I think you'll have an extremely hard time convincing people that liberals care about the effectiveness, cost or otherwise, of the war on drugs since they don't care about the effectiveness of any other government policy.
what on earth does this even mean?
wanting effective policies is not something that is determined by one's political leanings; certainly there are differences in what is considered a positive or negative effect and how any degree of effectiveness is measured, but that does not negate the goal of those across the political spectrum of achieving an effective policy
the fact that the majority of those in law enforcement and in the judicial system support decriminalization is not something I will dismiss as a consideration