Should You Reward Bad Ideas?

In order to create good products or service you have produce an large amount good ideas. In order to create remarkable or great or outstanding products or services (innovation) you have to produce a vast amount of ideas: good, neutral, bad, very bad and absolutely crappy ideas. Actually you should not rate them at all in the brainstorming phase. Why? Because at some point of time in the brainstorming process there will be something excellent popping up. This usually happens when people stop rating, criticizing or filtering their own and the ideas of others.

So, in short, in my opinion you should not only reward but encourage all ideas, especially the bad ones! What do you think?