Define an index s of public service access as a random variable with density f(s),
with an eligibility access threshold s∗ separating better off from worse off individuals.
The access variable s can be based on an inverse scale of physical distance of each
household’s residence from the nearest public service utility (with s ∼=
0 no access,
and s → ∞ prompt access). Following the additive decomposition property of
integration, the SWF can be formulated as a weighted average of mean access of the
population below and above the threshold, respectively (as given by the first and
second terms of equation (2.1). This reflects an efficiency objective, i.e. maximising
the average access, and a distribution objective, captured by the weights vw and
vb. As in Brent ([7]) relative to a multi-objective SWF accounting for economic
efficiency, income distribution and numbers effect, the number of uncompensated
losers (N) is added here as a third objective in the SWF (a parameter αN measures
a social negative weight on N, and its subscript denotes that this weight also depends
on social valuations of individuals in N).