Determinism can be readily added by means of a simple procedure (the name of which I have forgotten—hopefully a fellow commenter can chime in here): Along with

Determinism can be readily added by means of a simple procedure (the name of which I have forgotten—hopefully a fellow commenter can chime in here): Along with their vote, each voter submits a random number between 1 and N, where N is the number of voters. To select which ballot should decide the vote, all numbers are publicly revealed and added together, modulo N: the resulting number selects which ballot should be used. It is not possible for any individual or group to fix the final number in advance, since even a single non-cooperating individual can alter the final number in an arbitrary way. Obviously this simple form can only be used if N is known in advance, but I think that if you instead select a sufficiently large maximum (several times larger than the probable N) the randomness property should remain.