It’s that time of year and the emails are starting to arrive in the inboxes of professors (whether or not they have blogs). I’d say the most common are “Would you take me as your student?” and “Do you think your PhD program is the right fit for me?” and, somewhat more seldom, “Would you give me advice on my applications?”
Most of the professors I talk to just don’t answer these requests, or give curt responses. There are just too many. I feel badly, because these questions are sincere, so instead of answering all, I’ve written up advice on applications and details about whom I advise and how.
These applications are a big deal for the people writing them, and so the questions are understandable. They are crucial in some fields (psychology and some sciences, I think) where professors interview students like job applicants, and take them on as students from day one.
Not so in my fields–economics and political science–at least in the large departments. It might help if I pull back the curtain a little. Basically, these are often big programs that receive hundreds and hundreds of applications–possibly 20 or 30 per faculty member. We form a small committee to review these and make recommendations to the full faculty. So emailing individual faculty is unlikely to help.
There are exceptions, especially if your undergraduate advisor or another contact knows the professor personally. A personal note from them introducing you is very effective.