Usage of "if you would"

In a recent conversation the following sentence came up:

1. I would be honored if you would join me there, {name}.

A friend of mine stated that this is grammatically wrong and the correct way would be:

2. I would be honored if you joined me there, {name}

I think that both versions would be fine. Who is in the right here and who is in the wrong?

Your friend is misremembering technically correct grammar

in the sense that many foreign ESL tests will require students to learn that English has three forms of conditional phrases:

1. First conditional: If you join me, I will be honored.
2. Second conditional: If you were to join me, I would be honored.
3. Third conditional: If you had joined me, I would have been honored.

Essentially they break down into statements about the present or future that are possible but uncertain; statements about the present that aren't thought to be likely; and statements about the past that didn't happen but could have, had things been different.

You'll notice there's nothing unusual about 'would' in the then clauses, which is why @tchrist was defending their existence in the if clauses against the oversimplified ESL test idea that 'would' shouldn't ever appear there.

That said, your example doesn't actually qualify for these ESL forms, because you're not talking about anything that you think is contrary to fact.

...but still completely wrong.

'Would' is technically the past tense of 'will' and was used in conditionals to express the future from the perspective of past events.

If you had joined me [then], I would have joined you [after then but before now; implied '...but you didn't, so I didn't'].

But that sense of 'things could have been different' was too useful and eventually broadened to include cases where 'things could be different'.

42... d. Used in the 1st pers. instead of the normal auxiliary should...

44. a. In a conditional (or equivalent) clause with pers. subject, with implication of intention or volition: = ‘chose to’, ‘were willing to’...

In other words, 'If you would join me, I would be honored' is fine English. It's understood as someone—perhaps British or perhaps falling over themselves a little to be polite—saying

[No pressure. This is purely a hypothetical. I'm just letting you know that,] if [it were the case that] you would join me[, it would also be the case that] I would be honored. [If you did. Which you absolutely don't have to. Sorry to bring it up. Just letting you know. Sooo... Yep. It'd be nice. Thassallimsayin.]

You're just phrasing something that's perfectly possible in a hypothetical way to share some helpful information but to let the other person know that refusal is still perfectly acceptable. (It might still not be, people being how they are, but at least that's what your perfectly grammatical construction is implying and why people use it.)

The use of would in if-clauses is possible in polite and/or formal requests:

It would be nice if you would help me in the kitchen. (Are you willing to help me in the kitchen?)

(www.englisch-hilfen.de/en/grammar)

See also the following extract from MacMillan Dictionary:

I would be grateful if you could/would ... (formal used to make a request:)

• I would be grateful if you would examine Exhibit A. Do you recognise it?

When you have would in the “if” part, it essentially means “be willing to”:

• If you would please take your seats, we could get the movie started.
• If only you were willing to sit down, we could get the movie started.
• If you sat down, we could get the movie started.

Normally when the “then” part is a would/could type expression, the “if” part should be in the past tense, or the unreal were if it’s be.

Under most circumstances it’s only when you want the deontic sense (not the epistemic sense) of the modal verb will can you use that verb in the “if” part. This is probably the “rule” your friend is remembering. Non-native learners often double up their woulds in ways that come off as ungrammatical. For example, this one you normally cannot say:

• If we *would close early, I would be able to make supper.

That should normally be the simple past:

• If we closed early, I could make supper.

But there is also a habitual possibility:

• Whenever we would close early, I go to make supper.