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Might Is the Past Tense of May
There are two exceptions to this rule.
First, might is the past tense of may. So you have to use might when you are referring to the past. For example, even if it's likely that Squiggly went to a party last night, Aardvark shouldn't say, “Squiggly may have gone to the party’; he should say, “Squiggly might have gone to the party.”
The second exception is a gray area. When you're talking about something not happening, it can be better to use might because people could think you're talking about permission if you use may. This is clearer with an example. If you aren't sure whether you'll go to the party, and you say, "We may not go to the party," it can be misinterpreted to mean you don't have permission to go to the party, particularly in writing, where voice inflections don't help guide the meaning. But if you say, "We might not go to the party," then your meaning is clear. It's the safer bet.
So remember to use may when the outcome is likely and might when the outcome is less likely or uncertain. But also remember that you use might for everything in the past tense. Also, it's OK to use might when you're writing about negative outcomes, even if they're likely outcomes, if using may would make people think you were talking about having permission.
Finally, here's a bit of grammar terminology. May and might are both called modals, as are words such as would, should, and could. Modals are helping verbs that tell you more about the mood or attitude of the action verb. For example, you can tell that someone has a different attitude toward a party depending on the modal used. There's a big difference between I may go, I should go, and I would go.