"Democracy is fair because everyone gets a vote" sounds like a complete justification, but it collapses several genuinely distinct philosophical arguments into one vague appeal. Political philosophers have actually developed several separate justifications for democratic decision-making, resting on different underlying values — and because they're different arguments, they don't always point toward the same conclusions about how a democracy should actually be designed or what decisions it should make.
Instrumental justifications: democracy because it produces better outcomes
One family of justifications defends democracy instrumentally — not because participation is intrinsically valuable, but because democratic decision-making tends to produce better outcomes than the alternatives. This might rest on the idea that pooling many people's information and perspectives produces more accurate collective judgements than any single ruler or small elite could reach on their own, or on the practical observation that democracies have historically proven more resistant to catastrophic policy failures and more responsive to correcting mistakes, since leaders can be replaced without violence. Crucially, an instrumental justification is conditional: if democratic decision-making could be shown, in some specific case, to reliably produce worse outcomes than an alternative, the instrumental argument alone would offer no principled reason to still prefer democracy.
Intrinsic justifications: democracy because participation itself matters
A different family of justifications treats democratic participation as valuable in itself, independent of whatever outcomes it happens to produce. This might rest on an argument from political equality — that treating citizens as equals requires giving each an equal voice in decisions that bind them, regardless of whether that produces the objectively "best" policy outcome — or on an argument from autonomy, that being subject to laws you had no voice in shaping is a form of domination, and self-government is what makes political authority legitimate at all, quite apart from whether self-government happens to produce better or worse specific decisions. These intrinsic justifications don't depend on democracy actually outperforming alternatives on outcomes; they locate democracy's value in the process of participation and equal standing itself, which is precisely why instrumental and intrinsic justifications can sometimes point toward different institutional designs, even though both are routinely offered as reasons to prefer democratic government.
What we're still unsure about
That instrumental and intrinsic justifications for democracy are genuinely distinct arguments, resting on different underlying values, is well established and widely discussed in political philosophy. What remains a live, substantive debate is which justification, or combination of justifications, should actually take priority when they point in different directions — for instance, when a case can be made that a less participatory decision-making process might produce better outcomes on a specific issue, philosophers disagree sharply about how much weight the intrinsic value of participation should carry against that instrumental consideration, a tension current democratic theory hasn't resolved into a single settled answer.
This sits inside Democracy & Its Justifications, one of seven topics in Political Philosophy, one of five domains in Philosophy, one of seventeen subjects the app can quiz you on.