Claudio Puebla delivers a very extensive examination of Whiteness. Much of the site is intensely technical, but some of his broader observations bear quoting.
The “ideal white” is defined by a perfect reflection value for all wavelengths of light: “No losses means that the reflectance values are 1 for the whole wavelength range (or 100%); this defines the ideal white, a body rarely encountered in nature.”
As described on the Theory page, the “whiteness” of a shade is determined by three elements: base white, shaded white, and fluorescent white. Though observers cannot distinguish the elements in a shade, differences in any of the three elements will result in colors not matching under some lighting conditions (“metamerism”). Two colors gauged at the same level of “whiteness” may be metameric along any of three axes.
White’s lightness makes it extremely useful where visibility and contrast are important. Puebla states that this has led to “the use of color mixing techniques as a means to increase the perceived whiteness is quite widespread in the industrial areas of paper, textiles, detergents and plastic.”
On the Assessment page, he describes how mixing varies amongst cultures:
Considering now the personal taste for certain whiteness it can be said that this varies with cultural background of the observer as well with the final application of the white object.
As such people with a cultural background of the Far East prefer a reddish white, Europeans prefer a neutral white, while in Latin America shaded bluish whites are preferred. On the other hand neutral bluish whites are preferred for objects suggesting freshness (like bottles for mineral water) but a reddish white are favored for white underwear garments.