Deranged X-Mas - a Gift Exchange Puzzle

While planning a holiday gift exchange this week, my wife casually challenged me with a sort of tricky probability puzzle: Sara and I were talking today and realized that we were off by one on the rotation because last year we went sledding instead of buying gifts. It should actually be: * Sara gives to Jonny * Jimmy gives to Thurop * Amy gives to Lisa * Jonny gives to Sara * Thurop gives to Jimmy * Lisa gives to Amy