I must be missing something about the diplomatic proposal gauge. I proposed this exchange to the AI, giving them two technologies in exchange for some adamantium. The gauge is a little positive. Yet they refused. They did so multiple times and another AI refused a very similar exchange with a very similarly positive gauge. Can someone please explain what I'm missing?

The manual (!) states that "[t]he gauge indicates the likelihood that the other empire will accept your deal." So, being slightly positive means that the other empire is very unlikely to accept your offer. But I don't know what factors into the likelihood and what the various thresholds (smiley symbols) really mean. The manual doesn't say. Meanwhile, does "slightly red" mean that there is a chance that the other empire might still accept? Or is the gauge an indication how far your offer is off, i.e. a measure how much you need to improve it? 

I've always assumed that if it's positive, even a little bit, the deal will work out. And I think that for the most part that has proven to be the case. If the behavior was consistent I would be okay with it, it would just be a matter of interpreting the bar correctly. But I am almost 100% certain that I have played multiple games where slightly positive deals were my goal and they were accepted. I will keep my eyes open just to make sure though. Btw I reduced the amount of adamantian I was asking in the above deal a little and they accepted, Same with the other AI that I mentioned above. So in their case, the deals were a little agreeable, but not enough? Idk that just seems weird to me.

I think there is some kind of error, if the bar is on the positive side, they should always accept, the thing is maybe they can't uphold certain deals, like a trade agreement, they can't uphold the influence cost, but that should be reflected before trying the deal, same goes for vital resources they are not wanting to change. The bar should help maintaining positive relationships with AI, if you fill that bar, you get a relationship bonus.

The main issue is that there are some "secret conditions" for some agreements. If they have absolutely 0 want for something you are trading, they will never accept even if it is blue. If they don't get any benefit from a trade agreement (such as if they do not have trade hqs, or do not have them researched), they will never accept.