Why does a random rota end arguments a fair rota does not?
A written rota can be perfectly fair and still be resented, because somebody wrote it. Whoever drew up the list chose who got the bathroom, and every week afterwards the list is evidence of a choice they made. A draw removes the author. The outcome can be worse and it will still be argued about less.
That is the whole mechanism, and it has nothing to do with luck. Nobody minds being chosen; they mind being assigned. What a household gets from the wheel is a process no one in the household can be accused of tilting, and that is worth more than an even split one person has to defend.
How do you weight the jobs that come round more often?
Give the daily jobs wider slices. Dishes at three, vacuuming and laundry at two, bins and the floor at one: the rim now shows the week’s actual workload rather than six equal names, and everybody can see which job is the big one before it is drawn.
Be clear about what that buys you, because elimination changes it. In a run where each person spins once, every job goes out exactly once whatever the weights are — they only decide the order. Weights start mattering when there are more jobs than people: the wide ones are the likeliest to find an owner before the wheel runs out, and the narrow ones are what waits until next week.
What if somebody draws the bathroom three weeks running?
It happens, and pretending it cannot is how a household stops trusting the wheel. With six jobs, the bathroom lands on one person about one week in six; three in a row is uncommon rather than impossible, and it is nobody’s doing.
The fix is to run elimination over something longer than a week. Put the four weeks of a month on one wheel with the names on it, draw the whole set at once, and each person carries one turn at the bathroom across the month instead of a fresh one-in-six every Sunday. Anything the wheel is not told, it cannot take into account.
What else is this wheel good for?
It is the plain picker wheel with a rota on it, so weights and elimination behave the way they do everywhere else. Where somebody in the house is too young to read the list, the picture wheel puts the job on the rim as a picture instead.
The same wheel with exercises on it hands out the next one on the workout wheel. With a class register on it rather than a job list, it becomes a classroom pick.