I think any means to make users use the search option reduces the number of duplicate questions. Therefore, I propose to encourage its use.
Although this is an interesting idea, I would suggest to not make the change for the following reasons:
- Many duplicates are from new users who don't care or don't even know about badges and reputation. (Many of them don't even accept answers.)
- There is not a good way to track if a person searched in order to prevent a duplicate. What would be the criteria for the badge? 100 searches? Would a user who searches for "bob" and then asks a duplicate question about SQL get credit toward the badge?
- I think either punishing with negative reputation for duplicate questions or making the search box larger for new users would be a better investment.
Users who don't know that they should search before asking won't know that there are badges either.
Searching before asking is a common etiquette of all online communities and is better known to general public (i.e. new users) than badges.
Besides, I thought that badges were to be awarded for promoting good behavior. This would be promoting the absence of bad behavior.
It's like giving someone award for not robbing a store. It is expected behavior, not exemplary good.