Change Contexts to Improve Arguments

Well, I somewhat strongly disagree (will I get cookies now?).

Assuming a similar amount of information is exchanged*, introducing strong social conventions will overshadow the arguments and skew their results. Probably without the participants even noticing. Being on someone's home turf, being served food, the ballast of thousands of years of social evolution, all of these are detractors from factual debate. Yes, the experience will be more amenable, filled with polite "Aaaah, I see what you mean!" interjections, and everyone will leave fuzzily happy, well fed, socially status-affirmed and postprandially somnolent. Quirrell would approve, as the cookie-dispensing host. But when looking for the correct -- even if unpopular -- deduction?

There's a reason I have more respect for people who implicitly embrace Crocker's Rules, having no need for being cuddled, especially when such cuddles will (in my opinion) inevitably sway the course of the arguments.

When you're invited to debate a couple of friendly Jehova's Witnesses (See me adhering to online social conventions? In fact, any religion could be inserted here.) over some tea and cookies, and everybody leaves fuzzily happy thinking "what a great exchange!", you did something wrong. If truth was your objective, that is.

* (otherwise the medium allowing for more exchange mostly wins by default; a long series of Facebook exchanges would allow for more mutual updates than a short tete-a-tete)

I use to have more fruitful disagreements

So, you've had a more polite, pleasant, and civilized discussion. But was it more fruitful?

I think it's a very good idea. Discussions often derail into argumentative wars of this kind. Of course, there is also the opposite failure, referred to in some of the other comments, namely that people agree too much, don't point out flaws in others' arguments for fear of upsetting them, etc. In order to resolve that, you need a different strategy, just like different biases require different counter-bias techniques. That does not establish that this strategy is not helpful to improve the kind of discussion described here (which, by the way, is very common).

The general idea of changing contexts is also very interesting. It seems to me that how discussions unfold is to an extremely high degree due to situational features. For instance, at my previous department, the discussions in the small seminar room were nearly always more cooperative and fruitful than those in the large seminar room, which felt much more official and somehow prompted people to take a more adverserial stance visavi the speaker. Probably we should change contexts more often to find out under which circumstances the discussions tend to become most fruitful.

I like the writeup and the idea very much. I can think of times when I've used something similar in the past, but the bit about recruiting people to do get milk didn't occur to me at the time.

I'm kinda torn, I see it as a very useful technique to defuse a situation and get people reminded about why they talk to each other in the first place. And of course the actual consequences of having a blazing row, which isn't as apparent when we're separated by keyboards. On the other hand as already pointed out a bunch of other social conventions then come into play. ('Home turf', shyness, social dominance, etc.)

At the very least, it's an important option to have in our toolkit.

Then, once the logistics were set, we all broke bread (sorta) with each other and had a shared, pleasurable experience.

Did anyone fundamentally change a strongly held opinion?

You're 100% correct when you say that changing venues and having the arguing parties work together had changed the tone and flow of the debate experience but I can't agree that changing context will ultimately improve an argument. I would like to discuss some things I believe to be at play here, but not mentioned.

The difference between arguing online and arguing in person can be of significant importance to how the two parties interact (argue). I will go ahead and propose that if the two parties had instantly (after your request to speak in person) transported them selves to a room and sat right in front of each other without the cookies or you even being present, even then their tone and ferocity would change from what it was online. I believe that when we are online we are no longer bound by the effects of communication between body and mind (similarly time depending on the online medium). When we are online we do not read the body language of those we are speaking with and we all know that body language makes up for a very large portion of how communication plays out.

When the two parties are instantaneously transported from their chairs to being right in front of each other they are subjected to a larger portion of their emotional consciousness then they were online. Their expectations of people and how they communicate in person becomes in affect. Those attributes of the arguing parties personalities weren't all at play when the conversation was happening online.

Their characteristics while the argument was online could even be considered as dissociative to their true personality traits. Which means, yes... Changing context will effect arguments, but I wouldn't go so far as to say it will improve one. Who knows... Maybe one of your guests had a sexual desire for cookies and so became aroused which made them care less about the topic being argued and so didn't fight back as hard as they might have online.