You should never try to explain democrazy using the root of the word - otherwise you would have to mention that below 10% of the population of ancient greek cities were considered part of the “demos”. It just goes to show how little we gain by looking for a “true” meaning of words, searching in its linguistic roots.
Most modern democrazies generally go by majority rule, with two systems kinda holding it in check: Majority of areas and basic rights (edit: “Majority of areas” is not used often, rather, every country uses their own expression).
The first one means that not only do you need a majority of the votes to win an election, but areas (usually states) have certain privileges. Think of the US, where less populated states got an overproportional amount of votes in the electoral college. Even without “winner takes all” you could have situations where winning the popular vote is not enough. Or Switzerland, where every change of the constitution needs to be approved by a majority of Stände (=states) on top of winning the popular vote.
The basic rights you mention are something completly different. They are agreements about stuff so important, so unquestionable, that it can not be voted away. The exact definition varies depending on where you live, but usually its stuff like freedom of speech etc.
And sometimes we see a majority expressing their wish for a stronger protection or a wider definition of basic rights, but a minority with special constitutional status voting against it. So the two systems can even be in a direct conflict.
In your example, minority protection by majority of areas would mean that both land and lake have to vote the same in order to press for change; basic rights would mean you cant vote on the fishs right to survive. In that case they would both have the same effect, but still, they are very different in kind.
Now, if we wanted to apply those concepts to AoE it gets tricky. Voting by area is not impossible, but would be very strange. Maybe you could introduce stuff like “a majority of flank and a majority of pocket players has to agree to go rnd”. Other than that, i dont really see an option.
And using the basic rights argument falls flat pretty quickly, as you realized yourself
So overall, i think in the case of AoE there is little reason to not go by majority rule.