## Thursday 18 November 2010

### Testing whether we are liked

I've noted before that, for our wedding back in 2002, Susan and I decided against sending out A and B list wedding invitations. Standard drill in the US, for my NZ readers, is to have a biggish wedding. First you send invitations to the A list, see how many reply, then see how much space you have to send invitations to folks on the B list. We didn't want to do that. Instead, we assigned probabilities to each invited guest's attendance and sent out invitations such that the expected number of attendees matched the capacity of the venue. Risky play? Sure. So long as we weren't biased in our guess, we'd be fine on average. But this was a one-shot event and we had no clue about the variance of our estimates. But it all worked out. 225 invites turned into 125 positive replies. We had capacity for 125. All was good.

But we were briefly terrified. The 75% probability folks turned into acceptances a lot faster than the lower probability folks turned into rejections. Excel recalculated the expected number of guests as we updated our estimates with outcomes. I think it touched 170 briefly. And then came the late declines, and all worked perfectly.

Jeff Ely says that this is because people like us (or, more likely, like Susan).
An invitation is an option that can be exercised at any time before the date of the party. The people who did not respond immediately are waiting to decide whether to exercise the option. If she’s a true friend then this is because she has a potential conflict that would prevent her attending. She is waiting and hoping to avoid that conflict. When she is sure there is no conflict she will say yes.

The other people are hoping for an excuse not to come. Once they get a better offer, manage to schedule a conflicting business trip, or otherwise commit themselves, they will send their regrets.

In both cases, when the party is imminent, the option value of waiting is gone. Those who want to come but haven’t gotten out of their conflict give up and send their regrets. Those who hoped to get out of it but failed to come up with a believable excuse give up and accept.

So, a simple measure of how much your friends like you is the proportion of acceptances that arrive in the final days. Lots of acceptances means you better set aside a few extra drinks for yourself.
Our acceptances came early; the rejections, worryingly late. And so Ely's test suggests that folks liked us. Excellent.