Why not just let the union strike and hire replacements? How many unionized workers couldn't easily be replaced? Typically, the only (private sector) unions left are unskilled or low-skilled labor. For instance, my local supermarket is unionized...like they couldn't replace hourly minimum wage people?
What's the benefit to even negotiating with them, compared to sitting down at the meeting and telling them flat-out that you have no intention of increasing their compensation, and that they should feel free to strike? You tell them that you can't in god conscious tell them anything else, because it would be negotiating in bad faith, since you aren't going to change anything, regardless of if they strike or not?
You really think it would be that tough to find replacements in this job market?

