An option is more risky if the value of its possible outcomes is more widely dispersed (higher variance). An agent is risk averse in a pure sense if they prefer safe options over risky ones, even when the riskier options (gambles) would give more of what they value in expectation. (Conversely, an agent is risk neutral if they are indifferent between options with the same expected payoffs, and they are risk seeking if they prefer gambles to equal-expected-payoff safe options.)

All payoffs in this definition of pure risk aversion are expressed in terms of what the agent values. As a consequence, risk aversion is on this definition quite distinct from the most common notion of risk aversion in economics, whereby diminishing marginal utility of money causes people to prefer low-variance, lower-expected-value monetary tradeoffs. Risk aversion is also related to, but distinct from, ambiguity aversion (Wikipedia 2006).

This form of pure risk aversion appears to be irrational under a variety of assumptions, as mentioned in expected value theory. Indeed, risk averse agents in this sense can be exploited in ways that seem to count against risk aversion (Yudkowsky 2008). However, some have defended it as rational (e.g. Buchak 2013). If risk aversion is rational, some form of risk-averse decision theory might be appropriate....

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