On a technical level, you're probably right about diamonds. It's probably a legitimate signalling hack in the romantic sense to buy a zirconia and pass it off as a real diamond. This will probably be a short-term play if women start catching on.
I also disagree that a private gesture ever works as well as a public one, if that's the comparison. Public gestures signal commitment to a wider group, therefore increasing the cost of defection. Public commitments are one of the prime examples of costly signalling (as compared to private commitments) out of game theory. Not saying I'm a game theory authority, or that game theory is always right, but this is textbook.
I agree that burning a pile of cash is even better than giving diamonds in terms of signal-quality.
Seems to me that the global human cost is lower if you have middle-men involved. You have a similar signalling cost but humanity overall retains some value by paying the middle-men, whereas the burn-cash strategy leans 100% towards signalling at the cost of value retention.
Edit - potentially lower if you have middle-men involved.
What I meant with that is that diamonds are a bad public gesture, because no one other than your immediate partner will ever be able to evaluate the authenticity of the diamond. If you're going down the diamond route, you might as well do a private gesture because diamonds already can't be easily publicly verified. If you're concerned about being public, then skip the ring entirely and pay for your partner to go on an expensive trip, or donate money to get something named after them. These are gestures that a fraudster would be unable to easily replicate.
> Seems to me that the global human cost is lower if you have middle-men involved.
If your concern is that you don't want the money wasted, then at least donate it to a charity, or give it to a local business. Some of them would even be willing to officially recognize or publicly name something after your partner, which again would be good public signaling because it would be hard to fake.
The investment signaling theory of diamonds is that we've all decided that in order to efficiently signal, we're going to give money to someone we have no relationship with, who isn't providing a useful or unique service, who has a long history of unethical practices (even if they've cleaned up a bit recently), and who employs the majority of their workforce and conducts the majority of their investments outside of our communities.
If society was actually thinking about engagement from a purely rational signaling point-of-view, it wouldn't pick diamonds as the way to signal. But somehow the diamond industry convinced society as a whole that they were an essential part of the process. What I would contend is that I don't think there was anything rational about that advertising campaign; it preyed on people's emotions, their vanity, and their misconceptions about how the market worked. It's a prime example of an industry making a social system less efficient and more harmful than it otherwise would be in its natural state.
My point is that regardless of whether you think of a diamond as an investment, or as an inherently meaningful item, or as game-theory signaling device -- it's really bad at being all of those things. No matter what direction you come at it from, diamonds are a kind of crappy scam.