On the occurrence of large gaps in small contingency tables

TL;DR

This paper investigates the rarity of large integer programming gaps in small contingency tables and questions the effectiveness of linear programming as a heuristic for disclosure detection.

Contribution

It clarifies that the margins causing large gaps are rarely encountered, challenging previous assumptions about linear programming's utility in this context.

Findings

Large gaps occur in rare margin configurations

Linear programming may be less effective for disclosure detection in typical cases

The concept of 'rarely encountered' margins is formalized using standard pairs

Abstract

Examples of small contingency tables on binary random variables with large integer programming gaps on the lower bounds of cell entries were constructed by Sullivant. We argue here that the margins for which these constructed large gaps occur are rarely encountered, thus reopening the question of whether linear programming is an effective heuristic for detecting disclosures when releasing margins of multi-way tables. The notion of ``rarely encountered'' is made precise through the language of standard pairs.