A 2nd day of Yom Tov is observed outside of Israel because of sfeika d'yoma - (doubt which day Rosh Hodesh was declared, and thus, which day is the 1st day of the holiday.)
The Torah states that one should sit in the succah for 7 days. Thus, outside, of Israel, since we are not sure which day was the 1st day of Succot, I would think that this would mean that we should sit in the succah for eight days. Thus, if that's true, why should there be a debate about this. Furthermore, since sitting in the succah is a Torah commandment, following the rule of safel brachot D'Oraitah lehacmir, (in cases of making blessings related to a Torah-bound mitzvah, we are stringent), it seems that we should be making the bracha on this, as well. So, why don't we do this?