A decision matrix is a decision-making tool that is used to evaluate a set of alternatives.
Typically a decision matrix will have a set of criteria and a weighting for each criterion.
The alternatives are scored for each of the criteria and then are assigned points by multiplying the score by the weighting. The alternative that has the most points wins.
The real purpose of the decision matrix is not to determine which alternative gets the most points. Oftentimes the scores or the weightings are changed in order for a particular alternative to come out ahead. This is not necessarily a bad thing.
The real purpose of the decision matrix is to view the decision and the associated alternatives from all perspectives. When you have a robust set of criteria that you are evaluating the alternatives from, often the best decision becomes self-evident.
When you make the focus being a robust set of criteria, that results in examining the alternatives for the decision based on the criteria. Regardless of the outcome, you will end up with a better decision.