I've played this game a lot, but there's one aspect I've never understood, and that's winning over minor nations. In a recent game, there was a country for which:
I had been their favorite trading partner since turn 1,
their affection for me rating was light green,
we had a pact,
I owned all the resource tiles in the country,
and I was buying from them every turn.
And then, boom. They accept someone else's colony status, and I'm boycotted. HOW CAN THAT POSSIBLY HAPPEN? There had been no lost-favorite-status message, either.

Later in the same game, another minor nation: pact, dark green, favorite trader, owned most of their resources, buying from them, *and* I was at war with their #2 trading partner and had that country blockaded, *and* I was giving this minor country a $1000 locked grant each turn. But turn after turn, they declined my colony invitation. There was nothing I could do to seal the deal.

Can anybody shed some light on this for me?

Actually the grants seem not to be as effective as the % of trade. But I never understood this either. Happened to me quite often as well. I even made a test: I cheated too get more money, I put 5k grant every turn, 75% trade and still some of the minor nations did NOT join, WTF? Seems to be a bit hard-coded, I assume. I even build up my military and economy to levels which were unsustainable too see if this does matter, nope didn´t matter.

Yes, the grants don't seem to work, but I listed that to show I was using every means at my disposal, and still losing out. Since you reminded me, I also had granted these examples (I think) 50 and 100% trade subsidies, respectively.

Maybe my mistake for not making it clear enough ;)

The money I pushed into them was unsustainable at every level! I had to give me a few times money to achieve this and I still lost those races. And nowhere the AI could have spent more than me. So there seems to be something hardcoded into the game.....I didn't bother to check if it is always the same or whatsoever....Since then I just declare war on them on turn one ;) Meaning I can always just conquer them WITHOUT penalty later-on in the game ;)

Sometimes a high subsidy rate gets them back in the fold. But I also have watched a minor slip slide away while I flail trying to keep them in the fold. Ingrats. LOL. It is frustrating.

This JUST happened to me!!!! (Haven't read the replies but I came here to ask this very same question!!!)

I was the most favored trading nation from turn 1, bought everything, had turned them green (light green) in the relations tab, asked if they would join, they turned me down. So I started a monthly grant, and after the first months grant I get a message that they've joined this other major power "without a fight". No warnings, no nothing. WTF???

Hardcoded.... *sigh*

Yeah, I'm now 100% convinced this game cheats, even on normal setting. This and the fact that in six games in a row now I've been declared war on almost inevitably around the early to mid-1830's and am hit with navies and armies the size of the current American military industrial complex and yet I"M ALWAYS NUMBER ONE IN INDUSTRY. I'm number one in industry yet can't crank out the numbers these guys are cranking out. No way. No way.

I know the manual says that at normal there are no advantages either way, but there's no way this happens EVERY TIME. No way. There is simply no way that they could have the massive navies AND armies that they do, and sustain them playing by the same rules as me when I've always got the best industry going.. After the sixth game, and before I started the seventh, I played a "for grins" game where I just dedicated myself to building a Navy (every AI would have fleets in every sea zone around my country, and let's face it, every province or nearly every province in the game are coastal, so you have to cover lots of sea zones). Starting from turn 1, I focused and built up a Navy that would've made the admirals in the current Pentagon proud. I have multiple ship fleets patrolling in every sea zone close to me with a sizable backup in dock for escort and emergency defense.

And this time I was close to matching them, but, when I failed to stop an invasion before it occurred, I would lose the ensuing land battle because it was simply IMPOSSIBLE to sustain and build such a Navy AND a large defense force. Yet these guys had such Navies AND every time one would slip through my naval defense they would ALSO HAVE huge armies that wiped out my meager minutemen, regular or two, and artillery.

They may have intended for it to be even, but I'd bet my last dollar that when they wrote the formulas for simulating the things the human player does, they made an error (or they flat out lied about it being even on normal) that resulted in their simulation not being exactly even. Because there's no way possible I'm seeing what I'm seeing SIX STRAIGHT TIMES if they're playing by the same rules.

So frustrating. It's my number one complaint about Civ games, hell, about ALL games. Developers take the easy and lazy way out to improve AI. Rather than take the time and effort to come up with algorithms for good AI, they simply give the AI numbers advantages. It would be like me playing chess against someone with three queens, six rooks, and 8 bishops. Sure, it's more of a challenge, but it's also not FUN.

I've really liked this game (obviously, I started playing very recently and am now on my SEVENTH straight game.) and won't give up on it because I'm sure it's beatable despite the cheating (just like the Civ games are) but man I wish developers would put more time and effort into making better AI's rather than taking the easy way out.

OK, first of, you get a warning BEFORE they can invade, this gives you EXACTLY one turn time to move your land army in there.

Best defense are the heavy guns (only) with like 2 mobile backups as they can move AND shoot. The AI WILL retreat quite early ;) The trick is actually don't kill them, just damage them enough first, a 10 percent unit will only do 10 % of damage ;) And always have a general with them: If your unit shows red down to 60% and yellow till 40% (so 20% routed) you will only do 40% damage, a general will improve it again. A general will also slow down your losses! SO more stars a general got, so better.

Blocking their home port, will make them move their fleets back (even if you just use 1 single ship (most of the time)
Get your army trained (So let them attack) The winner will get more exp. then the looser. For winning you don't need to kill all units.

Upgrade your forts! If you have a 2 cannon fort, it will only get downgraded if the enemy (or yourself, if YOU attack) kills BOTH cannons. So if you have to decide, get your own cannon killed or the fort one, choose the fort one. ZOC (Zone of control) is important as well, works similar to civ. so block riders from your cannons, they are deadly for them! But just one cheap unit in front, will prevent them from using melee attack (or in case of the fort, the wall ;)

Navy: It is gaining exp. as well, but not so worthwhile. Defend your home port and harass the enemy. Most of the time with a smaller group of land units, you can defend your nation, so your navy is free to go after their ships by blockade their home port, just keep refreshing damaged units. Mostly forget about the fast attack ships, go for the big guns only (again) ;) The fast ships/raiders are IMHO not worthwhile.

What the game IS simulating is the food consumption for the armies, take the food away and you can decimate the enemy army (might take a few turns though).

Just a few tips ;)

I made a very detailed post about this here: http://www.gog.com/forum/imperialism_series/everything_you_ever_wanted_to_know_about_courting_minor_nations_and_more_imp1_and_imp2

Later in the game the AI will put everything into the remaining minors, and if you don't do the same, they will snatch em up. But I recommend not to waste 10k each turn on such a race, it is much cheaper to do war. But if you are ahead with a minor and you see the AI making inroads (click on the minor to see its status with the others), then you need to step up (meaning 10k), because once they catch up, the 10k and 100% subsidy race will go on forever and they will join nobody.

Also LOL @Oldfatguy...7 games? I played this game like 10 years and can still improve. After 7 games you should not be whining about the AI already. I don't worry about the cheats, if they ain't there, the game would be way too easy and suck, a problem Warlock - Master of the Arcane has for example,where "Impossible" means impossible to lose. If you don't want the AI to cheat play some lower difficulty, like normal or whatever. Oh I see now, this is on normal, sorry dude, you are just not very good yet, it does not mean the AI cheats. Repelling the first attacks is no problem even on nigh-on-impossible.
I worry more about the terrible major power diplomacy in Imp1, once at war, always at war, and even if you get peace, the declare war again next round, makes for a dull game. (they improved this in Imp2 at least)

Don't be so harsh, the force is strong with this young one. :)

When nation A declares war on minor nation X, then if X can ask for help from nation B. In return it becomes its colony immediately. Maybe that's what happened?

Also if you and another great power are in dark green relations with a minor nations, almost always the AI will win out. Also they will not join you if they have another great power as dark green. Try to get them to dark green and to join before any other power has dark green with them.

Once dark green, I always do a one time 10,000 grant to sweeten the deal

The AI definitely isn't playing by the same rules. I think we've all played games where you reduce them to just their capital, completely wipe out their merchant fleet, yet they're STILL able to maintain a 30+ unit army.