected outcome (that he existed - although, perhaps my problem is that this is not the case!) and 2: it relies heavily on probability as there is little solid evidence.
One popular claim is that coins were minted with his face on them. I want to use Bayes to find how likely a face appearing on a coin is for someone who existed. As I understand it, there should be 4 combinations:
Existed; Had a coin minted Existed; Did not have a coin minted No Existed; Had a coin minted No Existed; Did not have a coin minted
The first issue is that there are infinite people who never existed and did not have a coin made. If I narrow it to historic figures who turned out not to exist and did not have a coin made it becomes possible but also becomes subjective as to whether someone actually thought they existed. For example, did people believe the Minotaur existed?
Perhaps I should choose another filter instead of historic figure, like humans that existed. But picking and choosing the category is again so subjective. Someone may also argue that woman inequality back then was so great that the data should only look at men, as a woman’s chance of being portrayed on a coin was skewed in a way that isn’t applicable to men.
I hope i have successfully communicated the problem i am grappling with and what i want to use it for. If not, please ask for clarifications. A friend in academia suggested that this touches on a problem with Bayes priors that has not been settled. If that is the case, is there any suggested resources for a novice with limited free time, to start to explore the issue?