Random jury methods involve randomly selecting a group of citizens from the general public, who are entrusted with the responsibility of making a public decision (e.g. electing a representative)
Once selected, jury members have a period of time with intensive access to information about the candidates (probably including interaction with the candidates themselves) before they have to make their decision.
There are various voting procedures that the jury could use to choose a winner. Since they should all be able to fit in a single room, the advatages of an iterative procedure would probably outweigh the disadvantages.