K. Nyborg J. of Economic Behavior Org. 42 2000 305–322 311
5. Homo Politicus with shared responsibility
Homo Politicus with shared responsibility is the person who interprets the valuation question as follows: “What is the maximum amount I find it socially right for everybody to
pay, in order to ensure this project?” Formally, shared responsibility will be interpreted as a requirement that 1x
i
= 1x
j
= 1x
for all i, j ∈ N . Thus, any individual income changes apart from this equal per person payment are disregarded. Let a
j
be the willingness to pay for a marginal change in the public good of Homo Politicus with shared responsibility. Then, we get from Eq. 4.1 that
a
j
= γ
j
β
j
1y 5.1
Here, β
j
= 1n
P
i∈N
∂V
j
∂ω
j i
∂ν
j
∂x
i
, which is the average welfare weight according to j ’s ethical views attached to individual income. Similarly, γ
j
is the average welfare weight attached to individuals’ access to the public good, γ
j
= 1n
P
i∈N
∂V
j
∂ω
j i
∂ν
j
∂y .
In general, a
j
may be smaller or larger than p
j
. To illustrate the relationship between the two, let 1y = 1, and denote j ’s beliefs about i’s personal valuation p
j i
, so that p
j i
= ∂ν
j
x
i
, y; α
i
∂y∂ν
j
x
i
, y; α
i
∂x
i
implying that p
j
= p
j j
. Then, we get that a
j
= P
i∈N
p
j i
β
j i
P
i∈N
β
j i
5.2 Thus, the difference between a
j
and p
j
depends on both the difference between j ’s own personal valuation and her judgment of others’ valuation, and the welfare weight she
attaches to every individual’s marginal income change. Note that even if we require p
j i
= p
i
, i.e. every individual’s ordinal preferences are respected, a
j
will generally differ from the average personal marginal valuation 1n
P p
i
: 1
n X
i∈N
p
i
= 1
n X
i∈N
∂ν
j
x
i
, y; α
i
∂y ∂ν
j
x
i
, y; α
i
∂x
i
5.3 While Eq. 5.3 is calculated using a sum of ratios, and thus can be estimated using only
ordinal measurement of well-being, a
j
is a ratio of sums 5.2, which does indeed require a cardinal well-being concept. 1n
P p
i
and a
j
coincide in the case that β
j i
= β for all i; but
if the weight ∂W
j
∂ω
j i
varies between persons, or if j believes that different people have a different marginal well-being of income, they will generally differ. For p
j
and a
j
to be equal in general, one must have both β
j i
= β and p
j
= 1n
P p
i
. It is important to note that a
j
does not provide a monetary measure of the individual’s personal preferences. Rather, it reflects a mixture of ethical views, subjective beliefs about other people’s preferences,
and a particular assumption regarding the project’s effects on other people’s income. For non-marginal changes, compensating and equivalent surplus measures must be interpreted
similarly.
312 K. Nyborg J. of Economic Behavior Org. 42 2000 305–322
6. Homo Politicus with sole responsibility
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