But when speculating about the past, “might” is often more appropriate, though increasingly speakers seem to prefer “may” for such uses.
I just heard an newscaster say that the death of an infant “may have been prevented if it had been vaccinated against pertussis.” “May have been prevented” sounds as if there were some doubt about whether the infant died. “Might have been prevented” would be much clearer and more appropriate.
Here’s an extract from my "may/might" entry on p. 145 of the book:
Most of the time “might” and “may” are almost interchangeable, with “might” suggesting a somewhat lower probability. You’re more likely to get wet if the forecaster says it may rain than if she says it might rain, but substituting one for the other is unlikely to get you into trouble—so long as you stay in the present tense.
But “might” is also the past tense of the auxiliary verb “may,” and is required in sentences like “Chuck might have avoided arrest for the robbery if he hadn’t given the teller his business card before asking for the money.” When speculating that events might have been other than they were, don’t substitute “may” for “might.”
When you are uncertain what has happened and are making a guess, then you may want to use “may”: “I think he may have thought I would really like an oil change for my birthday.”
These days I rarely hear “might” used by people reporting events from the past. Newspeople and politicians seem to vastly prefer “may.” Why is that?
My theory: teachers and parents have insisted for years that in asking permission to do something it is more polite to say “may I?” than “can I?” This may have led people to think that “may” is a “nicer” word in all contexts. Or it might not have.
Anyway, sometimes “might” makes right.