Why is the apparent magnitude of β star higher than that of α star in some constellations?

This is because the magnitude measurement tools were relatively simple when this rule was first used to name stars. Mainly depends on visual inspection. So it can't be accurate to the decimal point. Only 1 and 2 stars. There is no such thing as 1.3. Then it is stipulated that those with the same magnitude in the same constellation should be named from head to toe according to the constellation. Therefore, it is possible that the beta star is slightly brighter than the alpha star. But they must have the same integer bit size.