greatest number of people; the largest majority
Used in contexts like politics, ethics, or social philosophy to refer to the largest group of people, often in the phrase 最大多数の最大幸福 (the greatest happiness of the greatest number).
Policies aimed at the greatest happiness of the greatest number are called for.
多数 means 'many' or 'a large number', while 最大多数 specifically means 'the greatest number of people'.
Compound of 最大 (greatest) and 多数 (large number). The phrase 最大多数の最大幸福 is a translation of Jeremy Bentham's 'the greatest happiness of the greatest number'.