I have done some research and found many interesting things about birth order and only children. For only children it says the child is pampered and spoiled, the center of attention and self-centered. I have known some kids that are an only child and I would have to agree. However, this would probably be an example of an availability heuristic for me because I only know a few and I am sure there are many only children that do not follow.
Another group this website talks about is first-born child. It says that the first-born child believes that they must gain and hold over superiority over other children, be right and controlling, strives to please, sometimes strive to protect and help others, and have responsible behavior. I am a first-born child I do like to be right, controlling, responsible, and stick up for my sisters. However, I disagree that first-borns' try to gain superiority over other children. If I ever say that I am the best child, I always am joking and not serious.
On the website, I think there are points people could agree with and also points people could disagree with. I think it's interesting but I think this information isn't completely reliable because it is impossible to have general traits for everyone just based on birth order. On the website it even says that the following characteristics will not apply to all children in every family so not extremely reliable.

http://childdevelopmentinfo.com/child-development/birth_order.shtml
Are First Born Kids The Best?
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I think birth-order research is really interesting. There seems to be compelling evidence that some of these characteristics are true for first-borns/only-childs, but like you said it could be an availability heuristic. I am a first born child, and I definitely feel like the most responsible child in my family. My sister is ten years younger than me and I feel like I pretty much helped raise her. My aunt also used to tell me that when I was younger (like five or six) I would always be watching/taking care of my brother who is two years younger than me. I don't feel the need to be superior though either. It's more about taking care of the people I'm with.
I am also a older sibling and I do have a sense of wanting to protect be a role-model and be responsible to my siblings but I agree that this does not imply that I am the best. I think that an older sibling sometimes feels the need to be a older role-model for their siblings and I think that people may confuse that with a sense of superiority complex.
I think this topic is very interesting, because it raises a lot of points, but yet at the same time these points aren't always reliable as you said. I am the second child of two in my family, and I do find that my older sister always has to have control over situations and very responsible. But, yet at the same time I feel as though I could apply some of these characteristics to myself as well.
I definitely agree with you about people agreeing and disagreeing with the things on the website. Me being an only child I wouldn't consider myself spoiled or self-centered. I didn't get all the things I wanted growing up. But then again I do know kids who are only children that do act spoiled and stuck up. I think it's a very controversial issue and there is no right or wrong answer because I think it depends on the parents.
Like you said, it is very hard to generalize this information appropriately seeing as how it is focused on a single variable and does not take into account other variables. I have a good friend who an only child but she is most selfless person that I know and I think that is simply because of how her parents chose to raise her. I would be interested in how money/socioeconomic standing affect this statistic because I think that children who are older and who are only children that are raised in a low-income house hold have a large responsibility to change their life. I would say that the development of an only child is interesting because there is not a brother-sister bond shared within the family which was an important aspect of my life growing up (having a brother).