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Why incomplete evidence does not always mean unknown

Can a partial count ever settle a governance question?

By João Livio·pH7x Knowledge

30-second answer

Yes, on one side of the comparison. Evidence collection is monotonic: collecting more can add to what was seen and never remove it. A collector that stopped at 20,000 items saw at least 20,000, so "is the count above 10,000?" is already settled, while "is it below 50,000?" is not.

What this proves

A partial count is a lower bound, and a lower bound decides every comparison that only needs the low side. Against a threshold, one side of each operator is final the moment the bound crosses it.

What it does not prove

  • The exact value. A lower bound of 20,000 is compatible with 20,001 and with two million.
  • Anything on the open side. Without an upper bound, "fewer than X" can never be concluded from partial evidence, no matter how thorough the partial collection felt. A tool that concludes it is guessing.

PowerShell

powershell
# A site owner list that includes one unexpanded group:
# 1 named person + 1 group of unknown size
$namedPeople = 1
$unexpandedGroups = 1
$atLeast = $namedPeople + $unexpandedGroups   # every group holds >= 1 principal

if ($atLeast -ge 2) { "at least $atLeast owners: the two-owner rule passes" }
else { "cannot conclude: expansion needed" }

Example output

text
at least 2 owners: the two-owner rule passes

Explanation

The example is the real case. A rule requiring two owners can pass on a site with one person and one unexpanded group, because whatever the group holds, the total is at least two. The same evidence can never make the rule fail: failing needs "fewer than two", which needs an upper bound, which partial expansion does not provide. This split, provable pass on one side and honest unknown on the other, is what separates reasoning from optimism when the data is incomplete.

Production considerations

  • Record bounds as bounds. The moment a partial count is stored as a plain number, the next reader treats it as exact and the reasoning above silently breaks.
  • Equality can never be decided from a bound alone; only ordered comparisons have a decidable side.
  • State why the collection stopped (throttling, permission, page limit); the reason determines whether collecting more is possible at all.

References