Personnel Economics: Paying the Babysitter

Very applied personnel economics. During an upcoming stay in Florida with the extended family, all six adults want to go out to a fancy dinner, leaving the six kids alone (since their parents say the older ones – boy, 14; boy, 13; girl, 12; girl, 11 – can care for the little boys, ages 7 and 4). The older ones have had a lot of successful babysitting experience, and their parents say they typically get paid. But what payment mechanism is both efficient (will induce careful babysitting) and equitable?
One of the mothers suggested letting the two girls play together, making the older boys the sitters, and paying only the boys. Hearing this, the 11-year-old girl said, “Not fair; and anyway, we girls are more responsible than the big boys.” Another approach is to make all four big kids the sitters. I suggested this, with payments in proportion to their ages. The same granddaughter, perhaps aware of federal law, argued for equal pay for equal work. Okay, but the difficulty with putting all four big kids in charge and paying them equally may be that it diffuses responsibility and may not lead to sufficient care being taken – the classic free-rider problem. What to do?