A new online journal in mathematics, Rejecta Mathematica, only publishes papers that have been rejected from traditional peer-reviewed journals. I’m not 100% sure, but it doesn’t seem to be a joke. I don’t know about mathematics, but in economics getting rejected by a journal is not necessarily a sign that your paper is bad. The refereeing process contains some signal, but also some noise. However, I don’t see how a rejection can be a sign of anything good per se, and surely the expected quality of a rejected paper is less than the expected quality of a not-rejected paper, unless the refereeing process is seriously biased or flawed. I also don’t really see why authors would want to publicise that they’ve been rejected by publishing in a journal that specialises in rejected papers. So it’s hard for me to understand how this journal is valuable and why authors would want to use it. The one possibly good argument the website gives is that by reading this journal you can find out what doesn’t work, so you don’t waste time trying it yourself. Maybe, but I think much better ways to improve traditional journals seem to be (a) speed up the refereeing process, and (b) reduce the time to publication.