Cardinalities in proofreading

TL;DR

This paper justifies Pólya's error estimation formula in proofreading by developing a probabilistic model of proofreaders and analyzing its efficiency, highlighting differences between realistic and probabilistic models.

Contribution

It provides a rigorous probabilistic justification for Pólya's error estimation formula in proofreading contexts.

Findings

The model accurately estimates total errors based on proofreaders' findings.

Efficiency bounds are derived using large deviation principles.

Discussion on the differences between realistic and probabilistic models.

Abstract

In 1975, G. P\'olya suggested that if two proofreaders found $a$ and $b$ errors in a text, of which $c$ errors were found by both of them, then a reasonable approximation of the unknown number $e$ of all errors is $e\approx ab/c$. We justify this formula by constructing a realistic model of proofreaders and estimating the efficiency of this model with the help of the bound on large deviations in the Probabilistic Method. In conclusion we discuss the distinction between realistic and probabilistic models of problems.