From a social and business point of view, it might be good to look at the markets for portraits today, depending on whether you think true artists should paint to commission. Maybe do a little research and see who is buying the portraits, from which countries and why they are buying them. For example, would it be for commercial premises or just as an investment?
There are always lots of arguments around realsim too. A painting of the Queen in Britain was recently slated for being 'too realistic' and for making her look old and stern and emotionless. Yet nowadays, because we have actuality of image in our lives (with iphone cameras, you tube video news etc) we don't swallow romaniticisation so easily any more. It might also be interesting to look at how portrait painting has changed down through the ages and to make an argument in your dissertation as to whether or not you think it is still relevant today.