Given two people, predict whether they will get along.
The matchmaker problem must be ridiculously well studied with billions of examples available and thousands of years of human history, yet it seems very far from a rigorous science with very low predictive ability by most people.
Is there some taboo which prevents study in this field?
Perhaps the problem is difficult. Perhaps changes in society ("technology") make past examples poor predictors of the future. The invention of the dishwasher allows two people who both hate doing dishes get along where previously they could not. Perhaps the outcome of whether two people get along most depends on events uncertain at the time of prediction (e.g., employment). Perhaps, like chaos theory and weather, the outcome depends on very little things impossible to measure at sufficient precision at the time of prediction.
Unfortunately, one instance is somewhat well studied: Stockholm syndrome causes people to get along.
Assuming the problem can be solved in general with high accuracy, one can take the next step to a sinister application: programming someone from birth (probably parents programming a child), to be able to get along with someone else. (This next step requires knowing what external actions and experiences influence the compatibility matrix.) It's a modern take on an arranged marriage, where you have the illusion of free will even though you don't.
Maybe encourage study in the field by legalizing gambling on it.
Can a computer predict better?