(featured image: Michael L CC BY)
How to avoid awkward silences and uncivilized exchanges around the festive table
Chances are that you will either be hosting, or a guest at, a mega dinner party in the next few days. Yes, “It’s Christmas!”, as Noddy Holder has been yelling in his cosy West Midlands accent for 46 (!) years. Up and down the land, search parties are sent out to locate the once-a-year table extension leaves, extra tables and chairs are mobilized, spare crockery and cutlery retrieved from dark corners or borrowed from neighbours, in order to accommodate everybody.
A typical Christmas dinner will have 8-10 people round the table happily chatting amongst each other. The more the merrier? That is not so sure. A paper by experimental psychologists Jaimie Krems and Jason Wilkes (who is also a mathematician) observed that conversations rarely involve more than four individuals. The genuine difficulty of sustaining a casual conversation with five or more people even has a name: the ‘dinner party problem’. How come?
More than four is a crowd
The authors start from a biological explanation: our limited working memory. Earlier research has found that we have a hard time remembering more than about four chunks of information. Perhaps, over many generations of evolution, the neurobiological cost of being able to model more than three other minds in a conversation outweighed the benefits. That would explain why there is a limit.
But why four? To model human sociality, dyads are the relevant unit (you cannot be social as a singleton), so the authors look at the number of possible dyads in groups of increasing size. There is just one in a group of two, three in a group of three people (Alice and Bob, Alice and Chris, Bob and Chris), six in a group of four (add Dave and you get three more than with a group of three: Alice and Dave, Bob and Dave, and Chris and Dave), and so on, following the sequence of so-called triangular numbers: 1, 3, 6, 10, 15, … But is there something strange happening when the number of dyads goes from 6 (for a group of four) to 10 (for a group of five)?
Aha, there are two kinds of dyads, the authors argue: inclusive ones (the ones you’re part of) and exclusive ones. In a group of three people, there are two inclusive dyads (for Bob they are Alice and Bob, and Bob and Chris) and one exclusive one (Alice and Chris). For a group of four, there are three of each (respectively Alice and Bob, Bob and Chris, and Bob and Dave; and Alice and Chris, Alice and Dave, and Chris and Dave). From groups of five people onward, the number of exclusive dyads is ever larger than the number of inclusive ones.
So, in groups of four or less, Krems and Wilkes conclude, one would never be dyadically outnumbered. That would prove advantageous in, for example, building or maintaining one’s reputation, or persuading others by leveraging alliances. Just imagine having to do this with six other people, either in one group of seven, or in two groups of four. In the first case, there are 6 inclusive dyads and 15 exclusive ones, so you would be seriously outnumbered. In the latter case, both groups has 3 of each, so the ratio is (3+3)/(3+3) or 1 – nicely balanced.
So, don’t be too surprised if you find that, once again, there is not a big group chat involving everyone around the Christmas dinner table, but multiple parallel conversations in groups of four or less– it is entirely natural. And if you run out of things to talk about, you can always bore the people in your foursome to tears by explaining why.
At least, sticking to the science of the dinner party problem might keep you away from potentially awkward, heated discussions between family members with different political preferences. But should the conversation veer in that direction, do not panic.
A recent post by economist Bryan Caplan could serve as an interesting, unifying approach to keep political discussions civilized. The title of the piece could be the name of a parlour game: Explain your extremists. He offers six possible scenarios how people more extreme than you yourself could be accounted for. For example, they may be right, but their proposed policies would be unstable, and a momentary victory would be overturned before long – “it’s better to ask for half a loaf that you can keep than to demand a whole loaf that will soon be confiscated”. Or perhaps they are wrong, because they have taken a good idea too far – “it’s better to eat half a loaf and maintain a healthy body weight, than to have a whole one and become morbidly obese”.
So, as a first question everyone in your group of four could be asked to explain where the extremists on their side go wrong. This in itself is likely to bring everyone closer together. But there is more: if you think some others are more extreme than you, then more moderate others might think you are an extremist yourself. Where and how would they say you get it wrong? This too will tend to nudge the people around the table away from the extremities towards the centre. That is the moment where things can become really intellectual, and everyone can explain what makes them believe they have discovered their side’s golden mean. This might keep you going until you drop.
Guessing the quality of a gift
At some point, there will no doubt be some gift giving. Are they expensive? Are they high quality? And does the price paid for them reflect the quality? Even though we ‘know’ (scare quotes intentional) that dearer items are not necessarily better, we often implicitly (or even explicitly) use price as a proxy for quality. We see a pricey Swiss watch as higher quality than a cheap Chinese one, and an expensive wine as higher quality than an inexpensive one. Of course, the relationship, even in our mind, is not without fuzziness. We can think of examples of decent quality inexpensive products, and of poor quality high-priced ones: quality varies, even at a given price. And that variability may not be the same at different ends of the whole price range: maybe all expensive items are great, and there are good and bad ones among the cheap ones. Or maybe it’s the other way around – the inexpensive ones are all lousy, and some at the pricy end of the range are mediocre while others are splendid. That phenomenon is called heteroscedasticity (careful pronouncing it if you’re already a little merry!) – different subpopulations have different variability.
Research by psychologist Bart de Langhe and colleagues suggests that this can distort the way we evaluate the quality of an item by its price. If, for example, low priced items in a category are consistently of low quality, we overestimate the quality of expensive products in the same category. Likewise, when the high-priced items are consistently of good quality, then we tend to underestimate the quality of the inexpensive items. “Heteroscedasticity breeds extremity”, as the authors say. (If you’ve all been quaffing brandy, this tongue twister might be a good laugh by now.)
So, as the wrapping is coming off the presents, you can – silently if you want to avoid trouble – consider to what extent either the giver or the recipient of a gift may have fallen for heteroscedastic quality illusion. And what about the gifts you yourself bought for others – is that expensive gift for Aunt Jo really as good as its price suggests? Now you know how heteroscedasticity messes up how you link quality and price, you will never be able to look at gifts with innocent eyes again.
And should you, at this time in the Christmas proceedings, still need another topic of conversation in your foursome (and you are all still sober enough), you could shift the discussion towards heteroscedasticity in beer, clothing, cars, or supermarket brands. Entertainment guaranteed.