In the bowl of a food processor, combine shallots, preserves, and vinegar. In a slow steady stream, while the machine is running, slowly add in the olive oil. Add salt and pepper to taste. This can be done by hand with a whisk, but you will achieve a smoother consistency in the processor.
Combine the lettuce, pomegranate arils, avocado, jicama, and mango in a bowl. Toss with dressing just before serving.