Thank you for that speedy reply.
I have not played tons of games yet, and since I do not have huge quantities of time (family, profession), I prefer to play on smaller maps.
Hence: Size = Small, largest one was Medium (but I did not enjoy that game because I lost track of what I had to do after a couple of days.)
The most difficult difficulty setting I have played on and not gotten wiped out militarily so far was Normal.

Please note that I am NOT saying that influence victories are easy, just that they are easIER compared to the other forms of victory, and correspondingly more difficult for the AI to react to AT THESE DIFFICULTY LEVELS.

In other words:
I would like to play a not-too-difficult difficulty setting (say, somewhere around normal or easier), where the AI is a challenge for me on the military side but not overwhelming, and still be able to have a challenge in the influence department. When I crank up the AI to get a challenge in the Influence department, I find I get whalloped militarily. I would, in other words, like to be able to play smallerish maps (max size = medium) and still be able to have all options open, if possible.
But perhaps I am misunderstanding something.

Thank you very much for listening and for your time and effort.

Actually one thing I noticed in a previous game was that an ally didn't seem to mind me influence-flipping his colonies. I built a few influence bases and bought a few others off of another civ. It was really interesting, since my ally was complaining about that other civ's bases, but didn't say a word about my own, even when his capital was rebelling. Are allies supposed to be that abusable?

Well of course it's easier to win by influence. You only have to conquer 75% of the galaxy.

It's easier still to win by alliance. You only have to conquer the ones that don't like you.

There's a reason why military victory gives more points then diplomatic or influence. Usually, when you win by either of these, chances are you were going to win no matter which path you chose. It's just chosing how fast you'll win.

Oh jeez. Sometimes I feel sorry for developers when they have to deal with this kind of stuff. It's too easy on the easy difficulty level! Make it harder at an easy level for the kind of way I like to win!

What a foolish thing to say.
I am not whining.
Rather, I am indicating that the victory conditions seem equally balanced at higher levels -- not, however, at levels around "normal". At these levels, certain styles of play become unbalanced (and also: unfun).
I think the developers are interested in making a game which players can enjoy. I think it is for this reason that they included various levels of difficulty -- so that people such as I may enjoy a game at the difficulty level suitable to our skills and time, rather than just for a certain target-group within that broad base of people who have purchased that game. I am attempting to voice this in constructive terms. I think your post is very unconstructive.

Thank you, however, to the others who have listened and for your input, it is most appreciated.

Once you step it up above normal you'll find a couple of the AI races will actually go for an influence victory at which point if you're not building influence starbases yourself you'll wind up having your own planets revolt!

This starts to show up one dificulty setting above normal (which is what I play on) although i've only seen it happen once or twice but the ai will sometimes decide to do it... Also whenever i've built influence starbases and ended up at with with another race they've been very good about quickly targeting my starbases and removing them from the picture... at which point all that influence i've gotten through them goes poof...

So I duno might just mean you're ready to step up another dificulty level... I've always found normal to be the first notch on the "easy" side while the next level up for me is the first notch on the "hard" side... I duno about you but I like it to be a tad more hard then easy...

Also if you ever decide to play on a huge/gigantic galaxy it's extremely usefull to use the "governors" tab/button/thingy thing - since it allows you to select mass production of ships / set rally poiints / and get a full view of the map... - really helps with that whole remembering what you were doing bit (belive me I know what your talking about all those planets and all that information GAH! hehe ) anyway enjoy the game.