## Undercover Economist

October 11, 2013 7:33 pm

# Guest list angst – a statistical approach

‘Assumptions look doubtful and like many economists, I appreciate the free market’s messy reliance on trial and error’

Here’s a ticklish problem: how many guests to invite to your party? If it’s a rave on a beach, as many as you like. But a formal affair such as a wedding will have a venue with firmer limits.

Ideally, one would invite the guests, wait for their responses, then book the venue, but that’s rarely practical. Yet none of the alternatives really satisfy. Sending invitations out in stages takes too long because people rarely reply quickly. And if the guests who were invited on Facebook talk to the guests who received gold-leaf invitations six months in advance, things may get awkward.

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#### Undercover Economist

An alternative is to be conservative, inviting no more people than the venue can accommodate. This feels like a shame because space at the venue is bound to lie idle while friends who could and would have joined are forced to stay at home.

Simply guessing at the acceptance rate isn’t much good either – few people hold enough weddings to master this, and anyway the rate may change after the groom’s first three or four marriages. And heaven forbid that one is forced to withdraw invitations after overshooting.

What to do? A young statistician with a wedding to organise, Damjan Vukcevic, recently outlined his experience in Significance magazine, a glossy rag published by the Royal Statistical Society. Vukcevic and his then-fiancée, Joan Ko, wanted to mail out all their invitations at once, filling the venue snugly without spilling over. Their solution: statistical modelling.

Vukcevic placed his guests into four categories, ranked in order of likely attendance, from “definitely” to “unlikely”. He assigned each category a probability and added some further assumptions: families would either attend all together or not at all; beyond that, one guest’s decision to attend would be uncorrelated with another guest’s. With a target of 100-110 attendees, and an absolute maximum of 120, Vukcevic and Ko celebrated with … 105 people.

A triumph for statistical modelling? Well, if Vukcevic was a “quant” at a hedge fund he’d be claiming his performance bonus – but we should look more closely. Vukcevic’s assumptions were flat-out wrong. For each of the four categories, the actual attendance rates were lower than forecast. (“Likely” attendees had an assumed attendance rate of 80 per cent and an actual attendance rate of zero.) Vukcevic predicted that the chance of having 100 or more invited guests attend was more than 99 per cent; only 97 did, a result which the model said was vastly unlikely.

Other assumptions look doubtful: a conflicting wedding, or football match, could reduce attendance probabilities of many guests at once. Vukcevic predicted invitations for three friends’ weddings and he overestimated the attendees every time – in one case by a dramatic margin.

And yet Vukcevic and Ko celebrated with “an ideal number” of attendees. How so? Another assumption proved felicitously flawed: that the chance of uninvited guests was zero. Happily for Vukcevic and Ko, their failure to account for wedding crashers cancelled out all the other mistakes. I wish them every happiness as a couple but this is hardly reassuring.

Do I have a better suggestion? Not really. But, like many economists, I appreciate the free market’s messy reliance on trial and error. I also think the embarrassment of inviting several waves of guests – or even disinviting guests – while large, is not so very large as to be out of the question.

This may explain why, at a recent party, I filled the venue perfectly – but only after multiple rounds of invitations and disinviting a few friends close enough to take it on the chin. One assured me she would forgive me if I wrote a column about party invitations and “the need to consider and plan to capacity”. I trust she is now satisfied.

‘The Undercover Economist Strikes Back’, by Tim Harford, is published by Little, Brown

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