Betty pledges to donate $1,000 to the Children's Hospital. On the basis of the pledge, the hospital orders additional equipment. Betty reneges on the pledge. The hospital sues Betty. If the court enforces the pledge, it will be

under the doctrine of promissory estoppel

Explanation:

Promissory estoppel is a doctrine of the law that prevents somebody that made a promise or a pledge from reneging on their promise. This is enforceable even when there is no contract. The beneficiary can sue for damages incurred if the damages are as a result of the pledge that has been made.

In this instance Betty pledged to donate $1,000 and on the strength of this pledge the Children's hospital orders additional equipment. The hospital has incurred expenses, so Betty reneging on her promise has resulted in damages. The hospital has a right to sue for recovery of damages.