1. People disagree about the facts, about principles of justice, about the principles of political economy, and so on.
2. Therefore, it is illegitimate to make reference to an external, objective standard by which to judge political outcomes.
3. Therefore, in order to resolve this disagreements in a fair way, we must have democracy.

As written, this isn’t valid. 2 doesn’t follow from 1 and 3 doesn’t follow from 2 and 1. If you read various democratic theory books, especially as written by political theorists rather than philosophers, you’ll nevertheless see this invalid argument made many times. Theorists don’t usually this argument by providing additional premises; rather, they just repeat 1, 2, and 3 in long-winded, obscure ways.

3 says we need democracy to resolve disagreements in a fair way.  But as David Estlund points out, if we care about fairness, we don’t need democratic voting. We can flip a coin, roll dice, or use a random number generator to pick policies or leaders. That would be more fair than any realistic democratic voting procedure.

Remember, “fair” here applies to the procedure; it’s not a judgment about whether the substance of the outcomes are fair. Economic egalitarians believe justice requires equal incomes. That’s a view about how to judge the outcomes of policies, not the procedure by which we select them. It’s possible to get equal incomes via unfair decisions procedures (say by the Leftist party gerrymandering election districts), and it’s possible to undermine that outcome with fair procedures (say by sortition leading to meritocrat coming to power.)

Another problem is that 3 paints democratic behavior as a largely cognitive, intellectual enterprise. This argument makes it sound as though democratic citizens have a wide range of different values and different beliefs about which policies will realize those values, which in turn leads to their political disagreements. But empirical work generally shows this is backwards. Rather, certain identities become attached to political parties for largely arbitrary reasons. Some people with those identities then post-hoc rationalize that they share the beliefs of their party.  For most voters, it’s not that their beliefs and values determine their political behavior. It’s more like the other way around. When a Democrat says “I support free trade” and a Republican says, “I support protectionism,” this is not usually a sincere economic disagreement. Rather, it’s more like a Steelers fan waving her Terrible Towel and while the Seahawks fans wave their 12th Man Towels.

Now let’s turn to the idea that disagreement means there are no external standards. On its face, this is a bizarre, half-assed form of moral relativism.

I say half-assed because the person defending this position says that there are objective moral standards about how to resolve disagreements, but no standards about what we should decide when we disagree. You get a weird deontological defense of democratic procedure combined with a bizarre moral voluntarism about the substance of our decisions. (Does it make it better if they say, “Oh, no, I’m just talking about the legitimacy of the decision”? “Sure, X is objectively just, but we can’t do X because the people haven’t voted to do X. Or we can legitimately violate X because the people said so.”)

The more plausible view is that people have at least a core of rights and duties which are not mere artifacts of political fiat. Democracy–if it’s justified–is at least partly justified for its tendency to produce certain desirable outcomes, such as stability, efficiency, prosperity, and a tendency to recognize and respect rights.

Consider this hypothetical dialogue:

“Hey, Alan Turing, we voted on whether or not you have the right to have consensual sex with another man. 85% said of us said no in a fair referendum. What do you say to that?”

Good response: “First, go read Euthyphro. If it’s implausible that God could make something just by fiat, it’s even more implausible that the British people could. Second, if 85% of badly motivated, largely ignorant and irrational people in a given geographic area check a particular box on a particular day, that doesn’t make my rights disappear. Rather, it just means that 85% of people are vile, contemptible assholes who used their power in illicit, immoral ways. I don’t owe them obedience; they owe me an apology.”