We have a bridge. It’s 60’ long. The width varies according to how brave you are (see poll above.). This bridge has a 500’ drop off. There are no handrails or anything to brace onto. (No balancing polls allowed either.) There is a slight wind of about 10 - 15mph at your face.
Which bridge are you willing to cross for the money indicated in the above poll? Also, one must walk across the bridge. No crawling is allowed.
If I become less brave half-way, will it widen automatically ? 
I said 3 ft. wide but, I’m not looking at a 500’ drop right now either.
I’ll give you $100 to not make me cross it.
I’m not convinced this is about overcoming fear of heights, unless there is a safety net (and I’m pretty sure you didn’t intend there to be one). I don’t consider myself afraid of heights, per se (I can happily walk across ravines on a normal bridge, look over the edge, stand on a glass floor above a 500’ drop, etc.), but I am afraid of needlessly killing myself. So I haven’t answered the poll because without a safety net, I wouldn’t do any width (well, almost - make it 10’ wide and I would consider it) for any amount of money. The key factor is the wind - OK, you say it’s in your face, but wind is unpredictable - one sharp crosswind could easily throw you off, to your all-but certain doom. Or on the smaller widths, a trip or a slip would do you in, or just unexpected dizziness halfway across could tip you over the edge, even if you could guarantee no crosswinds. It’s just too big a risk, for me.
I just don’t think I could do it. I’d want to, and I’d feel ashamed for the rest of my life for rejecting the dare but I value my life over money, and this just screams DANGER to me.
I could cross a 2 ft. wide bridge no problem so that’s how I voted. I think I could do the 1 ft. wide bridge, but as randompattern said, I’m not looking at that 500 ft. drop right now.
You forgot None of the above.
Dammit! You just made me realize I forgot to put a “No way, No how” option!
There’s no vote for "none of the above’?
MAYBE the 3ft one. $100 isn’t enough to compel me to do much of anything, let along something that terrifies me.
None of the above for me.
All that follows is predicated on the assumption that the bridge is stable, since the OP didn’t specify its construction. You’d need lots of support to keep the smaller widths from bouncing and flexing like a trampoline. If we’re talking about bouncing bridges…no. Well, maybe the 4’ one, but I’d want to watch it for a while first.
I routinely cross short distances on 4" beams, but not over dangerous heights, and not 60’ spans. I would be concerned about fatigue, wind effects, and possibly vertigo, so I’d be dubious about walking the 6" version over that distance. I would want to advance sideways by shuffling my feet, rather than one foot in front of the other; it’s more stable, but also slower and more tiring. One leg tremor or cramp away from death is not a place I want to be. If it were “Cross the bridge or stay here and die”, I’d head right out and probably be okay, but I’m not risking it for cash.
The 1’ bridge is not actually much better in this regard–it’s still not wide enough for me to abandon the shuffle transit. If I’m already giving up $900K, I’ll give up another $60K to switch modes.
The 2’ bridge is wide enough to walk one foot in front of the other, with enough spread for some balance. Also, it’s probably wide enough to take a knee to rest or regain my stability, if necessary. Sitting here at my ease, I picked it. I might reconsider on actually looking down at the drop, though. 
For the sake of a complete analysis, the 3’ and 4’ bridges are practically the same as walking on flat ground, as long as you don’t look off the sides.
None of the above. I am not afraid of heights in the usual meaning of the term, but I am afraid of falling off a narrow, windy bridge into a 500’ chasm.
As someone else said, it’s not just about fear of heights, but also safety. I’m a klutz. Even with no fear of heights, it wouldn’t be prudent for me to walk around on narrow bridges. I really doubt that I could stay on a 6" line painted onto concrete for all 60’.
I answered the 2’ bridge. This should be wide enough to feel safe and have some margin for error. The 4’ bridge wouldn’t be worth it for $100 - while I would rationally feel safe, there’s just enough fear of heights to make the experience unpleasant. The 3’ bridge might be the option I’d actually take, but it might depend on how much I really needed the money that day and just how stable the bridge is.
Do we get a warm-up practice? I’m sure I could do the one-foot bridge if I gave myself some time to desensitize and make sure of my balance.
I answered 2 foot. For one feet wide, I’ve done this with a cliff face on one side (and an around 500 foot fall on the other), in fact for about 10 feet it went down to less than a foot even if it wasn’t 6 inches.
So 2 feet without a cliff face to balance against is no problem.
How do you think the OP is funding this whole venture? 
I chose “2 feet wide” on the grounds that I don’t need more money.
I did gymnastics as a kid. A balance beam is less than 4 inches wide. We did rolls and backflips on the damn things. I think I can handle the 6 inch wide crossing even now.
ETA: I did a Ropes course in high school. One obstacle was crossing basically a telephone pole about 6–7 m long, suspended at roughly the same height. While some people had problems with the height, it caused no issues for me.