“Intuition comes first, strategic reasoning second” Jonathan Haidt, The Righteous Mind, p 367

"...human intuition is organized around causal...relations" Judea Pearl, The Book of Why: The New Science of Cause and Effect, p. 746 (Kindle pagination)

Moral intuitions are gut-level assessments of right and wrong. Causal intuitions are gut-level expectations of outcomes: if x, then y is more or less likely to follow. A causal intuition is a hunch that things will turn out a certain way. Causal intuitions are the product of, but not reducible to, prior experience, prior causal reasoning, natural biases, and heuristics. Causal intuitions vary according to specificity and time frame.  Put into words (artificially but for the purpose of explication), examples of causal intuitions would include: "if I give a dollar to this street person, he'll use it to buy liquor and I will hasten his death" and "since the future is unpredictable, I'll just go with my first impulse and trust that it will all work out." 

Moral intuitions are grounded in causal intuitions. Strategic thinking is just another way of saying goal-directed thinking. A goal is a desired outcome of behavior.  Moral intuitions do not happen in the absence of desired outcomes. Insofar as moral intuitions inform individual or collective behavior, moral intuitions are implicitly strategic. So take that, Jonathan Haidt! 

Here's a theory: one can have causal intuitions about trade-offs and long-term effects.  Moral intuitions that seriously incorporate causal intuitions about trade-offs and long-term outcomes are "cooler" than moral intuitions that rely on the causal intuitions about localized and immediate effects.

But is one's level of "compassion" best measured by the warmth of the feeling?

References:

Gigerenzer, G. (2008). Moral intuition: Fast and frugal heuristics? In W. Sinnott-Armstrong (Ed.), Moral psychology—Vol. 2. The cognitive science of morality: Intuition and diversity (pp. 1–26). Cambridge, MA: MIT Press.

Haidt, J. (2012). The Righteous Mind: Why Good People are Divided By Politics and Religion. New York: Pantheon Books. pp. 9–11. ISBN 978-0-307-37790-6.

Pearl, J.  (2018) The Book of Why: The New Science of Cause and Effect. Basic Books, New York.