St. Patrick's Day question (Why "Paddy"?)

You’re probably right, yes. Obviously, there’s considerable variation on both sides of the pond, but a typical American pronunciation of water might be “wodd’r”, whereas a typical British pronunciation would be “wawtuh”. The only sound they actually have in common is the initial “w”.

Having said which, it is a little surprising that a waitress couldn’t work out what was meant, in context. But njtt’s is the umpteenth example I’ve come across of exactly the same miscommunication, so it does seem to be common.

Funny, I posed this same question last night. From the random bartender, so you have to take this with a gain of salt, Paddy is short for Patrick, and Patty is short for Patricia. It made more sense last night…

While google results don’t necessarily prove more popular usage (sometimes results can be swayed by one particular reference that dominates the results), I think in this case the premise in the OP is pretty much shown to be wrong

I concede I may have overstated the case. But the current St. Patrick’s Day Joke Thread has eight separate Paddys and no Pattys.

Whatever it is, it’s not unusual. Here’s the Wikipedia page on American English:

(Emphasis mine.)

So there’s rules where it occurs and where it doesn’t.

What I should actually say is that “latter” and “ladder” have the same sound in the way I articulate it and in the way I hear most Americans articulate it, but it’s neither quite the unvoiced “t” or the voiced “d.” It’s an alveolar flap vs. a voiceless (in the case of “t”) or voiced (in the case of “d”) alveolar plosive. It sounds to many speakers like a voiced “d”, because it is indeed voiced. (And, interesting to me at least, I do pronounce “writer” and “rider” differently, with that form of Canadian raising mentioned in my accent.)