Which is the correct word to use here: "consensus" or "majority"?

Solution 1:

While consensus is not necessarily a unanimous stance, it is usually a vast majority - nearing complete agreement. I would expect a rate of 80% or more if someone said that an opinion was consensus.

Majority simply means the larger part. That is why a lot of companies have an owner with a majority share of 51%; so that under any circumstances they will always own the larger part of the company. It doesn't matter that the difference is so small (51-49% is just 2%) - if it is larger, it is a majority.

Hope that helps.

Solution 2:

Consensus means "general agreement," while majority means "the greater number."

The NOAD reports the following note, about the usage of majority.

Majority means more than half: fifty-one out of a hundred is a majority. A plurality is the largest number among three or more. Consider the following scenarios: If Anne received 50 votes, Barry received 30, and Carlos received 20, then Anne received a plurality, and no candidate won a majority. If Anne got 35 votes, Barry 14, and Carlos 51, then Carlos won both the plurality and the majority .