One thing that popped into my head immediately was the usefulness of a system like this to implement various kinds of democratic "dead man switch" type construc

One thing that popped into my head immediately was the usefulness of a system like this to implement various kinds of democratic "dead man switch" type constructs. For example, let's say a dissident posts a dangerous leak to a bunch of sites in encrypted form. They then distribute the key to 60 of their friends with a threshold of, say, 25 (slightly more than 1/3) and say "combine your keys if anything happens to me."