In my understanding, karma cannot be passed down from ancestor
to descendent.
Karma is individual, and karma means actions/volition or a
momentum that forms imprint in our 8th consciousness. If the seed
is not there, committed by the individual through his action from
mind/speech/action in his past life or a past time, he will not
have such karma at all. And he will not have such karmic
ripening.
First of all we must understand that there is no such
thing as a collective 8th consciousness. There is only
individual streams of 8th consciousness, individual mindstreams, no
collective mind. A collective mind/consciousness is a non-Buddhist,
外道 concept. This does not mean that supernatural powers and mind
reading (and so on) cannot occur, they occur due to the
non-locality/emptiness/dependent arising nature of consciousness,
but has nothing to do with a collective mind... and the true nature
of all being's consciousness is luminous and empty.
Conventionally speaking, we MUST take it that mindstream, karma,
and various physical-mental conditionings are separate, individual
streams, (i.e. not 'collective') even though ultimately they are
empty of self and phenomena, merely dependently arisen appearances,
each moment is spontaneous and absolute in itself, and inseparable
from causes and conditions. Why do I say they are individual?
Because there are different sets of causes and conditionings,
producing different sets of experiences. There is no shared entity
or consciousness of any sorts -- consciousness is inseparable from
causes and conditionings. Due to karmic vision, human sees red
flower, dog sees black and white, ghost sees river as fire, and so
on. Nothing 'shared' at all -- only causes and conditionings
producing illusory appearances, fundamentally empty, yet a vivid
appearance of luminosity. Every experience is different due to
different conditionings, there is no such thing as a 'same' or
'shared' consciousness, even though all diverse phenomena have one
taste -- luminous-emptiness.
However, it is possible that a group of people, committing the
same deeds, plant the same kind of seeds, and as a result create
what we call collective karma.
That means, in each individual 8th consciousness mindstream,
through the same sort of actions they performed together, they each
form the same kind of imprints in their 8th consciousness. As a
result, some time in the future when conditions are ripen, they
will 'collectively' ripen together.
HOWEVER, this has nothing to do with ancestors passing down
karma into descendents. This is because the ancestor and the
descendent are separate mindstreams, and if the descendents have
not had the same karmic seed as the ancestor in their 8th
consciousness, they cannot possibly have the same sort of
occurences.
But, it is possible that through the karma of an individual,
i.e. the conditions are there, to conceive a child with illnesses
and things like that due to the karma of his own action. This is
not because his own karma caused the child to have illness, but
because somehow the causes and conditions are there, both the
parent and child have the same resonating causes and conditions to
be born in the same family.
For example, there is a true story about two parents who had
been good in their whole life, but conceived a retarded child. They
found a venerable to ask about the karmic causes, the venerable
told him that this child was a druglord in his past life. The
parents ask why do they have to be born in my family? The venerable
answered that you two were his accomplice in his past life. So now
you have to take care of him for your whole life. Because of the
various karmic conditionings, they all appear in the same family.
It is not because of their ancestors, or not because of one
person's personal actions, but due to every single person's karma
that such congregation is possible.
Therefore good ancestors can get good descendents, but in the
case of a 'great grandfather' or 'great great grandfather', I can't
really see how that is possible. It could be possible that the
person himself is the great great grandfather in his past life.