Many genealogists seem to have faith that a special Genealogy God exists able to tell them whether a relationship they have found or suspect is the truth. Particularly where information is conflicting they look for some omnipotence to tell them what to believe.
T'aint so! What you have instead is freedom. You are the judge of what meets your standards of proof. Others may choose to set themselves up as the judge of your standards. You have the freedom to judge their standards.
You can choose to follow codes of professional practise and seek to meet the "genealogical proof standard." In the US the self-appointed Board for Certification of Genealogists (BCG) has a web site that lists the elements:
- a reasonably exhaustive search;
- complete and accurate source citations;
- analysis and correlation of the collected information;
- resolution of any conflicting evidence; and
- a soundly reasoned, coherently written conclusion.
A rule of thumb some people use is that you need three pieces of evidence to support a relationship, and it should be independent evidence. It might be a child's birth certificate and the father, mother and child together as a family in two censuses. Even if all the paper records align in this way there is still the possibility of deliberate deception. A child fathered by a woman's husband's brother is a situation that might be easily concealed and that not even a DNA study might uncover. In practice its often impossible to know if the evidence is independent.
Unfortunately genealogy has not yet reached the stage of development where people work with a probabilistic assessment of the confidence in a relationship or fact. Such a systematic evaluation would show you can never be 100% certain ... although I can only say that with a high probability! You would set your own standard, be it 90%, 99%, or 99.999% confidence. Even the most enthusiastic adopter of the approach that the best fit in the IGI is good enough might have second thoughts if informed there is only a 40% chance it is correct. That 40% figure is not the result of any study, just chosen for illustration.
In my view a statistical approach is what the genealogical community should be aiming for, but I doubt the BCG powers that be would be comfortable with statistics and Bayes' Theorem.