Equality of Opportunity in Supervised Learning — TEI-tagged view

Moritz Hardt, Eric Price, Nathan Srebro · 2016 · law · arXiv:1610.02413 · full text at the source · TEI xml · tagged edition · index · concepts · authors
Where this record's text came from. faceted 2026-08 by reading the locally held text (pdftext); every evidence string verified as an exact substring of that text before merging. The paper is primarily a definitional and theoretical contribution (proofs of Bayes optimality, near-optimality, and unidentifiability) plus an empirical case study on 301,536 TransUnion TransRisk FICO scores; the controlled method vocabulary has no 'theory' value, so system-or-tool-building was chosen for the post-processing construction. The FICO study is an illustrative case study, not a hypothesis test, so replication status is untested. 2026-08-14, 2026-08-15 and 2026-08-17 schema-0.3 passes: every quote verified as an exact substring of the staged text and anchored at merge time; concept terms verified present; every edge endpoint an existing node.
Some quotes on this page contain (cid:NN). The PDF this text was extracted from encodes 17 characters in a way that names no letter, so the extractor could not say what they were. The quotes keep them because a quote is reproduced exactly or it proves nothing — the marks are the source’s, not the tagging’s.
Other fields define these differently the same word, defined another way in another discipline
supervised learning 3 fields · discrimination 2 fields · classification 2 fields · fairness 2 fields
Tags on this paper every tag the record carries, whether or not the words occur in the text below — a number is how many papers in the corpus carry that tag; a tag with no number is unique to this paper
fairness7 equalized odds2 discrimination12 supervised learning15 protected attribute equal opportunity2 demographic parity2 oblivious fairness through unawareness2 system-or-tool-building173

Our tag layer for this paper

Cross-disciplinary analysis
content-tags & facets: phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text
phenomenondiscrimination against protected attributes in supervised learning— “As machine learning increasingly affects decisions in domains protected by anti-discrimination law, there is much interest in algorithmically measuring and ensuring fairness in machine learning.”
claim-typemethod— “We propose a simple, interpretable, and actionable framework for measuring and removing discrimination based on protected attributes.”
method — evidence— “We give a simple and effective framework for constructing classifiers satisfying our criterion from an arbitrary learned predictor.”
mechanismA NAMED APPROACH IS SHOWN NOT TO DO WHAT ITS NAME PROMISES: `fairness through unawareness` - simply ignoring the protected attributes - is called INEFFECTIVE, because redundant encodings let the protected attribute be predicted from other features anyway. Removing the variable does not remove the information— “However, this idea of “fairness through unawareness” is ineffective due to the existence of redundant encodings, ways of predicting protected attributes from other features [PRT08].”mechanisms[0]
mechanismAN ESTABLISHED CRITERION IS SATISFIED BY EXACTLY THE BEHAVIOUR IT WAS MEANT TO FORBID: demographic parity PERMITS accepting qualified applicants in one group and UNQUALIFIED individuals in the other, so long as the acceptance percentages match - and the authors add that this can arise NATURALLY when one group has little or no training data. The criterion is not merely weak; it is passed by the discrimination it names— “Unfortunately, as was already argued by Dwork et al. [DHP+12], the notion is seriously flawed on two counts. First, it doesn’t ensure fairness. Indeed, the notion permits that we accept qualified applicants in the demographic A = 0, but unqualified individuals in A = 1, so long as the percentages of acceptance match. This behavior can arise…mechanisms[1]
mechanismA CRITERION IS SHOWN TO FORBID THE GROUND TRUTH: demographic parity would not allow the ideal predictor that simply equals the true outcome - which, the authors say, CAN HARDLY BE CONSIDERED DISCRIMINATORY as it represents the actual outcome. The case arises whenever the target is correlated with the protected attribute— “Second, demographic parity often cripples the utility that we might hope to achieve. Just imagine the common scenario in which the target variable Y —whether an individual actually defaults or not—is correlated with A. Demographic parity would not allow the ideal predictor (cid:98)Y = Y , which can hardly be considered discriminatory as it…mechanisms[2]
mechanismTHE NEW CRITERION IS ENGINEERED SO THE PERFECT PREDICTOR ALWAYS PASSES, AND SO THAT IT GETS EASIER AS ACCURACY RISES: the authors state that unlike demographic parity theirs always allows the perfectly accurate solution, and that the criterion is easier to achieve the more accurate the predictor is - explicitly ALIGNING fairness with the existing objective of supervised learning rather than trading against it— “Unlike demographic parity, our notion always allows for the perfectly accurate solution of (cid:98)Y = Y . More broadly, our criterion is easier to achieve the more accurate the predictor (cid:98)Y is, aligning fairness with the central goal in supervised learning of building more accurate predictors.”mechanisms[3]
mechanismTHE CRITERION PERMITS ONE ROUTE AND PROHIBITS ANOTHER BETWEEN THE SAME TWO VARIABLES: the prediction may depend on the protected attribute but ONLY THROUGH the target, so the definition ENCOURAGES features that predict the target directly and PROHIBITS abusing the protected attribute as a proxy for it. What the definition constrains is the PATH the dependence takes— “Unlike demographic parity, equalized odds allows (cid:98)Y to depend on A but only through the target variable Y . As such, the definition encourages the use of features that allow to directly predict Y , but prohibits abusing A as a proxy for Y .”mechanisms[4]
mechanismA PROPERTY IS DEFINED FOR PROPERTIES, NOT FOR PREDICTORS: `oblivious` is given a formal definition one level up - a PROPERTY of a predictor or score is oblivious if it depends only on the joint distribution of outcome, protected attribute and prediction. The definition's subject is other definitions— “A property of a predictor (cid:98)Y or score R is said to be oblivious if it only depends on the joint distribution of (Y , A, (cid:98)Y ) or (Y , A, R), respectively.”mechanisms[5]
mechanismTHE CRITERION IS RESTRICTED TO WHAT IS OBSERVABLE, AND THE RESTRICTION IS JUSTIFIED BY OBSERVABILITY RATHER THAN BY CORRECTNESS: in many cases only oblivious analysis is POSSIBLE, because the functional form of the score and the training data are not public - and going beyond it would require SUBJECTIVE INTERPRETATION or, as the paper prints it, `casual` assumptions about specific features (causal is meant), WHICH THE AUTHORS AIM TO AVOID. The definition is cut to fit what can be seen— “In many cases, only oblivious analysis is possible as the functional form of the score and underlying training data are not public. The only information about the score is the score itself, which can then be correlated with the target and protected attribute. Furthermore, even if the features or the functional form are available, going beyond…mechanisms[6]
mechanismA WEAKER CRITERION IS OBTAINED BY RESTRICTING THE STRONGER ONE TO ONE OUTCOME, AND WHICH OUTCOME IS AN INTERPRETIVE CHOICE: the authors say they OFTEN THINK OF one value as the ADVANTAGED outcome, then relax the requirement to hold only within that group, WITHOUT SPECIFYING ANY REQUIREMENT for those who will ultimately default - and name the result `equal opportunity`. The asymmetry that makes the weaker notion weaker is supplied by the reading of the outcome, not by the mathematics— “In the binary case, we often think of the outcome Y = 1 as the “advantaged” outcome, such as “not defaulting on a loan”, “admission to a college” or “receiving a promotion”. A possible relaxation of equalized odds is to require non-discrimination only within the “advantaged” outcome group. That is, to require that people who pay back their…mechanisms[7]
mechanismTHE CRITERION IS PRESENTED IN TERMS OF WHERE IT PUTS THE COST: it is described as SHIFTING THE BURDEN OF UNCERTAINTY from the protected class to the decision maker, and thereby INCENTIVISING the collection of better features - ones depending more directly on the target than on the protected attribute - and of data allowing better prediction for all groups— “It can also be viewed as shifting the burden of uncertainty in classification from the protected class to the decision maker. In doing so, our notion helps to incentivize the collection of better features, that depend more directly on the target rather then the protected attribute, and of data that allows better prediction for all protected…mechanisms[8]
mechanismTHE PAPER PROVES THE LIMIT OF ITS OWN ENTIRE FAMILY OF DEFINITIONS: a NON-IDENTIFIABILITY result shows that different dependency structures, WITH POSSIBLY DIFFERENT INTUITIVE NOTIONS OF FAIRNESS, cannot be separated by ANY oblivious notion or test - not merely by theirs. The contribution is a proof about what the class of measures cannot see— “We capture the inherent limitations of our approach, as well as any other oblivious approach, through a non-identifiability result showing that different dependency structures with possibly different intuitive notions of fairness cannot be separated based on any oblivious notion or test.”mechanisms[9]
mechanismTWO SITUATIONS THAT DIFFER IN EXACTLY THE WAY THE CONCEPT IS SUPPOSED TO TRACK ARE SHOWN TO BE INDISTINGUISHABLE: the authors construct two dependency structures which can have FUNDAMENTALLY DIFFERENT INTERPRETATIONS FROM THE POINT OF VIEW OF FAIRNESS and yet be indistinguishable from their joint distribution - so no oblivious test can resolve which applies— “We will argue that while these two scenarios can have fundamentally different interpretations from the point of view of fairness, they can be indistinguishable from their joint distribution. In particular, no oblivious test can resolve which of the two scenarios applies.”mechanisms[10]
mechanismACCESS TO THE FEATURES DOES NOT RESCUE IT - THE PAPER CLOSES ITS OWN LOOP: without ATTACHING MEANING to the features or making CAUSAL ASSUMPTIONS about them, no further insight into the two scores is gained. Subjective interpretation was excluded in order to make the criterion objective, and here the authors state that without it nothing more can be learned— “Without attaching meaning to the features or making causal assumptions about them, we do not gain any further insight on the two scores.”mechanisms[11]
mechanismA PROPERTY IS NAMED, GIVEN A USEFUL MEANING, AND THEN SHOWN NOT TO MEAN WHAT IT SOUNDS LIKE: having MATCHING conditional ROC curves does correspond to being deterministically correctable to non-discrimination - but the authors state plainly that it DOES NOT AT ALL mean the score is itself non-discriminatory, since it can be biased according to the protected attribute and need correcting— “But as our examples show, having matching ROC curves does not at all mean the score is itself non-discriminatory: it can be biased according to A, and a (deterministic) correction might be necessary in order to ensure equalized odds.”mechanisms[12]
mechanismA PROPERTY OFFERED AS A FAIRNESS MEASURE IS EQUIVALENT TO THE SCORE USING EVERYTHING THE PROTECTED ATTRIBUTE OFFERS: matching conditional frequencies means the score includes ALL POSSIBLE INFORMATION the protected attribute can provide about the target, so the score is IN A SENSE OPTIMALLY DEPENDENT on that attribute— “That is, the score R includes all possible information the protected attribute can provide on the target Y . Indeed having matching conditional frequencies means that the score is in a sense “optimally dependent” on the protected attribute A.”mechanisms[13]
contradicts fairness through unawareness (ignoring protected attributes)— “is ineffective due to the existence of redundant encodings”claim_relations[0]
builds-on Dwork et al. [DHP+12], "Fairness through Awareness"— “Unfortunately, as was already argued by Dwork et al. [DHP+12], the notion is seriously flawed on two counts.”claim_relations[1]
builds-on Kleinberg, Mullainathan and Raghavan [KMR16] on calibration within groups— “In a recent concurrent work, Kleinberg, Mullainathan and Raghavan [KMR16] showed that in general a score that is calibrated within each group does not satisfy a criterion equivalent to equalized odds for binary predictors.”claim_relations[2]
contradicts demographic parity as a non-discrimination criterion— “We argue that, unlike demographic parity, our framework provides a meaningful measure of discrimination, while demonstrating in theory and experiment that we also achieve much higher utility.”claim_relations[3]
senseequal opportunity vs equalized odds - TWO CRITERIA, ONE STRICTLY WEAKER, AND THE PAPER PRICES THE GAP: equal opportunity relaxes equalized odds to the advantaged outcome group only, and in the case study equal opportunity keeps 92.8% of maximal profit against equalized odds' 80.2%, so a claim citing 'Hardt et al.' without saying which criterion is a claim about neither— “Equal opportunity is a weaker, though still interesting, notion of non-discrimination, and thus typically allows for stronger utility as we shall see in our case study”senses[0]
senseoblivious - IN A FORMAL SENSE THE PAPER DEFINES: a property is oblivious if it depends only on the joint distribution of target, protected attribute and prediction, which is what makes the criterion checkable from published statistics and also what makes it blind— “In line with other studies, our notion is oblivious: it depends only on the joint statistics of the predictor, the target and the protected attribute, but not on interpretation of individual features”senses[1]
sensedemographic parity - THE CRITERION THIS ONE IS DEFINED AGAINST: it requires the decision to be independent of the protected attribute, which the authors reject because it forbids the perfectly accurate predictor and costs the most utility of the four thresholds they compare— “Demographic parity requires that a decision—such as accepting or denying a loan application—be independent of the protected attribute”senses[2]
differs indemographic parity as a non-discrimination criterion — THE AXIS IS THE FAIRNESS CRITERION. 'We argue that, unlike demographic parity, our framework provides a meaningful measure of discrimination, while demonstrating in theory and experiment that we also achieve much higher utility.' Two criteria, and the disagreement is over which one MEASURES discrimination - not over any fact about a dataset.— “We argue that, unlike demographic parity, our framework provides a meaningful measure of discrimination, while demonstrating in theory and experiment that we also achieve much higher utility.”— “unlike demographic parity, our framework provides a meaningful measure of discrimination”claim_relations[3]
evidence status noteconcept — DAMAGED GLYPHS IN THIS QUOTE: (cid:98). These are raw PDF font glyph indices that leaked out in place of the characters they stand for - usually a mathematical operator. The quote is verbatim to the staged text and its anchor is sound; the STAGED TEXT is what is damaged. NOT repaired: the cid-to-character mapping is defined by the font embedded in that particular PDF, so guessing it would produce a clean and unverifiable quote. Repair needs the source PDF and is a re-staging job.— “Unlike demographic parity, equalized odds allows (cid:98)Y to depend on A but only through the target variable Y . As such, the definition encourages the use of features that allow to directly predict Y , but prohibits abusing A as a proxy for Y”concepts[1]
for which uselimitation — everything the criterion can detect: IT DEPENDS ONLY ON THE JOINT STATISTICS OF THE PREDICTOR, THE TARGET AND THE PROTECTED ATTRIBUTE, BUT NOT ON INTERPRETATION OF INDIVIDUAL FEATURES— “it depends only on the joint statistics of the predictor, the target and the protected…limitations[0]
for which uselimitation — any use of the criterion as a fairness certificate: SATISFYING OUR NOTION (OR ANY OTHER OBLIVIOUS MEASURE) SHOULD NOT BE CONSIDERED A CONCLUSIVE PROOF OF FAIRNESSlimitations[1]
for which uselimitation — every application of the method: HAVING ACCESS TO RELIABLE LABELED DATA IS NOT ALWAYS POSSIBLE, and the labels may themselves carry the bias being measuredlimitations[2]
for which uselimitation — the optimality claim: THIS DOES NOT MEAN THAT THE PREDICTOR IS NECESSARILY GOOD IN AN ABSOLUTE SENSE - near-optimality is relative to other constrained predictorslimitations[3]
for which uselimitation — a verdict of non-discrimination obtained from this criterion: the authors show no oblivious test can resolve which of two dependency structures applies, so two scenarios with different intuitive fairness are indistinguishable to itlimitations[4]
for which uselimitation — the suggestion that inspecting the model's features would settle what this test cannot: the authors state that without attaching meaning to the features or making causal assumptions about them, no further insight is gained
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
limitations[5]
for which uselimitation — the deployment of this criterion on individual decisions: achieving it cannot be done with a single threshold per group and requires randomization
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
limitations[6]
for which uselimitation — the incidence of the utility cost reported here: the authors state the cost is borne by the company using the classifier, which can invest in better classification, rather than by the classified group, which cannot
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
limitations[7]
evidence status notemechanism — The span contains '(cid:98)Y', which is Y-hat - the circumflex accent failed to map and the extraction emitted a glyph code. 367 of these are in this file and almost all are this same hat. The quote is an exact substring and anchors correctly; the mathematics is unreadable in it. Damage shape 6. Unavoidable here: the sentence's subject IS the predictor.
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
mechanisms[2]
evidence status notemechanism — The span contains '(cid:98)Y', which is Y-hat - the circumflex accent failed to map and the extraction emitted a glyph code. 367 of these are in this file and almost all are this same hat. The quote is an exact substring and anchors correctly; the mathematics is unreadable in it. Damage shape 6. Unavoidable here: the sentence's subject IS the predictor.
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
mechanisms[3]
evidence status notemechanism — The span contains '(cid:98)Y', which is Y-hat - the circumflex accent failed to map and the extraction emitted a glyph code. 367 of these are in this file and almost all are this same hat. The quote is an exact substring and anchors correctly; the mathematics is unreadable in it. Damage shape 6. Unavoidable here: the sentence's subject IS the predictor.
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
mechanisms[4]
evidence status notemechanism — The span contains '(cid:98)Y', which is Y-hat - the circumflex accent failed to map and the extraction emitted a glyph code. 367 of these are in this file and almost all are this same hat. The quote is an exact substring and anchors correctly; the mathematics is unreadable in it. Damage shape 6. Unavoidable here: the sentence's subject IS the predictor.
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
mechanisms[5]
evidence status notemechanism — RE-SLICED. My first cut ran straight through a WORD-ORDER SCRAMBLE (damage shape 5): the staged text reads "since the distributions , (cid:101)R) agree ... The over (Y , A, R features are correlated", with two clauses interleaved and a superscript hoisted. It would have been perfectly verbatim and unreadable. The span now keeps only the closing sentence, which carries the claim and is clean.
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
mechanisms[11]
replicationuntested
limitationthe criterion is oblivious - it uses only joint statistics, not the interpretation of individual features
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
limitations[0]
limitationSatisfying the proposed oblivious criterion is not a proof of fairness (nor is violating it a proof of unfairness).
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
limitations[1]
limitationThe criterion requires reliable observed outcome labels, which are not always available and may themselves be biased.
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
limitations[2]
limitationThe near-optimality guarantee is relative to other constrained predictors only; the derived predictor need not be good in absolute terms.
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
limitations[3]
limitationNo test of this kind can tell two situations apart, and the authors prove it about their own class of test.
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
limitations[4]
limitationAccess to the features does not rescue the test, without assumptions the authors decline to make.
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
limitations[5]
limitationMeeting the criterion can require deciding individual cases partly at random.
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
limitations[6]
limitationWho pays for the fairness is a property of the design, and the authors name the payer.
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
limitations[7]
Content tags
content-observations: finding · quantity · variable · definition · key-term — grounded in the full text
findingdemographic parity is seriously flawed on two counts
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
content_tags.findings[0]
findingfairness through unawareness fails because of redundant encodings
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
content_tags.findings[1]
findingtheir criterion always permits the perfectly accurate predictor
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
content_tags.findings[2]
findingthe criterion aligns fairness with predictive accuracy
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
content_tags.findings[3]
quantity2 counts — ways demographic parity is flawed
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
content_tags.quantities[0]
quantityMay 2014 date — Obama Big Data report warning on discrimination
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
content_tags.quantities[1]
variableprotected attribute A (attribute non-discrimination is defined against)
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
content_tags.variables[0]
variabletarget Y (true outcome to predict)
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
content_tags.variables[1]
variablepredictor (model constructed from labeled data)
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
content_tags.variables[2]
variablefeatures X (inputs not evaluated by the oblivious test)
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
content_tags.variables[3]
definitiondemographic parity
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
content_tags.definitions[0]
definitionfairness through unawareness
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
content_tags.definitions[1]
definitionoblivious notion
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
content_tags.definitions[2]
definitionequal opportunity by design
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
content_tags.definitions[3]
key-termsdiscrimination, supervised learning, protected attribute, fairness, demographic parity, predictor, equality of opportunity, oblivious, sensitive attribute, classification
Concepts
terms this paper carries, each with the sentence it was cut from — the layer that joins one paper to another. Terms with no quote yet are on CONCEPTS.html.
conceptequalized odds
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
concepts[1]
conceptequal opportunity
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
concepts[5]
conceptdemographic parity
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
concepts[6]
conceptoblivious
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
concepts[7]
conceptfairness through unawareness
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
concepts[8]
Statistics — cross-field join keys
field-invariant statistical terms, used in their statistical sense (gated on a number / symbol / test). A p-value or a standard deviation means the SAME thing in physics, biology, psychology and sociology — so these are the strongest cross-field join keys. Grounded verbatim.
Bayesian
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
content_tags.statistics[0]

When we have changed our mind. Some entries in the table begin with a word in capitals and the reason for it. EVIDENCE CORRECTED — the finding still stands, but we had quoted the wrong sentence from the paper, and the quotation has been replaced with the right one. RETRACTED — the entry itself was wrong; it stays on the page, marked, with the reason, rather than being deleted. WITHDRAWN AND REPLACED — the entry was wrong, and a corrected version of it appears in the entries below. Each mark carries its own reason, in brackets, because the reasons differ from one entry to the next. An entry we have WITHDRAWN is removed from this page and kept in the record, with its reason. A line reading Audit and a date is a later re-reading of the entry against its whole sentence: DOUBTFUL means it was kept, and the reason says what is loose about it. Quotation marks inside the tagger's sentence. Where a tag is the tagger's own sentence, a phrase in quotation marks inside it is borrowed from the paper — the tagger's wording around it is not. The paper's own sentence is the evidence quote for that row; on this page it is withheld with the article, and the article is at its publisher. Nothing inside quotation marks anywhere on this page is ours: if it is quoted, it is the paper's. Whose words a concept carries. A concept entry records a term the paper itself uses, so the term, the sense given for it, and its evidence are the paper's own words, quoted where the paper fixes them. This is the opposite of a sense entry in the tag table, which is the tagger's sentence about how the paper uses a term. Where a concept entry could not be grounded in the paper's words, the entry says so on its own row.

Tag layer © the Meta-Tagging Project, CC BY 4.0. The paper text is © its authors/publisher and is linked, not reproduced. Excerpts shown are short quotations for identification and verification. · back to index · concepts · authors · עברית
© 2026 Shir Sivroni · ORCID 0009-0000-2597-2824