I appreciate the effort that has gone into this. There is still the issue of having to trust that those assigners don't collude with each other in secret, I wonder if there would be some way to solve that.
On Wed, Apr 26, 2023 at 4:36 PM nix via agora-discussion < agora-discussion@agoranomic.org> wrote: > On 4/25/23 20:45, Forest Sweeney via agora-discussion wrote: > > Agoran Mafia brought up a problem that comes by Agora now and again: The > > problem of someone needing a "special role" in order to participate in a > > tournament that requires secrecy (EG Mafia). I wanted to share my > solution, > > as this isn't the first time I've heard this problem in Agora. > An alternative, non cryptographic (or maybe more accurately, > cryptography by hand) solution: > > This involves the Herald and two Assigners. Assigners agree to an > ordered list of players (it doesn't particularly matter how they agree > to this). Something like 1) nix, 2) cat, 3) G, 4) 4st, 5) juan. > > The first assigner randomizes the a list of numbers 1 to 5 (assuming 5 > players) and send those out in order to the players. Then e sends eir > ordered list of numbers to the Herald. So if e generates [2,4,3,5,1] e > sends that list to Herald and sends 2 to nix, 4 to cat, and so on. > > The second assigner does the same thing with a list of letters A to E. > Let's say [E,C,B,A,D]. > > At this point, each player has a letter and a number (nix has 2E, cat > has 4C, etc). Each assigner knows who has their half but not the other > half. The Herald has both lists, and knows what pairs exist, but doesn't > know who has each pair. The Herald uses eir knowledge of the existing > pairs to generate a table such as the following: > > .A B C D E > 1M M D D A > 2M D D A M > 3D D A M M > 4D A M M D > 5A M M D D > > On this table we end up with the following roles: > nix (2E) mafia > cat (4C) mafia > G. (3B) defender > 4st (5A) A special role > juan (1D) defender > > The roles are distributed properly, and there are sufficient plausible > combos on the board to not be able to tell what any person's role is > based on any of the info that anyone has. > > -- > nix > Prime Minister, Herald > >
