Unless someone comes up with a good construct, I find the very concept of a soul to be an impossibility.

One idea for what a soul is: it's like genetic imprinting (incipient abilities, personality traits, tendencies and predilections), only it's not genetic, and biologically unrelated people in different generations can have identical ones.

In that case - who cares? Except for the creepiness and also curiosity factor, if you've ever wondered what kind of a life you'd have, had you been born in a different time and place.

In my opinion, "soul" = personality (to include beliefs, abilities, etc.) + memories + past experiences (continuity of participation). One example of a reborn soul is Lews Therin Thelamon's possession of Rand.