Due to scope neglect, framing effects, and other cognitive biases, the result of an expected utility calculation executed correctly may produce an answer different from first intuition, making it "intuitively unappealing". If you can tell that it's probably the intuitions that went wrong and not the calculation, the skill shut up and multiply is the ability to accept that, yes, sometimes the expected utility math is correct and we need to deal with that. Contrast do the math, then go with your gut. If you're not sure which of these applies, use "do the math, then go with your gut" until you've built up more experience.

The specific application of Shut Up and Multiply to the Torture versus Dust Specks case has proven quite contentious. One reason this case was cited as an exemplar of where "shut up and multiply" should apply was a claim that the usual reasoning behind answering "SPECKS" can be reduced to circular preferences.

Blog posts

One Life Against the World
Circular Altruism, The "Intuitions" Behind "Utilitarianism"
Money: The Unit of Caring
Purchase Fuzzies and Utilons Separately
Torture vs. Dust Specks

External links

Is Valuing Life Undervaluing it? by Katja Grace
You Can Put a Dollar Value on Human Life by Yvain
The Value of a Life by Nate Soares
Critical discussion by "A scientists Thesis" on Tumblr
Eliezer Yudkowsky doesn't undestand ethics by Sean Goedeke

See also

Scope insensitivity
Fuzzies, utils
Pascal's mugging
Bite the bullet
Rationality
Utilitarianism, expected utility