The auxiliaries may and might are often used interchangeably. Most of the time, interchanging them doesn’t seem to matter.
Strictly speaking, might is the past form of may, but may often occurs in past tense constructions, and might is used in sentences about the present or future.
Both may and might are used when the speaker is not sure about something:
I may watch a movie tonight.
I might watch a movie tonight.
The use of may in the first sentence implies a stronger possibility than might, but for many listeners, the choice between may and might barely registers in this context.
May and might are used to show that something has possibly happened in the recent or distant past.
They’re late. They may have forgotten our address.
They never arrived last night. They might have forgotten our address.
The may in the first sentence suggests that the people are still in transit, their arrival remains imminent, and there’s still a possibility that they have not forgotten the address.
The might in the second sentence places the expected arrival in a more distant past and the forgetting of the address is more likely to be past as well.
Again, most speakers would probably not notice if may and might were interchanged in these contexts.
There is, however, a context in which the use of may in place of might leaps out as glaringly incorrect. Here are examples, with corrections.
INCORRECT: His letter from New York may have been too late to prevent a dissection, but Kroeber had been passionate about respecting Ishi’s wishes for a proper burial.—Ishi’s Brain, W. W. Norton & Company, 2004.
CORRECT : His letter from New York might have been too late to prevent a dissection, but Kroeber had been passionate about respecting Ishi’s wishes for a proper burial.
The letter was too late. The dissection was performed. The only correct choice is the past tense form, might.
INCORRECT: Seattle school shooting killed one — but it may have been much worse if not for ‘hero’ guard with pepper-spray—Headline, National Post.
CORRECT : Seattle school shooting killed one — but it might have been much worse if not for ‘hero’ guard with pepper-spray.
The attacker was in fact prevented from killing another person.
INCORRECT: If not for Joseph’s bravery and quick actions, his brother may have been killed.—Do The Right Thing site.
CORRECT : If not for Joseph’s bravery and quick actions, his brother might have been killed.
Thanks to Joseph’s actions, the brother was not killed. May suggests that the brother was perhaps killed.
INCORRECT: Another child may have been the next victim if it hadn’t been for a woman [who alerted police].—Announcer on Inside Edition.
CORRECT : Another child might have been the next victim if it hadn’t been for a woman who alerted police.
The perpetrator was apprehended before he could attack another child.
Distinctions between may and might continue to weaken, but for the present, careful speakers may wish to pay attention to their use with constructions relating to the past.