Please explain, with the use of examples where appropriate, the difficulties brought up by the concept of social welfare and how these difficulties are overcome. (essay question)

Requirements:

Student should use the required reading (particularly Kenneth Arrow's (1950) and Thomas Cool's (1997) papers) regarding the problem of aggregating individual preferences into social preferences. Student should explain how social welfare preferences can be depicted using the concept of social welfare functions.

Student should show an understanding of the three desirable properties of any function attempting to show social preferences and why this causes a problem (reference to Arrow's paper) Student should show an understanding of why the third condition is excluded (reference to Cool's paper)

Use relevant examples for this such as the voting mechanisms shown in the lecture notes and the problems faced when aggregating the individual preferences. Mention / depiction of more than one method of aggregation as well as appropriate use of logical / mathematical notation will score more highly. As well as reference to wider reading sources where appropriate.