> Shareholders receive power proportionate to their buying power. Citizens get a single vote.
Historically, there did exist experiments that not each person has the same voting power (for example the Prussian "Dreiklassenwahlrecht" [three-class franchise]):
Depending on the amount of taxes you paid, you were assigned to one of three classes. The sizes of each of these classes were chosen so that each class paid 1/3 of the whole tax volume. The votes in each class elected representants for this class.
The idea is obvious: those who pay a lot more taxes should have more influence.
Thus: each citizen has the same voting power is just the "currently fashionable" implementation of democracy.
> You sometimes cam buy your way into citizenship. As a shareholder, it is your given right to vote in a shareholders meeting.
Maybe - depending on your jurisdiction. Just like whether you have citizenship or not.