Democracy is commonly associated with political equality and/or majority rule. This essay shows that these three ideas are conceptually separate, so the transition from any one to another stands in need of further substantive argument, which is not always adequately given. It does this by offering an alternative decision-making mechanism, called lottery voting, in which all individuals cast votes for their preferred options but, instead of these being counted, one is randomly selected and that vote determines the outcome. This procedure (...) is democratic and egalitarian, since all have an equal chance to influence outcomes, but obviously not majoritarian. (shrink)