One thing, I wasn't aware after two years of play is how much influence is worth. I usually guess it is worth some 10 gildars. 

well, boys and girls it is not. 

I just had a war with Magnar. I took three of his cities. he reclaimed one of them and with strong army headed to crush my steamrolling champion. 

plus he launched a small army to claim my other undefended city. 

complete surprise on my side. still I fired up a diplo channel, and tried to bargain for a peace. imagine my disappointment when I saw -1590 near the peace treaty. I had about 100 gildar, and 0.1 income.  no chance to do this in gold. 

BUT I had 150 influence (three quests done by Relias). imagine my surprise when offering 50 turned this value into plus three thousands something. 

I dropped down and got peace for 20 influence. 

so the suggestions is to simple add description contextual to the offer, perceived value of one unit of influence, warg, horse whatever. 

on the side note, I was unable to throw into bargain my unspent research. a nice option would be to declare war on someone else, or giveup a city.