Samuelson-Bergsons Social Welfare Function:

It implies that W (Social Welfare of the Society) is the dependent variable and  where i=1...n, the utilities of n individuals of the society, are the independent variables. W is the monotic transformation of increases, W also increases other things remaining the same. This utility function is expressed in terms indifference curves known as  Social Welfare Indifference Curve.  It represents the combinations of utilities achieved by two individuals (two dimensional diagram) through locus of points such that each point on the curve gives the same level of social welfare to the society.  The higher is the level  of social welfare indifference curve the higher is the level of welfare for the society.  Figure explains it. It may be noted that there  exists some level of substitution between the utilities of the two individuals.