An obvious example is the "three wolves and a sheep deciding on dinner" problem. Democratic, not egalitarian.
Both democracy and egalitarianism have many forms and interpretations and open up unresolved philosophical problems. Bundling them together just causes more confusion.
Can you be more specific about what you think the difference between fairness and equality is? For example, if one person is smart enough to become a doctor and another isn't, but then doctors get paid more than housekeepers, is that the difference? The system is fair (anyone smart enough and willing to can become a doctor) but not equal (some people aren't smart enough and doctors get paid more).
But using that as the difference is more of a communist ("to each according to his needs") ideal than a democratic one.
And authoritarians generally don't even care if the system is fair -- if it's unjustly enriching their own people then it's authoritarianism working as intended.
I guess there in theory there could be libertarians that have very high criteria for what an informed choice would be. To a point where it would be democratic. But that is probably closer to social liberalism.
One can of course question whether most authoritarians care much about their own ideology. But as an ideology they do care that the system is fair, just not society overall. People do believe that it is fair to have a "strong leader". They might not care much if the leader is enriching themselves as they aren't equals. They would care if the leader loses face and don't seem as "strong" as thought. Because then their position would be unwarranted.
I think this is a misunderstanding of why people want money. Because none of that stuff is boolean. You don't have education or not. Harvard and community college are both "education" but they're not the same.
Even when people buy a sports car, it's not because they derive $60,000 worth of benefit from fast acceleration, it's primarily a method of status signaling. Which in turn creates social opportunities in everything from business networking to romance.
You can create a minimum floor for everyone (NB: a UBI is an outstanding way to do this across all domains), but "money buys stuff" applies to pretty much anything, including incremental amounts of education, community and security.
> One can of course question whether most authoritarians care much about their own ideology. But as an ideology they do care that the system is fair, just not society overall. People do believe that it is fair to have a "strong leader".
This is fundamentally impossible. There is conflict in politics not only because of misunderstandings but also because different people have different interests. The "strong leader" will have to make choices that benefit some people over others. If all you're doing is redefining fairness to mean whatever the leader decides it is then you're not creating a fair society, you're just creating a society and defining fairness as whatever subsequently happens.
In some sense that is also what we do with the output of the democratic process, but that only has a claim to fairness as a result of the fairness in the inputs (one person one vote). With authoritarianism the selection process can make no such claim, not least because the existing "strong leader" would by definition have enough de facto control to stay in power indefinitely and then anoint a successor at the end.