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In the context of secure multi-party computation protocols, when a dishonest majority is considered, it is assumed the worst case scenario, i.e., all the corrupted parties are controlled by the same adversary.

Having all the corrupted parties controlled by the same adversary is the worst case scenario since it means that the corrupted parties can be forced to cooperate so as to achieve a result that is desiderable for the adversary. This makes sense since proving security in this context implies the protocol to be secure for any number of adversaries.

However, in the context of a majority voting protocol it is crucial if the parties can cooperate or not. Indeed, a cooperating majority of corrupted parties may influence arbitrarily the output of the protocol. On the other hand, a non-cooperating or partially cooperating majority of corrupted parties can hardly influence the output of the protocol (since it is unlikely they all vote in the same way).

Are these cases already treated somewhere in literature?

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  • $\begingroup$ I believe that from a voting perspective it is only relevant the size of the biggest set of parties corrupted by the same adversary. However, it should be assumed also that parties corrupted by different adversaries do not cooperate. $\endgroup$
    – Lorenzo
    Jun 5, 2020 at 10:27
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    $\begingroup$ Voting is among other important MPC problems. I believe that you can easily google the subject: for example, the PhD thesis "Multi-Party Computation: Efficient Protocols, General Adversaries, and Voting" on it.iitb.ac.in/~madhumita/research_topics/… $\endgroup$
    – Crypto Learner
    Jun 6, 2020 at 17:40

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