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 2016).
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.
However, it seems that altruists should be close to risk-neutral in the economic sense. Though there may be some diminishing returns to altruistic effort, the returns diminish much more slowly than e.g. the marginal personal utility of money does. This means that the reasons for economic risk-aversion that apply in standard economic theory apply less strongly for altruists.
Risk aversion is important to effective altruism because it informs how rational and altruistic people should make their decisions. Since it seems that altruists should be close to risk-neutral in economic terms, then unless we should use a decision theory that is risk neutral in the pure sense advocated for by Buchak, it may be best for altruists to be approximately risk-neutral overall. Risk-neutrality leads to some interesting and surprising conclusions, such as prioritizing risky careers (Shulman 2012), taking unusual financial risks to increase an expected donation (Tomasik 2014), or donating to only one charity (although there are countervailing considerations) (Snowden 2015).
Buchak, Lara. 2013. Risk and rationality.
Defends risk aversion as rational.
Shulman, Carl. 2012. Salary or startup? How do-gooders can gain more from risky careers.
Tomasik, Brian. 2016. When should altruists be financially risk-averse?.
Wikipedia. 2016. Ambiguity aversion.
Yudkowsky, Eliezer. 2008. The Allais paradox.