So a situation I'm sure everybody runs into often enough is this:

You make a preflop raise with a short stack in a loose game with AK, and go to the 3-4 handed. You flop a pair -- lets say an ace for this scenario, along with a flush or straight draw -- once again for this scenario, lets say a flush draw. It gets checked to you, and you make a standard bet, the next player calls and then a non-outrageous raise is made of 1-4x the original bet. It gets back to you with just you the first claler and the raiser in. Simply calling here is an option, but not one I like, as you giving a free card on a draw heavy board (open to discussion of course), so I think your options here are raising all in, or folding. I ran a few numbers on twodimes.net, and this is what I came up with so far

Likely hands of raiser:
Ax: 16 combos(8:1, 7:1 if kicker is above 2nd rank on board)
Flush Draw: 110 combos (1.6:1 fav)
set: 18 combos (48:1 dog, minus AA)
Top 2: 6 combos (6:1 dog0
top & bot: 6 combos (2.7:1 dog)
bot 2: 9 combos (3:1 dog)

Total possible combos: 165
Favorite: 126 (76%)
dog: 39 (23.6%)
when fav, on avg 4.5:1 fav
when dog, on avg 14:1 against

For the more mathematically inclined, what sort of stack:pot ratio does one need to move in vs. fold here? Any other thoughts are also welcome.

One helpful trick is to not play cash games while short-stacked.

I realize that might be too simplistic, cause you've obviously given this some thought, but you might try running this scenario by the Tournament folks. I think it's a bit more applicable in that setting.

I personally find that there are certain strategic advantages to starting out with a shorter stack, especially in looser games, but that's another topic all together.
Mostly I was looking for help on how one might mathematically determine which play is better, as it seems like such knowledge would transpose to other situations also.
The reason I didn't run it by the tournament folk is because I feel that this is an auto push in tournaments, which are often push fests to begin with, and the necessity for a quality hand is not as great (admittedly my expertise if existent at all is certainly not in the tournament area).