Assuming the people are mostly strangers, everyone would wear name tags. The first third or so of a party might involve mixers, ways to meet and learn a little about a lot of people. Then they would privately register, say, 100 votes each on the computer, divided between, and proportional to, those people they would most like to know better. The computer would compare who voted how much for whom and privately give three names to each person. No one would be referred to anyone who hadn't given at least one vote in return. I would know that each person on my list also had my name on theirs.
Rather than adding the mutual votes of each potential couple, the computer would multiply them to support mutual attractions over power plays. If Jane gives ten votes for Bill and one vote for Bob, and Bill gives ten votes for Jane, and Bob gives fifty for Jane, the mutual attraction of Jane and Bill wins over Bob's power play. This would also encourage everyone to spread their votes more liberally over several people.
Nothing would be printed out and the computer would not keep a record of who voted for whom. Nobody would know for sure how anyone else voted. The resulting matches would represent the complex permutations of every vote in the room.
Smart people would vote for people reasonably likely to vote for them, rather than simply voting for the most popular person in the room. Compassionate people would give at least one vote to one or two people they feel might not get any votes. If it turned out someone was not going to get any matches, the computer would cancel that game and people would have to vote again, hopefully with broader minds. For some people, this would still be somewhat of a reality check of who they could really attract, but they wouldn't be embarrassed by it. Smart people would also not rush immediately to the first person on their list, but would keep the names in mind as a potential conversation partners. If they didn't get the person they wanted most, there would be another such party, with completely different permutations, and they could try again.
Such a program was written for Windows, for exercise by a student. It worked fairly well but was not too user-friendly. It never got re-worked. I'm not much of an organizer, so it never got tried out. It had the inherent problem of just one available terminal. I may take up C programming one of these days and write one myself.