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10 is the safest number that there's ever been

Ritchie, Felix

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When checking frequency and magnitude tables for disclosure risk, the cell threshold (the minimum number of observations in each cell) is a crucial parameter. In rules-based environments, this is a hard limit on what can or can't be published. In principles-based environments, this is less important but has an impact on the operational effectiveness of statistical disclosure control (SDC) processes. Determining the appropriate threshold is an unsolved problem. Ten is a common threshold value for both national statistics and research outputs, but five or twenty are also popular. Some organisations use multiple thresholds for different data sources. These higher thresholds are all entirely subjective. Three is the only threshold which has an objective statistical foundation, but most organisations argue that this leaves little margin for error. Unfortunately, there is no equivalent statistical case for any number larger than three: ten is popular because it is popular. This is particularly the case for research environments, where there is no guidance. This paper provides the first empirical foundation for threshold selection by modelling alternative threshold values on both synthetic data and real datasets. The paper demonstrates that this is a complex question. The trade-off between risk and value is well-known, but we demonstrate that the protection of a higher threshold depends on the risk measure. There is no monotonic relation between a threshold and risk, as higher thresholds can increase disclosure risk in particular scenarios. The blind application of high-threshold rules might mask new risks. There is no unambiguous result, other than the simplistic ones that more observations reduces risk and higher thresholds reduce utility. Finally, the paper notes that a reconsideration of disclosure checking practices can reduce risk irrespective of the threshold for some risk scenarios.


Ritchie, F. (2022). 10 is the safest number that there's ever been. Transactions on data privacy, 15(2), 109-140

Journal Article Type Article
Acceptance Date Aug 1, 2022
Online Publication Date Aug 31, 2022
Publication Date Aug 31, 2022
Deposit Date Aug 11, 2022
Publicly Available Date Oct 1, 2022
Journal Transactions on Data Privacy
Print ISSN 1888-5063
Electronic ISSN 2013-1631
Peer Reviewed Peer Reviewed
Volume 15
Issue 2
Pages 109-140
Series ISSN 1888-5063
Keywords privacy, confidentiality, data governance, statistical disclosure control
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10 is the safest number that there's ever been (680 Kb)


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