EDIT: Illauna has explained that the Foreign Relations listed modifiers show how your relations are changing over time, not what your current relations are. So in other words If they sum to -2 then that adjustment will be applied to your current relations with the faction. Fair enough, I can see how that makes sense. However, I still think there's something weird going on. If I load the save game below and keep hitting End Turn, this is what I get:
Season 86: meet Capitar, Neutral. Modifiers are +2. Season 87: meet Magnar, neutral. Capitar is now Warm towards me, although their modifiers have now changed to -2. Magnar modifiers are +1.
Modifiers now don't change till Season 100, i.e. it's +1 each season for Magnar, -2 each season for Capitar. Magnar goes to Warm after one turn, fair enough. Capitar went to Warm after one season of +2. Their modifiers immediately change to -2, so in other words in one season they should be back where they started and turning negative. However it takes them nine seasons of -2 till they go back to Neutral. I don't understand why this is.
Modifiers change on season 100. Capitar goes to -6, Magnar goes to -2. Magnar has had 12 seasons of +1, so it should take six seasons of -2 to get back to where we started. In fact they don't go Neutral for nine turns, when the cumulative modifier should be -9. Interestingly this is the same number of turns it took Capitar to go to Neutral from Warm, even though in theory Capitar had twice as bad modifiers each turn (-2 as opposed to -1).
With modifiers having been -2 and modifiers now showing -6 since season 100, I'm expecting things to go bad with Capitar pretty quickly. However they don't actually change to Cool till Season 107. Interestingly this is 10 seasons after their last change (from Warm to Neutral). So what seems to be happening is that if relations change for any reason, they will not change again for nine or ten seasons after that. This means that the "first impression" an AI has of you is quite important, as if it's positive then they're unlikely to go to war with you for twenty seasons. On the other hand if their initial impression of you is negative they may go to war with you almost immediately.
Is this working as designed? I guess it makes sense that you don't want relations changing too fast. It is a bit weird though that even if modifiers immediately change direction so you "get back where you started" you don't go back to your original relations. It is also a bit weird that it doesn't seem to make a great deal of difference how much an AI likes or dislikes you; if they dislike you by -2 or -6, relations will probably get one step worse every ten turns.
Original post follows:
I may be the only person who actually looks at the Foreign Relations screen. However! I like it. It used to tell me why enemy factions liked me or didn't like me. Since 1.5, this is no longer true. I think the most likely reason for this is that the screen does not show all the new influence modifiers. There are other possibilities (like the Foreign Relations screen is a random number generator, or there are massive bugs in the new diplomacy AI). But at the moment I suspect that the Foreign Relations screen does not show the new modifiers.
Examples (all taken from a game started in the 1.5 beta as the Dead and using Primal Savage's AI mod, all AIs were Ridiculous). In each case, I've summed the reported influences and compared to the reported feelings that faction has for me:
Capitar is -2 and Warm?
https://www.dropbox.com/s/o806pndae3zx0em/2013-11-27_00002.jpg
Magnar is -4 and Friendly???
https://www.dropbox.com/s/ba5plu58o8vloyb/2013-11-27_00003.jpg
Magnar is -4 and Neutral?
https://www.dropbox.com/s/18cotc7fhu8olbm/2013-11-27_00005.jpg
Capitar is -6 and Neutral???
https://www.dropbox.com/s/mvmpzck3kk2rtk0/2013-11-27_00008.jpg?m=
A save game: (I've noticed before that Foreign Relations influence modifiers are not visible when you load a save game, however in each case you can hit End Turn before checking the Foreign Relations screen. In this save game you can keep hitting End Turn for a while before significant events intervene. I don't understand the reported diplomatic relations.)
Season 99:
https://www.dropbox.com/s/zrnju8zxgsc07yu/106.EleSav
This is one of the reasons I've asked for a bug fix only patch next. There are also the problems with Beastlord and multiple strategic units occupying the same tile.
On diplomacy, I also had Yithril ask for a Trade Treaty with me one turn and then Declare War on me the next turn; I've also had relations (as reported by the Foreign Relations screen) go from +2 with Magnar in Season 101 to -4 in Season 102, which seems a pretty dramatic swing. It would be great if this could be sorted out.