When should I use each of the following:
- This may help.
- This might help.
I always get confused about the use of may and might.
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We use might to imply less possibility than when we use may.
Might is also the past tense of may.
If he had run faster, he might have won the race.
If he runs faster, he may win the race.
It is also considered a politer and more formal alternative to may.
Might I borrow your car?
There are other places that may and might may be used, but these are the ones that might be confusing.
It's really a toss-up, see http://topics.blogs.nytimes.com/2009/07/14/may-might-muddle/
If even the NYT has trouble using them "correctly" then I certainly won't bother too much. Didn't honestly know these subtleties (and they are subtle) myself.
Some more googling led me to http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv162.shtml So the BBC World Service seems to agree with me ;-)
Come to think of it, actually, I tend to hear/put an emphasis on "might" in this context, which clearly indicated this "(a little) less likely as may" meaning.
I agree that it's probably a toss-up in the examples you give.
However, in some uses the meaning of "may" as regards permission changes things a bit.
"You might say that" means it's an open question whether you'd say it or not.
"You may say that" means you have permission to do so.
Again, this isn't specifically germane to the examples you gave, but if I really really wanted to choose the one that is less likely to be misunderstood, I'd choose "might" as the common alternate meanings of that are less likely to show up in similar contexts.
But it's really splitting hairs at that point as you're unlikely to be misunderstood in either case.