Equitable weekend and holiday rotation
Weekend and holiday rotation is the part of scheduling where the arithmetic is simple, the drift is invisible, and the resentment is durable.
The problem with "just rotate"
A list of eight people and a rotation through weekends is the obvious scheme and it fails in three ways.
Leave breaks the sequence. Someone away for their turn is skipped. Unless something records that they owe a turn, they have permanently gained one and everyone after them has permanently lost a position.
The group changes. Somebody leaves, somebody joins, somebody goes part-time. The new rotation is built from the current list, and everything accrued under the old one is forgotten — which systematically favours whoever has been there longest, because their skipped turns are the ones that got lost.
The calendar does not cooperate. Holidays do not fall evenly across the weeks of a rotation. With four major holidays and a rotation of six, the holidays land on the same two or three positions year after year.
Each of these is individually small and none of them self-corrects. They accumulate.
What the arithmetic requires
Equity over a long horizon needs three things that a rotation list does not have:
A count, not a position. Store how many weekends and holidays each person has taken, not where they are in a list. A count survives leave, a change of share, and the group changing size.
A share. Each person's expected count is their share of the total. For a full-time clinician that is the group average; for someone at 0.5 it is half. The measure of fairness is the gap between actual and expected, not the raw count.
A window. The horizon over which the gap should be near zero. Holidays need years; weekends need about a year.
Given those three, the assignment rule is just: next turn goes to whoever is furthest below their expected count. That self-corrects after leave, after a change of share, and after someone joins — because a new joiner starts at zero actual and zero expected, and accrues both.
Holidays specifically
Holidays deserve separate counting from weekends, because they are a different burden and because there are few of them.
With four holidays a year and a group of eight, each person should take one holiday every two years. Over a four-year window that is two each. Anything that tracks only this year cannot distinguish a person who has taken two from a person who has taken none, and both will be correct about how they feel.
Counting them individually — Christmas separately from Thanksgiving — is worth doing if the group considers them unequal, which most do. Otherwise someone can take four consecutive Christmases while their holiday count looks fair.
What to do about a legacy imbalance
A group adopting this will have an existing imbalance and no record of it. There are two honest options:
Start from zero and accept that past imbalance is not corrected. Simple, and unsatisfying for whoever is owed.
Seed the counts from whatever record exists, even an approximate one. A rough starting balance that the group agrees is roughly right is better than a clean slate everyone knows is wrong.
The second usually works better, because the imbalance people care about is recent and recent history is usually recoverable.
Common questions
Why does a simple rotation become unfair?
Because the rotation period and the calendar do not divide evenly, and because people join, leave and change their share. A rotation of eight people through weekends drifts the moment one of them is on leave for a turn, and the drift is never corrected unless something tracks it.
How long a window is needed for holiday equity?
Long enough that each major holiday comes round for everyone — so for a group of six sharing four holidays, several years. Any window shorter than that cannot see the imbalance it is meant to prevent.