Justice in an uncertain world: Evidence on donations to cancer research

Abstract

The paper uses information on actual and hypothetical charitable contributions to cancer research in the United Kingdom to elicit information on justice principles endorsed by donors. They face a choice between fund-raising contributions for several hereditary and lifestyle-related cancers. Donors’ choices of how much to donate to different cancers reveal how they view luck vis-a-vis risky individual choices. The estimation results reveal that donations are smaller for cancers with higher prevention rates, which is the probability that the potential cancer victim can avoid the cancer in question by some choice. We also find that provision of information on lifestyle-related causes of cancer adversely affects contributions. In contrast, information on hereditary causes has a positive effect on donations. Furthermore, a large share of donors indicated in their feedback that they chose donations to a hereditary over a lifestyle-related cancer to “punish” poor individual choices. These findings suggest that many donors lean toward choice egalitarianism, which conditions donations on the potential beneficiaries’ choices.

Appendices

Appendix A: Proof of Proposition 1

(i) We start with the analysis of the choice egalitarian ex ante donor’s choice problem. Using the assumptions about the values of $U^{P}\left (H\right )$ and $U^{P}\left (M\right ) ,$ the choice egalitarian ex ante donor’s utility function in Eq. 1 can be written as

$$ V^{xa}\left( d\right) =W\left( y-d,p_{s}\left( d\right) +\left( 1-p_{s}\left( d\right) \right) p_{r}\right) . $$

The first-order condition for the maximization of this objective function is given by

$$ \begin{array}{@{}rcl@{}} \frac{\partial V^{xa}\left( d\right) }{\partial d} &=&-W_{1}\left( y-d,p_{s}\left( d\right) +\left( 1-p_{s}\left( d\right) \right) p_{r}\right) \\ &&+p_{s}^{\prime }\left( d\right) \left( 1-p_{r}\right) W_{2}\left( y-d,p_{s}\left( d\right) +\left( 1-p_{s}\left( d\right) \right) p_{r}\right) \\ &=&0. \end{array} $$

(4)

Note that concavity of W and strict concavity of e imply that the second-order condition for the donor’s optimization problem is always satisfied. Denote the optimal level of d by d^∗. By the implicit function theorem, the effect of p_r on the optimal d^∗ is given by

$$ \begin{array}{@{}rcl@{}} \frac{\partial d^{\ast }}{\partial p_{r}} &=&-\frac{\frac{\partial^{2}V^{xa}\left( d\right) }{\partial d\partial p_{r}}}{\frac{\partial^{2}V^{xa}\left( d\right) }{\partial d^{2}}} \\ &=&-\frac{-W_{12}\left( \cdot \right) \left( 1-p_{s}\left( d\right) \right) -p_{s}^{\prime }\left( d\right) W_{2}\left( \cdot \right) +p_{s}^{\prime }\left( d\right) \left( 1-p_{r}\right) \left( 1-p_{s}\left( d\right) \right) W_{22}\left( \cdot \right) }{\frac{\partial^{2}V^{xa}\left( d\right) }{ \partial d^{2}}} \\ &<&0, \end{array} $$

where the last inequality follows from the sign assumptions on the second-order derivatives of W. Hence, the optimal donation is negatively affected by the prevention rate.

Next consider a choice egalitarian ex post donor. From Eq. 2, her objective function can be written as

$$ V^{xp}\left( d\right) =p_{s}\left( d\right) W\left( y-d,1\right) +\left( 1-p_{s}\left( d\right) \right) W\left( y-d,p_{r}\right) . $$

Differentiating it with respect to d yields the first-order condition for her optimization problem

$$ \begin{array}{@{}rcl@{}} \frac{\partial V^{xp}\left( d\right) }{\partial d} &=&p_{s}^{\prime }\left( d\right) \left[ W\left( y-d,1\right) -W\left( y-d,p_{r}\right) \right] \\ &&-p_{s}\left( d\right) \left[ W_{1}\left( y-d,1\right) -W_{1}\left( y-d,p_{r}\right) \right] -W_{1}\left( y-d,p_{r}\right) \\ &=&0. \end{array} $$

(5)

By the implicit function theorem and the properties of W, we have

$$ \begin{array}{@{}rcl@{}} \frac{\partial d^{\ast }}{\partial p_{r}} &=&-\frac{\frac{\partial^{2}V^{xp}\left( d\right) }{\partial d\partial p_{r}}}{\frac{\partial^{2}V^{xp}\left( d\right) }{\partial d^{2}}} \\ &=&-\frac{-p_{s}^{\prime }\left( d\right) W_{2}\left( \cdot \right) -\left( 1-p_{s}\left( d\right) \right) W_{12}\left( \cdot \right) }{\frac{\partial^{2}V^{xp}\left( d\right) }{\partial d^{2}}} \\ &<&0, \end{array} $$

which implies that the optimal donation of the choice egalitarian ex post donor is also negatively affected by the prevention rate.

(ii) By setting p_r equal to 0 in Eq. 1, a non-choice egalitarian ex ante donor’s objective can be written as

$$ V^{xa}\left( d\right) =W\left( y-d,p_{s}\left( d\right) \right) . $$

Similarly, setting p_r equal to 0 in Eq. 2, a non choice egalitarian ex post donor’s objective can be written as

$$ V^{xp}\left( d\right) =p_{s}\left( d\right) W\left( y-d,1\right) +\left( 1-p_{s}\left( d\right) \right) W\left( y-d,0\right) . $$

Since the prevention rate does not appear in both functions, the optimal donation of either donor is independent of p_r.

Appendix B: Choice Questions

Question 1

Suppose you have been asked to donate to research on cancer treatment of two cancers: non-Hodgkin lymphoma and melanoma.

Non-Hodgkin lymphoma is a type of cancer that develops in the lymphatic system, which is a network of vessels and glands spread throughout one’s body. The percentage of preventable cases of Non-Hodgkin lymphoma in the United Kingdom is around 3%, which means that about 3% of the cases could have been prevented by adopting alternative lifestyles (the remaining 97% are associated with hereditary genetic defects or other causes).

Melanoma is a type of skin cancer that develops from the pigment-containing cells known as melanocytes and that can spread to other organs in the body. The percentage of preventable cases of Melanoma in the United Kingdom is around 86%, which means that about 86% of the cases could have been prevented by adopting an alternative lifestyle (avoiding UV radiation associated with excessive exposure to sunlight).

Now you can decide whether to donate to one, both, or none of them.

Question 1.1

For donating only to non-Hodgkin lymphoma.

You have indicated that you would donate only to non-Hodgkin lymphoma.

Please indicate the amount that you would have donated. You can enter any positive number between 0.01 and 200. If you enter 34.75, that will mean that you would have donated 34 pounds and 75 pence. Please do not enter any currency signs.

Question 1.2

For donating only to melanoma.

You have indicated that you would donate only to melanoma.

Please indicate the amount that you would have donated. You can enter any positive number between 0.01 and 200. If you enter 34.75, that will mean that you would have donated 34 pounds and 75 pence. Please do not enter any currency signs.

Question 1.3

For donating to both cancers.

You have indicated that you would donate to both cancers.

Please indicate the amount that you would have donated to non-Hodgkin lymphoma. You can enter any positive number between 0.01 and 200. If you enter 34.75, that will mean that you would have donated 34 pounds and 75 pence. Please do not enter any currency signs.

Please indicate the amount that you would have donated to melanoma. You can enter any number positive between 0.01 and 200. If you enter 34.75, that will mean that you would have donated 34 pounds and 75 pence. Please do not enter any currency signs.