Cull and Waver

Cull spread her scoop over the poll. "First, the frame — who did we scoop? All ten were creatures loitering by the tart stall at noon." She smoothed the cloth. "We asked the folk already standing next to the berry-tarts; of course they leaned berry-tart. The honey-cake lovers were off at the cake stall, or at home, or working — never in the frame, so they couldn't have swung it however they felt. That's selection bias: the handful reports the tart corner and calls it the pond." She tapped the page. "Fix the frame — draw a little from every stall, the benches, the paths home, different hours — and at least the six-to-four stops being just the tart corner talking. But a fair frame is only the first half."

Then Waver drifted over the numbers, threads spreading wide. "Because even a perfectly fair ten," he said, "is a tiny sample, so whatever it says carries a wide margin." He set his threads a full hand's width to either side of the six. "From only ten answers, 'six out of ten' could as easily have come out five or seven purely by which ten wandered past — that's sampling error, and with n this small it's huge. The four-vote gap sits inside that wobble." His threads overlapped across both numbers. "So even after Cull makes the frame fair, ten is too few to crown anything. As far as ten answers can tell, the foods are tied — the lead is just the numbers breathing. A bigger handful would wobble narrower; ten wobbles too wide to be sure this close."

A young frog named Pip had been holding the festival banner, looking from one to the other in dismay. "You're each telling me something's wrong for a different reason. Cull, the ten weren't fair. Waver, ten's too few. Do I fix the fairness or the fewness?" Cull and Waver looked at each other and together said: "Both." "Watch," said Cull, and sent Pip round the whole festival — every stall, the benches, the paths home — to gather a fair handful this time, not just the tart corner. "And gather plenty," said Waver, hovering alongside. "The more you fairly ask, the narrower my threads close." Pip worked all afternoon and came back with sixty answers, drawn fairly from all through the festival. Cull checked the spread — every corner in it, no stall over-counted: representative. Then Waver hovered over the tally, thirty-one berry-tart, twenty-nine honey-cake, and drew his threads. This time, with sixty fair answers, they pulled in closer than before... and still, gently, overlapped across the two numbers.