For example, the word co·a·li·tion has its primary stress on the third syllable.
Therefore, on which syllable does the word el·e·phant have its primary stress?
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A decent set of rules comes from the TOEFL website:
(1) Stress the first syllable of:
(2) Stress the last syllable of:
(3) Stress the second-to-last syllable of:
(4) Stress the third-from-last syllable of:
Some languages have stresses placed relative to the end of the word, or relative to the beginning. English stress, to the extent it has a regular system, is placed relative to the end of a word. Both your examples have (or at least had) stress on the third syllable from the end of the word -- EL-e-phant, co-a-LI-ti-on. The latter example however has lost a syllable -ti- due to historical sound change, so in contemporary pronunciation, the LI stress winds up on only the second syllable from the end.
The Sound Pattern of English by Chomsky and Halle has a thorough-going but disputed analysis of English stress.