There was recently a celebrated spat between Cathy Newman, one of the main presenters of Channel 4 News in the UK, and Jordan Peterson, a well-known academic and clinical psychologist, on the causes of the gender pay gap. You can listen to it on YouTube, where it has been viewed over 9 million times. Peterson says that "statistics show" that only x% of the gender pay gap is due to prejudice against women. The exact value of x is not relevant to my question.
I recently read a discussion about whether human intelligence is inherited or acquired, with the conclusion that it's 50% nature and 50% nurture.
What would it mean, if anything, to say "The taste of a cake is 10% due to the proportion of flour to butter and 20% due to the freshness of the eggs."
My question is When is it sensible to assign percentages to the causes of some phenomenon? What kinds of statistical or scientific model are being assumed and what kinds of evidence could be adduced that such a model is appropriate? This is a big topic, so I would welcome pointers to clearly written articles on the subject, and also pointers to relevant books.