## 15. Should the Baby Be Fed?

One Saturday evening, a young married couple went to the movies, leaving their two children, aged three and six months, in the care of their grandmother. The grandmother, who took her duties very seriously, pondered whether the baby had been fed for the last time that day. She had no prior opinion on this matter. She could, of course, ask the older child, but there was a one in four chance that he would be wrong.

Assume that for the six-month-old baby, it is twice as bad to be left without the last feeding as it is to be fed twice. Which of the two "strategies" would you choose if you were in the grandmother's place:

1) feed the baby without asking anything of the older child
2) ask the older child and feed the baby only if the older child says he was not fed?
15. Let $\alpha$ denote the "harm measure" for an infant receiving two portions of food instead of one; then the harm of not being fed at all is estimated to be $2 \alpha$.

In the second strategy, the grandmother has one chance in four of making a mistake, whether she feeds the infant or not. Therefore, she risks causing the infant harm:

1) $\alpha$ - with a probability of $1 / 8 (1 / 4 \cdot 1 / 2)$;
2) $2 \alpha$ - also with a probability of $1 / 8$.

In the first strategy, she has one chance in two of making a mistake by feeding the infant an extra time. Therefore, she risks causing the infant harm $\alpha$ with a probability of $1 / 2$.

Since the expected harm in the second strategy is $1 / 8 \cdot (\alpha) + 1 / 8 \cdot (2 \alpha) = 3 \alpha / 8$, and in the first strategy it is $\alpha / 2$, the second strategy is preferable.