If my great-great-great grandfather was Irish, how much am i?

Do i consider myself as an Irish person?

You should be if your great great grand mother is you are

The convention many people use, and some here object to, is that you are 1/2 of what each parent was. Using that, and numbering the great grandparents instead of typing "great" lots and lots of time, we get 3rd GGP 1/1 2nd GGP 1/2 1st GGP 1/4 Grandparent 1/8 Parent 1/16 You 1/32

You could be more if some of your other ancestors were Irish. The other part of the convention is that you add the common heritages, so if you find out 2 other 3rd GGPs were also full-blooded Irish, you'd be 3/32nds. You could be less if your 3rd GGP was really half Scot and half Irish, but lied about it so no one would know he was partly Protestant.