Economics
In Wizard's First Rule Terry Goodkind posits the Quad as the most economical squad of assassins targeting women who can instill loyalty with a touch. She turns one and he kills one or two of his fellows, leaving the remaining survivor to kill him and the woman. Rarely he kills all three and the mission fails, but the usual outcome is a success.
A similar line of thought exists in your dystopia. If there is a high percentage (real or perceived) of traitors, then patrolling in pairs is ill-advised as the traitor can always kill his partner by ambush. Three is also a dicey proposition, because he can always kill one by ambush leaving a fight between two combat effective soldiers. Given that he'll kill the more dangerous one first the resulting fights would generally be won by traitors.
Four is the most economical unit which guarantees no traitor survives. Killing one squad mate by ambush still leaves the traitor at a 2-1 disadvantage, which is virtually impossible to overcome. In the extremely rare instance where all four members conspire together, one poisons the other three, or the traitor is a ninja and wins a melee you have to send out a larger unit to hunt him down. In every other case you've sent the minimum number of men to start with.
