Different civilizations obviously have different priorities. For example, Gandhi always seems to rush nuke technology and the Mongols will most likely start invading and spread like mad. Are these variables public knowledge? Can you tell by who you are playing what strategy they will adopt during the game?
While searching for why Ghandi likes nukes I came upon the chart I had in mind when I was asking the question. (Click to embiggen)
How to read the table
The listed AI values represent how likely an AI leader is to: - decide upon a way to win - react to what you and the other AIs do - react to wars, wonders being built, city-states etc. - build units, buildings, wonders and what type
The higher the value, the more likely the AI will act according to that strategy. For example, Alexander has a very high score in pursuing a diplomatic victory. He might not take that route, but its very likely. Oda Nobunaga has a very low "Warmonger hate" score. He is very unlikely to hate you if you're a warmonger.
There's still a die roll involved (and other factors like distance from your civ etc.) but these tables should give you a very solid base on which you can plan your game so it affects diplomacy in the way you want it to.
Exact columns mean the following:
Victory: chance of getting the "they think we try to win in a similar fashion" diplomatic penalty
Wonder: chance of getting the "they covet wonders we built" diplomatic penalty
Minor civ: chance of getting the "we compete for same city-states'" diplomatic penalty Boldness: unknown
Diplobalance: unknown, possibly chance for getting diplomatic penalties for attacking or denouncing a nation you have declarations of friendship with.
Warmongerhate: chance of diplomatic penalties for wiping out AIs, city-states and starting wars
Denouncewillingness: chance of denouncement, based also on number of active penalties
DoFwillingness: chance of wanting declarations of friendship, based also on active bonuses
Loyalty: chance of them backstabbing someone (war or denouncement)
Neediness: how likely they are go ask for resources/gold with DoF active
Forgiveness: chance of the AI forgiving old grudges (diplomatic penalties)
Chattiness: how likely they open up the screen and comment.
Offense / defense / city-defense: how likely they are to invest into offensive/defensive units or city defenses (walls, castles, military bases).
Military training: chance of building Barracks, Armories, Stables etc.
Recon / ranged / mobile / naval / navalrecon / air: Chance to build certain unit types
Navalgrowth / navaltileimprovement / waterconnection Chance to build lighthouses, seaports, fishing boats, harbors
Expansion, Growth, Tile improvement, Infrastructure: how likely they are to build settlers, workers, make tile improvements, roads
Production, science, gold, culture: chance of building production, science, gold, culture buildings and focus on working those tiles
Happiness: chance of building happiness buildings
GP, Wonders: first unkown, could be chance of building gardens or employing specialists, the other one is for chance of building wonders
Religion: unused (leftover from CIV4), currently affecting chance of going piety branch (positive) and going space victory (negative)
Diplomacy, Spaceship: how likely they are to go for UN or Science victory
Nuke: how likely they are to build Manhattan project and to build & use nukes.
Major civ approach
Neutral / friendly / guarded / hostile / afraid / war: How likely they are to decide upon having one of the stated attitudes, considering all other modifiers already in place
Deceptive: how likely their stated attitude does not reflect their real attitude. This is exactly the same model as was used in CIV4 (can declare at friendly, pleased, cautious) but otherwise does not affect current diplomacy (an AI that can declare war at Friendly and is thus deceptive, will still give you 300 gold for a luxury resource).
ignore / friendly / protective / conquest: how likely the AIs not to care / invest into (and do quests) / defend (civ X declares protection over CS Y) / conquer a city state.
This originated as a bug. In the early civ games, Ghandi was entirely peaceful, but once he adopted a peaceful government style like Democracy, something in the code looped and made his aggression go from 0 to 10, right about the time when nukes become available. The result is that Ghandi would suddenly become hyper-aggressive and build the most powerful army (read: Nukes) available. This rating in the newer games is deliberate as an in-joke to reference the original bug.