A billionaire may not be the smartest person on earth but they are smart enough on their own ways. First of all, they are smart enough to work hard. They stop their self from wasting the precious times and motivates their self to do repetitive and boring work. They mostly start their work as a low employee but with hard work, they make themselves climb the position of the top, where mostly they still do hard work. So this is actually very smart as they know they can achieve it with hard work. Also they must be smart in other areas too.
The world of business is so tough and competitive that you need to be super smart, hard working, efficient, talented and have all the soft skills that involve getting people to work with you. If you are a billionaire, there are tons of challenges to keeping yourself in a position when so many people want to take you down. Yes, billionaires are smarter, how could they not be?
We must also distinguish between entrepreneurs and those inherit their wealth. Now it could be argued that in general entrepreneurs tend to be smarter, that's how they are so successful but those who inherit their wealth often tend to be some of the stupidest people around especially if they have lived off their parents their whole life and don't know who to work for themselves.
Billionaires are not smarter than everyone else, and there is no way to prove which people are the smartest because you can not test and know every single person in the country or world. Not all billionaires worked to achieve the money they have though, they could have received it from parents.
Just because a person has a ton of money doesn't mean they're smart. It might mean they're crafty and more competitive (probably competitive to a pathological level); but it does not mean that they are smarter. Smart people generally don't define their self worth by money, because they have self esteem in other areas.
I would agree, for example, that Ted Turner knows a lot more than myself, on the subject of business, especially that involving cable television and the like. But that doesn't mean they're "smarter" per se. What I mean is, it's dangerous to say that they are smarter and more elite than the general public. That allows people like Ted Turner to talk about population control (which he has on numerous occasions) and all he has to do is say "why not control the population, I'm smarter and know what I'm talking about".
Or NYC's Mayor Bloomberg. I don't care how much money he's worth, that doesn't make his soda bans effective, and his being a billionaire doesn't mean we have to listen to him just because he's "smarter" than us in certain ways.
Have you remembered that Paris Hilton is a billionaire? A lot of them are not smart, most inherited their money from their smart ancestors. Their ancestors bought things back in the early/ mid 1900s and because it ended up to be much needed to this day, the product has grown in popularity. Plus, the price of inflation.
As we used to say in the home mortgage business, there is no correlation between IQ and personal net worth. A billionaire could be so endowed because he had a wealthy family to start with. Or he could have simply been lucky in making investments and hiring the right people.