Firstly, there is no way to measure correctly how the person is intelligent; while the IQ test is very controversial. Secondly, when the person X self-proclaimed that he is intelligent than others then there is a sign that he is probably the dumb one.
There are problems of attribution imo.People claiming to have invented stuff that is mentioned in books published before the reference was made.Fish and Trout for example.My IQ was 128 recently but without age adjustment it was 111.
Ego about one's own intelligence is likely detrimental to it's own advancement. The poll in my opinion is therefore paradoxical in nature. Having said that; I prefer to think I'm dumb all the time...at least that way I dont let my ego get in the way of expanding my mind or I can at least minimize that possible effect. ( if any) I'm willing to learn and listen to the opinions of others. I can admit to being imperfect or wrong if called on it. There is no shame in that...its how you grow in knowledge. Give credit to others when credit is due. It's the Mr "know it all" that thinks he's smart that usually sets himself up for a rude awakening some day...often when its too late. Such people are not able to adapt to the markets or bend with the wind (so to speak) I think it's better to be humble and unassuming about one's own intelligence. I suspect that truly intelligent people like a Stephen Hawking, Albert Einstein or someone like that is probably not even that aware of their own intelligence (except by the recognition of others) because they are too busy actually "using it" for the betterment of mankind. i.e. they dont have the time to care or ponder it as it serves no real purpose.
learned long ago, there is always going to be a smarter, better looking and wealthier guys than myself .... so why measure? are you happy .... now that has significance (i am pretty dumb by the way, but heck IF your profitable you can hire out for brains!)