I was offered a post-doc position at 2 institutions where I was invited for an interview by a PI. I am also invited for 2 more interviews the next couple of weeks at different institutions. Both institutions who sent the offer letter are expecting an answer and I think they assume that I will accept the offer. This is what I got from the conversation. I am really confused because I do not want to ruin my reputation if they get upset when I do not accept their offer. All what I did is that I showed interest during the interview. Is there any advice on how to professionally decline an offer without offending the PI. Also what is the best advice on how to choose between the 2 offers? Should I go to the 2 scheduled interviews or would I be confusing myself even more?
(1) It is perfectly normal to reject offers. The other side (professors, universities) rejects application every time they make an offer, and they know that, often, applicants apply to more than one position. You might want to be open about this, i.e. that you are considering another offer at a different institute as well.
(2) How to choose which offer is best depends on many factors, a lot of which are personal. Where do you want to work in terms of location, which institute fits your personality and ideal workplace, which group is bigger/smaller/more successful/gives more room for personal contribution? What about salary/teaching obligations/availability of lab space/equipment and research participants (if you need some)...
Ask some questions during the interviews to see which place suits you best. Maybe even walk around in the city, if this is of importance for you.
(3) As pointed to in (2), go to both interviews and then ask for information that will help you make your decision.