The ‘stop after k girls or N children’ policy

Extract

1. Introduction

In the article [1], a follow-up to my article [2], Christian and Trustrum cite empirical evidence that the probability of a family giving birth to a boy or to a girl may vary from family to family. Letting b_i and g_i = 1 − b_i respectively denote the probability of the ith family giving birth to a boy or to a girl, the suggestion is that b_i may be distinct from b_j for distinct i and j. As they point out, this has implications for the expected society-wide number of boys and girls. Following my discussion of the ‘stop after k girls’ policy, Christian and Trustrum introduce the related policy ‘stop after k girls or N children’. They argue that the expected number of children under this latter policy is an increasing function of b_i (when 0 < k < N). The present article complements their discussion by examining this alternative stopping policy in more detail.