I don't think it's as complicated as having the AI calculating the benefit of the alliance or the MPP for themselves. I think alliance being more expensive than MPP is a game design decision made by the programmers.
Looking at it from a game mechanic point of view, alliance and MPP both accomplish the same task -- getting some military help. MPP has the drawback that it could get you into unwanted wars, while both share the drawback that they lock you into 20 turns of war. Comparing the two, alliance is clearly the better choice, therefore it must be made more expensive. It's a classic strategic game choice of price vs. risk. Pay less, and you get a weapon that could back-fire on you. Want a top-of-the-line weapon? Well, it'll cost you an arm and a leg
According to this line of thinking, choice of alliance vs. MPP is about risk management. When it's down to just 3 civs, there is no risk, so MPP is the choice. When risk can be easily managed, like when you're strong enough that you don't care if rest of the world declare on you, then MPP is the better choice. There are also times when you have nothing to lose, like the "if I can't win this war then it's game over in 20 turns" kind of situations. Well then, risk be damned. Its time for International MPP Day!
In the other more "normal" situations, it's a matter of personal experience. I have had the pleasure of watching a MPP blowing up in my face
. The game went from ho-hum to O.M.G. to W.T.F. in a few short turns. That's why I swear off MPP's, and I think if people play long enough, eventually everybody will get to share the MPP Experience, like skisphereo just did.