Defending majority voting systems against a strategic attacker

Voting systems used in technical and tactical decision making in pattern recognition and target detection, data handling, signal processing, distributed and secure computing etc. are considered. A maxmin two period game is analyzed where the defender first protects and chooses units for participation in voting. The attacker thereafter attacks a subset of units. It is shown that when the defender protects all the voting units, the optimal number of units chosen for voting is either one or the maximal possible odd number. When the defender protects only the units chosen for voting, the optimal number of chosen units increases with the defender resource superiority (i.e., more resources than the attacker) and with probability of providing correct output by any unit. The system success probability always increases in the total number of voting units, the defender–attacker resource ratio, and the probability that each voting unit produces a correct output. The system success probability increases in the attacker–defender contest intensity if the defender achieves per-unit resource superiority, and otherwise decreases in the contest intensity. The presented model and enumerative algorithm allow obtaining optimal voting system defense strategy for any combination of parameters: total number of units, attack and defense resources, unit success probability and contest intensity.