A dominance mandate is an ideological belief that non-belief in the given ideology is intolerable. Adherents to any ideology which includes a dominance mandate must, at a minimum, work to convert others whenever possible. More extreme dominance mandates hold that those who leave the faith (apostasy) must be punished or even killed; the most extreme forms hold that those who cannot be converted (infidels) must also be killed.
Dominance mandates are definitionally incompatible with tolerance, although their ideological supporters will often use the tolerance-based arguments in support of their intolerance.
As a memetic trait, a dominance mandate obviously helps to spread belief in the ideology which possesses it by encouraging already-infected carriers to infect others (and to disempower those who may have resistance to the meme).