Option A - 100% chance to win 50 dollars (EV: +50)
Option B - 80% chance to win 100 dollars, 20% chance to lose 20 dollars (EV: +76)
You choose option B. It has more than 1.5 times the EV of option A! The man rolls a 100-sided die.
It comes up 6. You lose 20 dollars, he laughs and walks away.
You only have one life. EV calculations work best in frequentist worlds, worlds where you get to experience a particular choice over and over again. This might happen if you're choosing which route to take to work every day, or what restaurant to visit in your neighbourhood. However, these choices are the exception. The vast majority of choices in life, especially the important ones, are only offered once.
There are some frameworks which offer answers to these questions, including models that give diminishing marginal utility to money or maximise the geometric expectation. But these models work best when you can fit a number onto your outcome. In every choice you will be offered, the outcomes are usually far more rich and varied than simple monetary reward and loss (which is itself sensitive to your economic position, outstanding debts/obligations, necessary immediate expenditures...). While unlikely outcomes may contribute small amounts to your EV, they may contribute large amounts to your subjective experience. Very few people who commit crimes think they will get caught.
And that's the thing, isn't it? For choices that only come up once in your life, you have very little primary or secondary knowledge to construct your odds. Things that seem foolproof often are not, and volatility usually hurts you more than it helps. Decision theories only work if the payout matrices are clear, and making them clear is half the battle. This is why maintaining personal rules and standards in the face of uncertainty is important.
You have many years to live - do things you will be proud to remember when you're old.
- Fictional Shinka proverb. (John Brunner, Stand on Zanzibar)
You are offered a lottery by a man on the street:
Option A - 100% chance to win 50 dollars (EV: +50)
Option B - 80% chance to win 100 dollars, 20% chance to lose 20 dollars (EV: +76)
You choose option B. It has more than 1.5 times the EV of option A! The man rolls a 100-sided die.
It comes up 6. You lose 20 dollars, he laughs and walks away.
You only have one life. EV calculations work best in frequentist worlds, worlds where you get to experience a particular choice over and over again. This might happen if you're choosing which route to take to work every day, or what restaurant to visit in your neighbourhood. However, these choices are the exception. The vast majority of choices in life, especially the important ones, are only offered once.
There are some frameworks which offer answers to these questions, including models that give diminishing marginal utility to money or maximise the geometric expectation. But these models work best when you can fit a number onto your outcome. In every choice you will be offered, the outcomes are usually far more rich and varied than simple monetary reward and loss (which is itself sensitive to your economic position, outstanding debts/obligations, necessary immediate expenditures...). While unlikely outcomes may contribute small amounts to your EV, they may contribute large amounts to your subjective experience. Very few people who commit crimes think they will get caught.
And that's the thing, isn't it? For choices that only come up once in your life, you have very little primary or secondary knowledge to construct your odds. Things that seem foolproof often are not, and volatility usually hurts you more than it helps. Decision theories only work if the payout matrices are clear, and making them clear is half the battle. This is why maintaining personal rules and standards in the face of uncertainty is important.