We consider a computer simulation of color confusion for dichromats for any colors on any video device, which transforms color in each pixel into a representative color among the set of its confusion colors. As a guiding principle of the simulation we adopt the proportionality law between the pre-transformed and post-transformed colors, which ensures that the same colors are not transformed to two or more different colors apart from intensity. We show that such a simulation algorithm with the proportionality law is unique for the video displays whose projected gamut onto the plane perpendicular to the color confusion axis in the LMS space is hexagon. Almost all video display including sRGB satisfy this condition and we demonstrate this unique simulation in sRGB video display.