Player's influence on story

While discussing role-playing games with people less interested on the subject than I brought out a vital part in it: Player's ability to affect the overall story.

We already have multiple endings and branching story, but they're rather inadequate for this. Multiple endings may be because of something arbitrary, a last minute choice which is available regardless how they played, or similar flimsy cause. Branching story often devolves into single ending, and the branches often are sort of trivia about the whole thing rather than anything that has substance.

Therefore, we need something to better describe how much the player can influence the story and the character they play and the characters they meet.

Here's few that may need tags:
* Long term effects on storyline and gameplay, even if minor
* Actual changes in the story based on player's actions or choices.
* How the multiple endings come about, binary logic on what they did or didn't do at the end? or something farther reaching? Are they limited to the faction you chose to aid?
* Is there even a story? Is there a main story (main quest)?
* Is the game story driven? Being able to skip dialogs, cutscenes and such and still manage to beat the game usually would indicate that it isn't really story driven, even if there's loads of text. Of course, a lot of games do most things required by this automatically or have a log which tells you in one line what the previous character spent several minutes explaining.
* Has player any influence on the protagonist's development? Not "xp", character statistics, or such, but rather the person/personality (we have karma tag, but it's woefully inadequate). Does anyone in the game world care about their personal quirks? Do they have impact on anything besides a summary note in dialog?
* Do diametrically opposing choices have effect on storyline besides taking an alternate branch in the storyline which is forgotten once the next branch is reached? As in, do the branches eventually converge back into the only one storyline the game actually has? Multiple endings could be for each branch or for single converged branch at the end.

Consequences covers a small bit of this, though seems to be a bit too vague/generic.

Easy way to go about this is to identify how the player can influence the various endings, such as is it a choice at the end as it usually is, some choice long before it, certain plot points across throughout the game, or their actions overall (e.g. based on karma).

Well, I haven't given this much at all any thought and whenever I have, there's been no good ideas.

Just added early ending trigger to cover cases where the ending is chosen based on early decisions. I just can't make the name decently distinct from actual early ending.