Wanted -- a system to anonymously test the support of radical ideas
How often does it happen? There's an important idea or action which is controversial. The bravest come out in support of it early, but others are wary. Will support for this idea hurt them in other circles? Is the idea against the "party line" of some group they belong to, even though a sizeable number of the group actually support it? How can you tell.
What the world needs is a way that people can register their support for something anonymously and learn how many other members of their group also secretly support it -- but not who. However, once the support reaches a certain threshold, their support would become public. And not just public, but an actual binding committment to the support.
For example, Republicans may oppose the war, or the wiretapping, but are afraid to say so, even among their closer associates. What if really a lot of people feel that way, but nobody speaks up?
Now, obviously, you can do this with a trusted web site where people register and then can vote on issues. But you have to really, really trust the web site, because some of the positions such a system is designed to record are ones that could get you branded a traitor to the group. For issues like war, no web site could be trusted.
So can it be done cryptographically? Is there a way to do this in a public space? I think that with the use of things like Chaum's blinding algorithms, and fragmented keys (So that a secret message can be decoded in the presence of N of M key fragments, but no fewer than N) it would be possible to create a club, give everybody fragments of everybody else's key for a given message, and thus arrange that only after at least N votes of support arrive, everybody can decrypt the identities of the supporters. But it's a bit messy, and might require new generation of keys for every question and various other complex logistics.
There is a particular danger as well. Opponents of a proposition might well pretend to be supporters, in order to bump the support number above the threshold and reveal who the "traitors" are. The opponents would make sure to record that their support was fake in some notarized location so they can renounce it when the names are revealed.
As such, in a governing body, it would be necessary to make the measures of support non-repudiable, which is to say they would be binding votes.
Say you wanted to have a vote to legalize gay marriage. There might be lawmakers who would support it, but could not do so publicly while it's likely to lose. However, once it is assured to pass, they would accept making their support public -- as is necessary in an open legislature. People would see the tally go up, and once it hit a majority the vote would pass. This stops people from pretending to support something just to unmask the real supporters.
Of course none of this prevents regular open support or opposition on things. Would the temporary secrecy cause risks due to some temporarily reduced transparency? And of course on failed propositions, the transparency would be permanent. (Or perhaps permanent until the person leaves office or dies or whatever.) Would it be good or bad that we knew that 30% of the house would vote to ban abortion if they could win, without knowing who they were?