September 11, 2003
Hair Color Dye Sales and Observation Selection Effects
One of the arguments for the alleged attractiveness of blondes runs roughly as follows:
A. People try to make themselves more attractive
B. People buy dye their hair blond more than they do dark (as evidenced by hair dye sales)
From A and B it follows (according to faulty reasoning as I will show) that people (and esp. women) with light hair are more attractive than those with dark hair.
There are many things wrong with these reasoning, (*) but I will focus on a fault based on observation selection effects. (+)
The key parameter that we need to evaluate is the following: what is the probability that a person of hair color X will change it to hair color Y, which we'll note Pr(X->Y). For simplicity, let's assume that there are two colors, LIGHT and DARK.
Now, if Pr(DARK->LIGHT) > Pr(LIGHT->DARK) then light hair is preferred to dark hair. Suppose that we know that LIGHTSALES bottles of LIGHT hair dye are sold as opposed to DARKSALES bottles of DARK hair dye (@). Suppose also that NLIGHT people have naturally light hair and NDARK people have naturally dark hair.
Does LIGHTSALES>DARKSALES imply that light hair is preferred to dark hair?
The answer to this question is no, for a very simple reason. We can write the probabilities Pr(LIGHT->DARK), Pr(DARK->LIGHT) as:
Pr(LIGHT->DARK) = DARKSALES/NLIGHT
Pr(DARK->LIGHT) = LIGHTSALES/NDARK
So, LIGHTSALES and DARKSALES are not what determines preference for light or dark hair. Rather, it is the quantities written above.
Let's give a concrete example. Suppose that NLIGHT=1000, NDARK=5000 and LIGHTSALES=1000, DARKSALES=200. Light hair dyes are thus bought 500% more than dark hair dyes, but:
Pr(LIGHT->DARK) = 200/1000 = 0.2
Pr(DARK->LIGHT) = 1000/5000 = 0.2
So, it turns out that there is indeed no preference for light hair. The greater light hair dye sales are explained by the structure of the population: dark-haired people are commoner, and this is why there are more people who buy hair lightening products than there are those who buy hair darkening products.
Without hard data it is impossible to determine whether there is a preference for dark or light hair. The thing to remember though is that the argument from hair dye sales does not represent evidence in favor of the "attractive blonde" hypothesis.
(*) One of the main ones is the premise that what people think makes them more attractive actually do make them more attractive. Also, hard data on the sales of dye products, as well as their distribution (e.g., with respect to age, or with respect to the probability that a person of hair color X will change it to hair color Y) are not available.
(+)Nick Bostrom's website has tons of info about observational selection effects, including the more approachable Cars in the Other Lane Really Do Go Faster.
(@) We assume that these represent sales to people who want to change their hair color. Some portion of LIGHT or DARK hair dye sales will be used by those who use their own natural hair color, e.g., to hide the gray.
Further reading:
How Blondness Evolved
On the Evolution of Blondness
Hair Color, Personality and the Observer
Let's make this more realistic: Say, there are 3 colors: brown, blonde, and red. Red is the rarest in nature, so by your logic, red dye should be the most popular. But it's not -- blonde is.
Posted by: Steve Sailer at September 11, 2003 06:00 PM>> Let's make this more realistic: Say, there are 3 colors: brown, blonde, and red. Red is the rarest in nature, so by your logic, red dye should be the most popular. But it's not -- blonde is.
First of all, do you have any data on hair dye sales?
Second, my logic does not imply that red dye should be the most popular. What it implies is that red+blond will have combined sales more than brown, because there are more brown-haired people.
Since brown-haired people are the great majority, most sales will be by brown-haired people who of course will choose either red or blond. Ergo, red+blond sales will be greater than brown sales. But, the relative sales of red and blond will depend on the relative preference that people have for red and blond. I don't have data on this (in Greece reddish shades are quite popular), but if red dyes actually sell less then this proves that blond is preferred to red, and not that it is preferred to brown.
I need a hair colour dye