New characterizations of the unit vector basis of $c_0$ or ${\mathrm{\ell }}_p$

Motivated by Altshuler’s famous characterization of the unit vector basis of $c_0$ or ${\mathrm{\ell }}_p$ among symmetric bases, we obtain similar characterizations among democratic bases and among bidemocratic bases. We also prove a separate characterization of the unit vector basis of ${\mathrm{\ell }}_1$.