- He may do this. <present indicative>
- He might have done this. <past indicative>
The following is taken from the Economist style guide (US):
May and might are not always interchangeable, and you may want may more often than you think. If in doubt, try may first. You need might in the past tense. I may go to Leeds later becomes, in the past, I might have gone to Leeds later. And in indirect past speech it becomes I said I might go to Leeds later. Conditional sentences using the subjunctive also need might. Thus If I were to go to Leeds, I might have to stand all the way. This could be rephrased If I go to Leeds, I may have to stand all the way. Conditional sentences stating something contrary to fact, however, need might: If pigs had wings, birds might raise their eyebrows.
Do not write George Bush might believe in education, but he thinks the people of Greece are Grecians. It should be George Bush may believe in education, but he thinks the people of Greece are Grecians. Only if you are putting forward a hypothesis that may or may not be true are may and might interchangeable. Thus If George Bush studies hard, he may (or might) learn the difference between Greek and Grecian.
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