Anonymous, secure proof of identity after quorum?

let's saY there were 100 people charged with making a hard choice. No one is willing to publicly suport the hard choice unless they are certain the majority hold that opinion

Now, a watcher wants to create a website that correctly and anonymously reveals how many people would be willing to make the hard choice. Furthermore: As soon as a Majority have eXpressed that they are willing to make that hard choice, everyone who holds that opinion should learn each other's identities. And thus feel emboldened to publicly anounce their opinion.

There are many dificult parts here: how would you confirm, that only the 100 people are able to vote, and have their vote only count once.

How would they feel confident that their identity is anonymous?

I'm less interested in game theory about how people would try to trick the system, more in the technical feasibility of creating such a site.

Completely theoreticaly of course.