- "Would you pay $900 for a 90% chance to win $1000?"
- "Would you pay $100 for a 10% chance to win $1000?"
So the distribution of results really is different. It's not just a phrasing trick. I would still say no to the first and yes to the second. I like positive outliers more than negative ones. This doesn't seem irrational to me.
I'd say that most people rarely have enough data to split probabilities into more than about five bins: ~0%, fairly unlikely, coin flip (~50%), fairly likely, and ~100%.
It's all about managing the risk: generally speaking, I can afford to risk $100, but not $900. Furthermore, I've already spent/borrowed the second $1000 (We're TAKING my existing money, which I presumably have already planned on having). So the first is a windfall, but the second is a real need. So I WON'T risk a large amount of money for a windfall, but I WILL risk a small amount in order to meet a real need. I'd say that's 100% rational.
Bob