The Accidental Math Behind Brookings' Quorum Notices

Anyone who has flipped through Brookings' public meeting calendar this summer might have noticed a peculiar pattern. A 4-H barbecue. A welcome cookout for new residents. A university career event. None of these are city council meetings, yet each one comes stapled to a formal notice warning that four or more council members “may be present,” and that, should this happen, “no official city business will be discussed or acted upon.”

It looks almost comic, a legal disclaimer glued onto a plate of ribs. But the reason it keeps happening is not bureaucratic overcaution. It is math, and a fairly elegant bit of it.

First, the legal backbone. South Dakota's open meetings law defines a “quorum” as the minimum number of members of a public body who must be present for that body to legally conduct business. For the Brookings City Council, that threshold is a majority of its eight members, so five, though the notices tend to flag any gathering of four or more just to be safe. The law's logic is simple: government decisions should happen in public, not sorted out informally between council members at a cookout while everyone else eats potato salad. So even the possibility of enough members being in the same room at the same time triggers a notice, whether or not any city business actually comes up.

Here is the part that surprises people: given how small Brookings is, and how many councilmembers there are, these overlaps are almost mathematically inevitable, not evidence of anything organized.

It works a bit like the famous “birthday paradox.” Most people assume it would take a room of nearly 365 people before two of them share a birthday. In reality, you only need 23 people in a room for the odds of a shared birthday to cross 50 percent. The reason is that you're not comparing one birthday to one target date, you're comparing every possible pair of people to every other pair, and the number of pairs grows much faster than the number of people. With 23 people, there are 253 possible pairs, each with its own small chance of a coincidence, and all those small chances add up quickly.

Brookings' council quorum notices run on a similar principle, just with people and events instead of birthdays. The city has eight council members. Brookings, with roughly 25,000 residents, hosts a steady stream of civic-adjacent gatherings: 4-H days, welcome barbecues, SDSU functions, ribbon cuttings, ag events. Council members, being locally prominent and generally interested in community life, tend to show up to a good share of them. If each member independently has even a modest chance of attending any given public event, the odds that four or more of the eight cross paths at the same event, purely by the ordinary rhythms of small-town life, climb surprisingly fast. Not because anyone is scheming, but because there are only so many gymnasiums, parks and event tents in a town this size, and only so many months in the year.

This is the quiet statistical undercurrent beneath a very mundane-looking city notice. The law is not particularly worried about barbecues. It is worried about the exception, the one time a coincidental gathering turns into an actual conversation about pending business. Since it is hard to know in advance which gathering that might be, the safer and more transparent approach is to flag them all, treating every plausible quorum as if it might matter, precisely because occasionally, statistically, one will.

It is a small, almost invisible piece of civic machinery, the kind of thing that only becomes interesting once you notice the pattern repeating on the calendar. But it is also a neat local example of a broader truth in probability: coincidences that feel meaningful are often just the visible tip of ordinary math, working quietly in the background of things as unglamorous as a summer cookout.