The poster by itself probably wouldn't convince many people, but if it complemented a presentation it could be an effective tool.
If you're using it to go along with a presentation, it's important that you make it easy for all of your audience see and read. That means that you don't want to overload it with information. Everything on the poster should be visible to the person farthest away. Even in a small room, like a classroom, this can be challenge.
The poster MUST have a visual that is not primarily text, such as a picture, a graph, or a even a chart with a few, but not many, words. If all you do is write text all over your poster, it won't accomplish anything.
For a death penalty poster, you might include a chart about the demographics of prisoners who are executed. This would address the issue of whether the death penalty is administered fairly. How about a picture of the family of a prisoner who was executed and then later found to be innocent?