There are three possible ways for two couples to arrange themselves around a table, 60 ways for three couples to sit, and 2,520 ways for four couples to make themselves comfortable. The likelihood that guests at a scaled-up sit-down will settle on an envy-free arrangement — one in which no one wants to switch with someone else — is negligible. The odds a host will triangulate a similarly accommodating geometry are similarly low if that host thinks in terms of Ben enjoys talking to Sarah about Pickleball. But there's a workaround. Three (presumably fondue-addled) Swiss computer scientists found it [1].
Don't think about Ben or Sarah, or, heaven forfend, Pickleball. Think about archetypes. Seating arrangements become a far more tractable mathematical problem when hosts stop modeling guests as individuals and start by sorting them into archetypes with consistent preferences. Because consistent preferences limit the number of possible arrangements, the asymptotic explosion of seating options never occurs. Relatively few arrangements make sense. And the only social math required is classifying the guests – something we all do anyway.
