It might be possible if we analysed archival footage of public life and used facial recognition software to recognise smiles. With a large enough data set i think we could get a fairly accurate answer.

Could use OpenCV ( http://opencv.org/about.html )
and some smile detection algo ( https://github.com/opencv/opencv/blob/master/samples/cpp/smiledetect.cpp )

along with a bunch of footage from
http://www.archive.org

It would make a great headline "Big data proves Smiling is old-fashioned"