Might is sometimes right

Every verb has a past tense, and many of them are irregular! For example:

Know/knew
Ride/rode
Eat/ate
Think/thought
May/might

Let’s look at this last one, because many people are not aware that 'may' has a past tense. 

May/might

May (present tense) and might (past tense) indicate possibility. (Another meaning is permission: You may go. But I won’t cover that here.)

In most cases, you can use either may or might, and the meaning is virtually the same:
I may get fish for dinner. 
I might get fish for dinner. 

These days, we would usually say ‘I might’. 

May have/might have

These forms are used when talking about a past event or situation, and this is where it's important to know the difference.

• When you still don’t know the outcome at the time of writing or speaking, you can also use may have/might have interchangeably: 
  ✔ They may have watched the movie last night.
  ✔They might have watched the movie last night.

• When something did actually happen, you can’t use the two terms interchangeably: 
  ✖  His widow said that if he had been wearing a life jacket he may have survived.

The use of the present tense here wrongly implies that the man could still be alive. 

The correct use here is might have:
✔ His widow said that if he had been wearing a life jacket he might have survived.

Another example:
✖  Without six children to care for she may have written more novels. 
✔ Without six children to care for she might have written more novels.

Reporting direct speech

When reporting what someone said, change may to might:
‘I may request a refund.’ [Spoken words]
He said he might request a refund. [Reported speech]