What is the term for a society in which women dominate in family decision making?

The correct term for a society where women have the dominant role in family decision-making is "matriarchy." In such societies, women typically hold primary power, which can manifest not only in household decisions but also in broader social, political, and economic contexts. This contrasts with patriarchy, where men hold the dominant roles and make the majority of the decisions, particularly in family and societal structures.

Matrilineality refers to a lineage system where inheritance and family ties are traced through the mother’s side, but it does not necessarily imply that women have dominant decision-making authority. Gender egalitarianism describes a situation with equal rights and responsibilities for all genders, which does not reflect dominance by women. Thus, "matriarchy" specifically captures the essence of female dominance in decision-making within the family context.