There is a world not too different from our own, at a technology level not too different from our own, with a population similar to our own. Recently, scientists have discovered (by chance in an unrelated study) that there is a legitimate measurable brain wave pattern that matches between two people that can be considered "soul mates." (Assume the study is scientifically rigorous.)
The study found that these "pairs" of individuals share patterns of thought when separated by distance and when not interacting with one another. Similar to quantum entanglement, they think similar thoughts at similar times, even going to much as to share emotions in the vast majority of cases.
Naturally, as a result of the study, nearly everyone on the planet wants to find their match.
The scientists are busy working on commercializing a solution, but Joe is an enterprising young man who wants to beat them to it. He thinks that there's some way he can exploit this "mental link" if you will to pass messages to his other half. (Her name is Jane, but he doesn't know that yet.)
Some details about the system:
There is exactly one "match" per person. Ignore the situations where one of the matches is eliminated (death, other reasons)
Basic thoughts and motivations are shared in real time. As a result, when fully separated and outside major external influences, a pair of individuals that are "matched" will say similar things, act similarly, eat and sleep around the same time, etc.
The problem arises when two people know about the rule and attempt to "pass" messages to each other by thinking particular thoughts. If Joe thinks "Hello" then Jane also thinks "Hello", so simple things like this are passed easily. (It's important to realize that Joe doesn't cause Jane to think the same things, or vice versa, they just probabilistically happen to think the same things around the same time. Call it just a feature of this particular universe)
Jane and Joe are simultaneously thinking about how they would like to communicate with each other, but to their disappointment, all the "easy" ways they can think of don't work. If Joe and Jane think: "My address is: XXX Main Street," or even something as simple as: "I live in the city called: XXXXX", by the nature of the system, they each think the answer of that question that applies to them, so they have no insight into what the other is thinking.
Jane and Joe do have free will, but in this system, I think you'd have to consider it free will as a unit, together, where maybe one entity controls the both of them (and they make the same, or very similar choices.) That's the only way I can think to permit this system to coexist with a concept of "free will."
Is there any way for Joe and Jane to transfer any information about their selves as separate entities, in order for them to sell this process as a way of meeting your "match?"