Defending Threshold Voting Systems With Identical Voting Units

The threshold voting system consists of N units that each provide a binary decision (0 or 1), or abstain from voting. System output is 1 if the number of 1-opting units is at least a pre-specified fraction τ of the number of all non-abstaining units. Otherwise system output is 0. For a system consisting of voting units with given probabilistic output distribution, one can maximize the entire system reliability by choosing a proper threshold value τ. When a system operates in a hostile environment, some units can be destroyed or compromised by an aggressive media, or by a strategic malicious counterpart. One of the ways to enhance voting system survivability is to protect its units from possible attacks. We consider a situation when an attacker and a defender have fixed resources. The defender can protect, and the attacker can attack, a subset of the units. First, we formulate the problem of maximizing survivability of a threshold voting system by proper choice of system threshold and number of protected units, assuming that all the units are attacked. Then we consider a maxmin game in which the defender chooses an optimal system threshold and number of protected units assuming that the attacker chooses the number of attacked units that minimizes the probability of correct system output.