Final answer:
The most relevant decision-making principle for a government considering different sizes of social programs with respective marginal costs and benefits is Cost-benefit analysis, which utilizes marginal analysis to weigh incremental changes in costs and benefits.
Step-by-step explanation:
When a government is contemplating the implementation of a new social program and can choose from projects with varying sizes and respective marginal costs and benefits, the most relevant decision-making principle in this context is Cost-benefit analysis. This involves comparing what will be sacrificed against what will be gained to make a decision, weighing marginal costs against marginal benefits. Cost Benefit Analysis employs a T-shaped chart where costs and benefits are compared on each side, assisting policymakers in making choices that maximize societal welfare.
Marginal analysis is a cornerstone of this process, as it involves comparing the added benefits and costs of choosing a little more or a little less of a good. Instead of looking at total costs and total benefits, marginal analysis focuses on how these costs and benefits change when adjusting the level of output or scale of a project, guiding toward the most efficient allocation of resources.