Betelgeuse, Johannes Bayer and Purkinje effect

Betelgeuse is the alpha of Orion, and normally alpha means that it is the brightest star of its constellation. Johannes Bayer was the first in 1603 to order the stars with the greek letters in sequence of luminosity. Are several the cases when the alpha is less luminous than beta, and many more cases in which beta is dimmer than gamma et cetera. Why these incongruences? One of the reasons is because some stars are variable and this is the case of Betelgeuse, but other is the Purkinje effect which made the red luminous stars more brilliant to the naked eye, when we stare at them.