Indeed, but this engine doesn't exist, and in 15+ years of weaponised adtech, noone's been sufficiently economically incentivised to make it. Telling, no?

You're underestimating how hard it would be to build such an engine. Google and Facebook have sunk $billions into their knowledge graphs so far, and not made much of a dent.

Maybe. The current heuristic is "he has bought X so show him an ad for X", but would it be so difficult to flip that to "he has bought X so show him the next thing on the list of interests we know he has" or even just "anything but X". I strongly suspect noone is doing this because there is no point, they get paid the same regardless.

That's not the current heuristic; it's not nearly that simple.

Think about how you know if someone is interested in something. What does it mean to be interested? How does that translate into a sale?

A person just bought a vacuum cleaner. Does that mean they are interested in vacuum cleaners? Are vacuum cleaners things that people get interested in? Do people who are interested in vacuum cleaners buy more than people who are not interested in vacuum cleaners?

To us these answers are so obvious that it's humorous. To a computer, not so much.

There are many millions of interests, opinions, and things to buy--so count the combinations. We understand it all intuitively because we are adult humans with decades of experience in this society.

This is why search and ad companies hire so many AI researchers.

EDIT: to understand the financial incentives, see my other reply to you. In a PPC ecosystem it is better to match too greedily than to risk missing a customer ready to buy.

Amazon already does this. It is called "People who purchased this item also purchased this item"

That's the intuition, but I wonder if there isn't a spike in near-term repurchase behavior that the algorithms are correctly exploiting?

Ex: I bought a vacuum, but I'm unhappy with it. I bought a pool or oil filter, but it was the wrong one. I bought an X, but it was defective. I bought an 8-ct of paper towels because I run a cleaning service or property management company and use a lot of paper towels. I bought a pair of jeans and they're the wrong size or I bought a pair of jeans and they're exactly the right size and now I want to order 3 more pair so I can have the ones I like.

Years ago, we built a conditional offer engine and the humans operating it kept complaining that it was "broken" because it was suggesting non-sensical combinations. In split-run, those non-sensical combinations were clear winners, even if the humans couldn't get comfortable with them.

In the cases you provide, though, it seems to me (and I am certainly no expert) that you wouldn't need to advertise the same item again. If I bought a vacuum that I'm unhappy with, showing me another ad for it (which is what Amazon does) is the wrong thing to do. Not only will I not buy the same machine again, but I will google and research the products- I will ignore ads unless they are offering me a discount on the one I decide on. Likewise for wrong-sized jeans or buying three more pair.

Acxiom has done this in a more invasive way for decades: figure out women's menstrual cycle and then mail them ads when they will be most likely to make a purchase according to prior research.