Regardless of the organisation being a NFP or FP, philosophically, a CEO should not be a voting member of the governing entity (i.e. the Board) whose responsibility it is to oversight the performance of that CEO.

A voting CEO manages the submissions made to the Board, manages and adjudicates most of the assumptions upon which the submission is based (and which the Board is normally not party to), argues the submission before the Board, and then gets to vote on his/her own handiwork. Therefore, by virtue of this structure, the CEO has enormous power, some of which may be interpreted as self-validating.

It would be much more prudent to remove the voting power to secure a little more objective oversight.