Generally, you want to mix color for ideal conditions, not the common situation. It is up to people to do the best they can to adjust their systems to support a vivid and clear image. If you mix to try to make it look the best on some "average", not only will it look bad on any good displays, but it will also look bad on any well adjusted average displays.
The reason for this is because of gamut. The gamut of a display is the range of colors which it can produce. A good display has a wide color gamut and can make use of more colors. A display with a smaller gamut will have to make adjustments to bring colors within gamut or else colors will clip out and appear as the furthest color it can render (relative chromatic vs perceptual correction).
You want to mix to the widest gamut that will be used so that adjustments don't need to be applied on that display because different lower quality displays will not all have the same gamut. Some will display more on the blue side, some more on the red, etc. If you have mixed for a gamut that includes both, both of these lesser displays can make full use of their gamuts. If you instead mixed for some average in the middle, not only will they lose the colors they don't do from the average, but they will also lose some of the colors they are capable of displaying, further limiting an already limited display.
Video is crap in, crap out. You want to build the best possible input and then leave it up to the player to adjust. The only exception to this is if you know the exact target conditions and want to customize for those conditions specifically. You can always try to adjust visual information you can't display to look ok on your display, but you can't invent information that isn't there.
Also, one important caveat to remember. Just because one display is brighter doesn't necessarily mean it has better color reproduction, or even a wider color gamut. Newer consumer displays use localized brightness adjustments to allow for higher contrast ratios and thus can go brighter overall, but this is dependent on the idea that bright areas tend to be bright everywhere. The local contrast ratio may actually be very low, which means that while the screen may produced bright colors, it does not necessarily do well with sharp contrast or accurate color reproduction (such displays are also a major pita to calibrate for accurate color due to the display fighting you with its localized brightness adjustments.)
Ideally you want something like an S-IPS or S-PVA panel with low color distortion from viewing angle changes and a high static contrast ratio with little or no dynamic contrast adjustment (unless it does it at a per-pixel level). For best results, you also want to make sure that you have accurate color response curves for the display. To do this, you need either a colorometer (such as a Spyder or Colormunchi) or spectrometer that can analyze the actual output of your monitor and fine tune the output of your monitor for most accurate color.