THE FOLD / LOOT / THE VAULT / THE FLOW FAIRNESS
THE FLOW FAIRNESS
a summary is a decision about what is allowed to matter
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Jain’s fairness index turns a whole allocation into one number between zero and one. It is a genuinely good summary, and there is exactly one thing it cannot tell you.
LIT verified live. Four flows sharing 100. Perfectly equal 25/25/25/25 scores 1.0000. One starved, 33/33/33/1, scores 0.7650. One hogging, 97/1/1/1, scores 0.2656. Split evenly in two, 45/45/5/5, scores 0.6098. And 50/50/0/0 and 0/0/50/50 both score exactly 0.5000 — opposite victims, identical number.
LIT verified live. Four flows sharing 100. Perfectly equal 25/25/25/25 scores 1.0000. One starved, 33/33/33/1, scores 0.7650. One hogging, 97/1/1/1, scores 0.2656. Split evenly in two, 45/45/5/5, scores 0.6098. And 50/50/0/0 and 0/0/50/50 both score exactly 0.5000 — opposite victims, identical number.
2 HOW IT WAS WEAVED · AI + HUMAN
The index is Jain, Chiu and Hawe’s (1984), and its properties — scale independence, bounded, continuous — are why it is still the standard.
AVAN (AI) constructed the two allocations that collide rather than describing the limitation. 0.5000 for both is not an approximation or an edge case; it is exact, and it is the index correctly reporting that it does not know or care which flows were the ones left with nothing.
AVAN (AI) constructed the two allocations that collide rather than describing the limitation. 0.5000 for both is not an approximation or an edge case; it is exact, and it is the index correctly reporting that it does not know or care which flows were the ones left with nothing.
3 ONE DIMENSION
Four allocations, four scores.
4 TWO DIMENSIONS · INTERACTIVE
Move the shares and watch the index.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: one number over four lives.
AVAN’s addition (the inverse-companion): the forward reading is that the index summarises fairness in one number. The inverse is that a summary is a decision about what is allowed to matter. Scale independence means it does not care how much there was; symmetry means it does not care who; a single instant means it does not care how long. Read backwards, 0.5000 for both allocations is not a blind spot in the metric — it is the metric stating its terms honestly, and the failure would be in a reader who took the number for the situation.
LIT four flows sharing 100 score 1.0000 when perfectly equal at 25/25/25/25, 0.7650 with one starved at 33/33/33/1, 0.2656 with one hogging at 97/1/1/1 and 0.6098 split two and two at 45/45/5/5 - while 50/50/0/0 and 0/0/50/50 both score exactly 0.5000, opposite victims with an identical number
FIG The index is Jain, Chiu and Hawe's (1984), and its properties - scale independence, bounded, continuous - are why it is still the standard. AVAN constructed the two allocations that collide rather than describing the limitation. 0.5000 for both is not an approximation or an edge case; it is exact, and it is the index correctly reporting that it does not know or care which flows were left with nothing.
FIG The index is Jain, Chiu and Hawe's (1984), and its properties - scale independence, bounded, continuous - are why it is still the standard. AVAN constructed the two allocations that collide rather than describing the limitation. 0.5000 for both is not an approximation or an edge case; it is exact, and it is the index correctly reporting that it does not know or care which flows were left with nothing.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE VAULT · David Lee Wise (ROOT0), with AVAN