An intuitive explanation for the ecological fallacy I believe that it is called the ecological fallacy. People say that one cannot apply population-wide statistics to individuals of that population. So, just because some trait exists in a higher proportion in population A than it does in B, that doesn't mean that an individual from pop. A is more likely to have that trait than an individual from pop. B.
Now, this doesn't make sense to me. An individual coming from a population where a certain trait is more common, is more likely to have that trait than an individual coming from a population where said trait is less common, right?
I guess this depends on how one mathematically defines "common". The mean and the average are a bit scary statistical quantifications. I see how "the average" is problematic, but a weighted average is surely quite illuminatory of the real likelihoods?
 A: There is no one ecological fallacy; rather, it is a category of fallacies that share the trait you describe: incorrectly extrapolating a group property to an individual property.
Very often, it is because some correlation is being ignored.  You are correct that if Group A contains a higher proportion of, say, color-blind people than Group B, then a uniformly randomly selected person from Group A is more likely to be color-blind than one drawn from Group B.
But suppose the person from Group A is female.  Females are rather less likely to be color-blind than males.  With this additional information, the conclusion that this (possibly still otherwise randomly selected) person is more likely to be color-blind is no longer reliable.  This presumption that the conclusion is robust to such considerations marks it as an example of an ecological fallacy.
A: 
An individual coming from a population where a certain trait is more common, is more likely to have that trait than an individual coming from a population where said trait is less common, right?

Perhaps.
Let's assume that 14% of all men work in manufacturing, and 7% all women work in manufacturing. Does this mean that if I select a random man from the population (using a uniformly random selection method), I have a 14% chance of selecting someone who works in manufacturing? Yes, it does.
Now, it just so happens that last month, I was working in a General Motors factory. While I was there, I met an employee named Chris. Chris is a man. Does this mean that there's a 14% chance that Chris works in manufacturing?
The answer is no, of course, because I didn't meet Chris by selecting a random man using a uniformly random selection method, and because I have additional information about Chris. As a matter of fact, there is a 100% chance that Chris works in manufacturing.
A: I should imagine two different notions maybe mixed up here:
First, "one cannot apply population-wide statistics to individuals of that population" is correct if that statistics is not ergodic. Suppose you measure the Fast Blood Sugar of a population (one population, not two or more) and you realize that the average FBS of the healthy people is 80 with a standard deviation of 20, with 95% confidence. It means that if you take blood sample from a healthy individual and measure FBS, it most probably is within the range of 60-100. The fact is this is not quite right. For example, my FBS has been ~110 for the past two decades, and I am healthy sugar-wise! For me, an individual, the normal FBS is 110. If my blood sugar drops below 80, I would probably have a problem that I should look into it, if my doctor actually acknowledges the fact that "one cannot apply population-wide statistics to individuals of that population."
Second, statistics drawn from two populations with distinct traits (that affect the statistics) must be treated with respect to the population that the statistics is drawn from. In Bayesian interpretation of the probability, I suppose it constitutes the notion of apriori (or prevalence) knowledge about the population. However, it by itself is not enough to draw any conclusion.
