a policy offering a combination of rewards and punishment to induce behavior
The carrot and the stick approach were different approaches used by the British when the got control of Quebec after the Seven Year's War. They knew that right now they were out numbered by the Canadiens, so they had to be careful about how they would decide to keep them from rebelling, yet still enforce laws. The Stick Approach: The stick approach was an approach which used force and aggression. This approach would not give the opposition a chance to rebel because in a way it was a threat. A supporter of this harsh approach was the British Cononial Secretary, Earl of Shelburne. For example, if the British planned to use this approach on the Canadiens, they would: restrict the Roman Catholic religion, send all French government and church officials back to France, give the entire control of the fur-trade to the British merchants, not allow the Roman Catholic practitioners to take part in the government, and restrict the territory of Quebec to a small area.
The Carrot Approach: Unlike the stick approach, the carrot approach used sympathy, and coaxing. This approach is related to dangling a carrot in front of a horses head to get it to move, rather than striking it with a stick. When using this approach the opposition would have a voice in what the new laws should be, and in this case it was used to keep the oposition from rebelling. A supporter of this sympathetic approach towards the Canadiens was British Governor, Sir James Murray. For example, if the British were to use this approach towards the Canadiens, they would: allow all Roman Catholics to practice their religion freely, allow Roman Catholics and Protestants to take part in the government, allow the French to take part in the government, and allow the French into the interior, yet still giving some territory to the First Nations Peoples.
As you can probably notice the difference in these two approaches are huge, yet they were both used for the same reasons.