Secure Counting: counting members of a subset without revealing their identities

Suppose there is a group of N people some of whom possess a specific property. For example, their wealth is above or below a threshold, they voted for a particular candidate, they have a certain disease, etc. The group wants to find out how many of its members posses the property -- without revealing the identities. Unless of course it turns out that all members do or do not have the attribute of interest. However, in all other cases the counting algorithm should guarantee that nobody can find out if a particular individual possesses the property unless all the other N-1 members of the group collude. The present article describes a method to solve the confidential counting problem with only 3*N-2 pairwise communications, or 2*N broadcasts (the last N-1 pairwise communications are merely to announce the result). The counting algorithm does not require any trusted third parties. All communications between parties involved can be conducted in public without compromising the security of counting.