How do you pronounce "mayor"?

I have been split between two pronunciations of "mayor".

Most of the people I talk to pronounce it "mair" (like the horse).

But if you look on Dictionary.com the main pronunciation is "mey-er".

I wanted some clarification on which is the correct way and why there are two different versions of the word.

The British have been pronouncing "mayor" with one syllable since at least 1780 (See Thomas Sheridan's 1780 "General Dictionary of the English Language" in Google books). The general American pronunciation is two syllables.

I'm Australian and use the 'mare' pronunciation. I'm used to hearing Yanks say 'may-or', though - in movies and on TV. That said, I've just seen NYC's Mayor LaGuardia being sworn in on the History Channel - in the 1930s - both he and the officiating judge clearly said 'MARE'.

Paul