Interesting article from Harvard Business Review but I have to say that if you've gotten to the point where you have to ask, "What would it take to change your mind?" - then you really haven't done your job.
The way I learned and what has stuck with me is the following process when looking at advocating change (a new product or service). This process can be used for just about any new situation though:
1. Ask "What do you have now?" Force the person who you need to make a decision to look at what is currently in place.
2. What do you like about what is in place? Big mistake many make is to assume that just because some people are advocating change that everything about the current system is bad. In many cases there are features of the current system that people really like. They want change but they also want to keep the things that are familiar to them that works.
3. What would you like to change about what is currently in place? This question is the most important because it basically answers why do they want to make a change in the first place. It will also give you the clues to what the important decision factors will be.
4. How did the current system come to be? Why did you choose what is currently in place? This also reveals much about the decision process.
If you properly "qualify" the situation by asking the above questions and craft your proposed solution accordingly - then hopefully you won't need to ask "What would it take to change your mind?"