Normal Distribution
nothing is called 95% until it has been counted
Field

What decides whether a tuning list decides

The probability that a per-candidate tuning list changes which candidate a table selects is reported flat at about an eighth across list length, on a table and a world that are never varied. Vary how far apart the candidates are — one multiplier on the omitted coefficients, everything else held — and it runs from 17.6% to 1.5%, while the disagreement rate it is a factor of rises from 31.8% to 88.8%. The world where the candidates quarrel most about the tuning parameter is the world where the quarrel matters least, and a nested table turns over less rather than more.
The eighth was not a constant. The probability that a per-candidate tuning list changes which candidate the table selects, at each of 5 separations between the candidates, over 800 draws apiece. The earlier field reports this flat at about an eighth across list length, on a table and a world it never varies. Vary how much the omitted coefficients are worth — one multiplier, with the table, the list, the law and the sample size all held — and it runs from 17.6% to 1.5%, a factor of 11.75. The world in which every candidate is true is the world in which the tuning list decides most; the world in which one candidate dominates is the world in which it decides nothing.

The eighth that was not a constant

How often a per-candidate tuning list changes which candidate wins is reported flat at about an eighth across list length. Vary how far apart the candidates are instead and it runs from 17.6% to 1.5%.

 Two factors, opposite directions. The two factors the cost of a per-candidate tuning parameter is a product of, as the candidates are pulled apart, over 800 draws at each of 5 separations. How often the candidates disagree about the tuning parameter rises from 31.8% to 88.8%; the share of those disagreements that change which candidate the table selects falls from 51.6% to 1.7%. So the setting where the candidates quarrel most about the tuning parameter is the setting where the quarrel matters least, and a sweep that reads the rate and stops has read the factor pointing the wrong way.

Two factors pointing opposite ways

As the candidates on a table are pulled apart, they quarrel about the tuning parameter three times as often and the quarrel decides the winner thirty times less often. A sweep that reads the first factor has read the one pointing the wrong way.

 Flat along a row, apart between them. The probability that a per-candidate tuning list changes the winner, at three list lengths on three candidate tables, over 800 draws in each of the nine cells. Along a row — the reading the earlier field takes — it moves by a factor of at most 1.21, so that field's invariant survives on every table. Down a column it moves by up to 1.98. The list length is the dial that does not move this number and the table is one that does, and the earlier field varied only the first.

A table and a list

A nested ladder of candidates differing by one coefficient was predicted to turn over more often at every list length. It turns over less at every one, and its list changes the winner half as often.

 The same dial, on a list that steps by one. The probability that a per-candidate tuning list changes which candidate the table selects, at each of 5 separations, for both tuning parameters at a matched list length of 8, with errors from a first-order autoregression. The sieve order runs from 13.1% to 2.6%, a factor of 5.00; the whitening window, from 16.4% to 1.5%, a factor of 11.75. What is held is the number of options, the table, the law, the sample size and the seeds; what cannot be held is the size of a step, since an integer step and a geometric step are different amounts of change. The dial moves both, and it moves them by 2.35 times as much on one as on the other.

A step that is not a ratio

Run the separation sweep on a tuning list of integers rather than a geometric ladder and the two factors still point opposite ways. The invariant does not survive: along a row of integers the probability moves by 2.163 where along the geometric ladder it moves by 1.208.

 The same dial, on a list that steps by one. The probability that a per-candidate tuning list changes which candidate the table selects, at each of 5 separations, for both tuning parameters at a matched list length of 8, with errors from a five-period moving average. The sieve order runs from 29.5% to 5.8%, a factor of 5.13; the whitening window, from 26.3% to 4.8%, a factor of 5.53. What is held is the number of options, the table, the law, the sample size and the seeds; what cannot be held is the size of a step, since an integer step and a geometric step are different amounts of change. The dial moves both, and it moves them by 1.08 times as much on one as on the other.

The same dial under a second law

On a first-order autoregression, separating the candidates moved the chance that a tuning list changes the winner 2.35 times as far on a whitening window as on a sieve order, and the difference was put down to the step: an integer step is worth a third of a geometric one. Rerun the whole sweep with errors from a five-period moving average and the difference is gone — the probability spans a factor of 5.53 on the window and 5.13 on the order, a ratio of 1.08 — and near the null both lists leave about five and a half candidates within reach, where the autoregression left 3.6 and 1.9. The two factors still point opposite ways under both laws. The step's size was a property of the law the lists were tuned on.

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