Think about the following situation:
Elections are held by dropping notes with the symbol of the political party to a ballot box. In order to save on time, a new automatic counting machine is proposed to count the votes at each ballot box. But, since we don't trust machines, a small (relatively) number of ballots ($X$) is chosen randomly to also count by hand and thus validating the results of the automatic counters.
In order to select the list of sampled ballots, each party sends a representative with a list of $X$, supposedly random, numbers. The final list is selected using the following algorithm:
1. Sum up the ith entry from all the lists
2. Modolu the sum by the number of ballots
3. If the ballot already appears, drop the entry.
4. If the entry is new, validate
5. i = i+1
I know that if at least one of the lists is truly random, then all the lists will be random, but what happens if none of the lists is random?
In the case where all the actors are cheaters, and every actor has a specific list of ballots that they either want to be checked, or wants to make sure aren't checked. Will the resulting list be random, or is there a way for actors to build their list in a way that benefits them?
All the actors (political parties) are in competition with one another, but some actors are friendly to certain actors more than other, meaning, actors will cooperate with parties from the same political philosophy if it means hurting the opposing philosophy.