What a decision matrix is
A decision matrix lists your options down the rows and your criteria across the columns. Each option is scored against each criterion, usually from one to five. A weighted matrix multiplies every score by the importance of its criterion, so a strong performance on something you care about counts for more.
How to weight the criteria
Weights are where the honesty happens. Distribute a fixed total, such as 100 points, across your criteria before you look at the options. Deciding what matters first prevents you from unconsciously adjusting the weights to justify a favourite choice.
Reading the result
When two options finish close together, the decision is genuinely finely balanced. In that case, look at which criteria drive the gap and ask whether you would be comfortable defending that ranking. If not, reweight and try again; the exercise is as valuable as the answer.