Jason Grant was one of the founding members of Little Lamplight community. Before the Great War on October 23, 2077, he was a fourth grade student in Carrie Delaney's class at Early Dawn Elementary. On that fateful day, he was part of a field trip to the Little Lamplight caverns when the War broke out.
Over the following month, all of the adults who ventured outside the caverns to look for help never returned. Because of the dire situation, Jason stepped up to become the leader of the survivors in the caverns, as nobody else wanted to take responsibility and they listened to him anyway. A month later, they discovered the back entrance to Vault 87 and pleaded to be allowed in, but when somebody finally responded to them, the children were callously told that they were "already dead." Furious at all adults, Jason decided that they didn't need adults ever again.
Approximately two months later on January 26, 2078, the other Little Lamplight residents voted Jason in as their mayor in appreciation for his leadership. He presumably instituted the law that "mungos" (as they called the adults) had to leave the caves at age 16.
Despite similarities in voice and personality between Jason and MacCready, there appears to be no direct relationship between the two, other than both serving as mayor.
Jason Grant is mentioned only in Fallout 3.