In the situation that you want no individual to have the complete private key, but you do want to share the complete key between 3 individuals, of which any 2 can construct the complete key, what is the downside from doing something like this:
Orig key = 1 2 3 4 5 6 7 8 9 (abbreviated for demo)
key 1 = 1 2 _ 4 5 _ 7 8 _
key 2 = 1 _ 3 4 _ 6 7 _ 9
key 3 = _ 2 3 _ 5 6 _ 8 9
obviously any 2 keys would construct the entire key again.
Apart from the decrease of key strength to 1/3 of the original, are there any other potential issues ?
This would be used for "short term" escrow accounts where, in the case of a "winner takes all", the escrow would just communicate their key to whichever counterpart won. If the escrow failed to send, then the counterparties could choose another (trusted) escrow and transfer the funds to them.