Possibility Theory, a variant of probability theory, is well suited to analyze large-N measurements of variable reliability, obsolescence and redundancy. Very few applications are known from the humanitarian sector, and these are about stocks and flows of relief goods measured on continuous scales.
We demonstrate the usefulness of Possibility Theory in testing the binary hypothesis that the severity of humanitarian conditions in a given region and sector is high / not high. The test relies on numerous ordinal severity ratings produced by coders who review humanitarian reports with location, time, sector, affected group and context information. The statistic of interest is a measure of confidence that the true severity is high / is not high. This measure is continuous bounded in the interval [-1, +1] and thus easy to visualize in tables and maps. Also, we propose an allied measure of information gaps.
The demonstration data are from Colombia during a 14-month period in 2020-21 (18 May 2020 – 30 June 2021). Two organizations, iMMAP and Data Friendly Space (DFS), collected, excerpted and processed relevant documents of various types in a dedicated database application known as DEEP. In 2021, DEEP projects were operational in thirty countries. In Colombia, it delivered the information base for the Humanitarian Needs Overview (HNO) 2021.
The iMMAP / DFS coders parsed 357 documents (“leads”) and turned them into 1,540 DEEP records (“entries”). From these we derived 24,920 observations each with a location, publication date, sector and rating on a 5-level severity scale. Our algorithm produces confidence and information gap estimates at the aggregate level (pairs of Department [Admin1] and sector). All 33 Departments and 11 sectors are represented, although not for all pairs.
The Excel demonstration workbook uses the data from a subset of six Departments, keeping 10,624 observations. The workbook architecture is such that the user can change parameter settings, view the updated outcomes in Department X sector tables, and compare them to the ones under the initial settings, all in the same sheet. Those interested in the inner workings find explanations in column header comments and in the “back office” sheets that do the work of aggregation and gap measure calculation.
This companion note details the motivation to turn to Possibility Theory, minimal generic elements of the theory, our choices in adjusting for reliability, obsolescence and redundancy, the steps leading to the confidence measure, as well as the components of the gap measure. The note then describes the data generation and analysis workflow in the DEEP institutional environment. It presents select results from the whole-Columbia dataset. It explains the workbook structure and the functions of the various parameters, as well as some less common types of formulas. Deliberately, no VBA programming is involved.
Together, note and workbook demonstrate how an infrastructure like DEEP and unusual tools like Possibility Theory open a way to combine large sets of structured humanitarian observations in a quantitative severity measure. Our measure captures the degree of uncertainty in a more informative way than the usual rank order-based statistics for ordinals. In addition, the gap measure points to regions and sectors needing further investigation or needs assessments.
