Combine first 3 ingredients in a medium bowl, stirring well. Toss apples with next 4 ingredients in a large bowl. Add mayonnaise dressing, and toss to coat. (Salad can be prepared a day ahead; cover and refrigerate overnight).
Fold toasted pecans into salad. Line a serving bowl with radicchio leaves and spoon in salad or arrange radicchio leaves on each plate, and spoon salad into leaves.