Should your LinkedIn Summary (About) section be written in the first person, the implied first person (like most resume summaries), or in the third person?
I say first person because:
First-person writing comes across as more authentic and makes it easier for people to connect with you.
Writing about yourself in the third person can come across as arrogant and distant, and using the implied first person can come across as lazy, as if you just copied and pasted your resume summary.
LinkedIn is a professional SOCIAL network, a place for you to network with people one-to-one, and writing about yourself without the “I” can put a barrier between you and the reader.
I would add that the Summary is the place to tell people a little bit more about who you are – the real you -- not what you’ve done throughout your career. The Experience section takes care of that.