Been thinking more about this - seeing it is a great question from many angles -
The most common answer seems to be hard core single bit - say a dayton or something similar. And I understand that answer.
I think the question (no harm intended to thread starter) needs to be rephrased slightly - and I dont know the exact answer - but it seems we tend to think that all we have in the doom and gloom scenario is an axe - if that is the case, then a single bit would have to be considered heavily. If I dont have a hammer, knife, etc - the single bit comes into play big time.
On the flip side, if I have my other basics - some sort of hammer - whatever it is - a knife or two - channelocks, crescent wrench, etc - then now we have more flex space to work with - and I think this is where the double bit comes into play - especially if the parameter is that we only have an option for one axe -
Then you have to look at where you are at - terrain wise. I am no geography guy, dont know alot about other areas in the US let alone the world - but depending on where you are will make "a world" of difference in your choice. Here in wooded W Pa, I think I would go with a 3 1/2 to 4 lb double bit - especially if I have the other things mentioned - why?
1. 2 bits. depending on if I have a file, stone, etc - I want a back up, especially me.
2. conditions - eventually I will have to get down and dirty with the axe - I can see scenarios where things really go to S**T and the axe now becomes not only a wood working tool, but an all around tool - especially if others are limited - thus 2 bits. What if you have to make a trail or road - get in the dirt with stumps and rocks? What if you have no shovel - you go out one day on hunt and gather - your wife or kid uses your axe to break up ground to plant things, or to do some other non convential axe task?? - 2 bits the better, to me anyways.
3. Metal - again, depending, basic metal might become the new gold. how many guys can forge or reforge metal tomorrow? I cant. Not a clue. Thus big time auto inflation on what was a given yesterday. If I have an axe, and have to make it last, a double bit is the easy no nonsense answer here.
4. Handles - I think this is something that needs considered - a wood handle is going to break - sooner or later. Then what? Single bit, double bit, pretty much then who cares. With the way the eye is shaped in a double bit, would it technically be easier to haft than a single bit? Upon looking at some of my axes, I would think yes. Is this a fact? Nope, just one guy thinking to himself - So I am a redneck - with limited woodworking skills - my handle breaks - I need to make a new one out of this tree over here - so for a single bit I need a tear drop shaped eye, for a double - a thin handle shaved down on either side - my preliminary thought is that a rude and crude double bit handle I could make easier even out of a 2x4 then a single bit that would fit a 3, 3 1/2 lb dayton. Especically if my sb has an angle to it on the bottom. Or god forbid it is a jersey. Yikes. Again many variables here - so this is up for wide debate and should be.
5. Energy expenditure/calories needed/accuracy - all these to me favor the double bit. double bits grew in popularity for a few reasons, but one main reason is that all things considered, they are more accurate than single bit due to better overall balance, less wrist roll, etc. This means less inaccurate hits, less work overall, less calories burned, etc. This could be huge when it comes to the end - limited resources - water, food, etc. Every expenditure will count. Bit gets dull? Swap over to other bit, no need to walk back home or take time to refile. If I can be more efficient, this will go a long way towards survival.
Ok enough. Few things I have been thinking about for the last couple days. I think this needs discussion. Am I correct in what I stated? Doubt it. Might be. Might not be. So lets discuss. Someone please say : "Operator you couldnt be farther off here because ...." Lets open this up and think about it. I am sure there are many ways to think about and approach this - lets get after it.
Thanks!!