Robin Hood index instrument
| Definition | The fraction of a total count that would have to move from points above the mean to points below it to make every count equal. Equation 0.35. Also Robin Hood. |
|---|---|
| Example | If 20 percent of the rows take 60 percent of the retrievals, the Robin Hood index is 0.40. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id robin-hood-index, kind instrument. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation 0.35. |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/RobinHood.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation 0.35.
\[\mathrm{RH}=\sum_i\max\!\Big(0,\ \frac{N_i}{\sum_j N_j}-\frac1n\Big).\]
Conditions
- The fraction of the total count that would have to move from points above the mean to points below it to make every count equal, the excess above the mean over the total, which is half the total absolute deviation over the total. It is nonnegative, zero exactly at equality, at most one, and unchanged by a common scaling of the counts.
- The strata design reports it per area beside the skew, and the first run’s ratio of 1.30 against a bar of 1.5 is the number the abstention rule was written around.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Hoover’s index of concentration, applied to neighbour counts in
turboquant-pro’s strata design,
turboquant-pro/docs/STRATA_RFC.md:24-98, and chapter 0
section 0.16 of Data Mining as Observation.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/RobinHood.lean,
theorems sum_dev, excess_eq_half_abs,
robinHood_nonneg, robinHood_eq_zero_iff,
robinHood_le_one, robinHood_scale, at
observation-data-mining f3914f0; what the check covers is stated in the
book’s appendix
C.
Used in
Data Mining as Observation chapters 0, 10.
Related
hubness; anti-hub; Poisson ceiling; abstention.
See also
Book equations stated beside the entry’s terms, not defining it: 10.4.
Ledger rows that cite the entry’s records without naming it: NEG-14.
Sources-table rows that share a record with the entry without naming it: chapter 10 section 10.4.
Status
Generated 2026-09-10 by encyclopedia/generate.py; book
at observation-data-mining f3914f0; the commit of every record is listed
in the encyclopedia’s provenance.