Leadership candidates prepare for the Conservative Party French language leadership debate, in in Quebec City, on Tuesday, January 17, 2017. When it comes to social issues, there are stark differences between the 14 different candidates running for the Conservative leadership, which will be decided May 27. While Kevin O’Leary and Rick Peterson support same-sex marriage, legal abortion and doctor-assisted death, Brad Trost and Peter Lemieux are on the opposite end of the spectrum.