Does risk aversion give us a
good reason to diversify our
charitable portfolio?
James Snowden
Structure
• Risk aversion in economics
• Maximising expected utility means donating
to only one charity
• Do we have to maximise expected utility?
– With self-interested preferences
– With altruistic preferences
• Conclude that, in the central case, there is no
good reason for a pure altruist to donate to
multiple charities
RISK AVERSION IN
ECONOMICS
• “Risk aversion” gives us a good reason to
diversify investment portfolios
And
• But the justification relates to diminishing
marginal utility of money
Only umbrellas
Both stocks
• “my utility curve is one thing… my attitude
towards risk, is another thing” (Hansson,
1988, p. 137)
Probability
Utility
MALARIA CHARITY VS.
ANIMAL CHARITY
Assume no diminishing marginal returns
over the interval of a small donation
Or
$1,000
$500
$500
$1,000
• 50%: improve 100
animal lives
• 50%: no effect
• 50%: Extend 1
human life
• 50%: no effect
You decide you care more about extending 1 human life than
improving 100 animal lives
U(extend 1 human life) = 1.1 > U(improve 100 animal lives) =1
States: Neither
charity
effective
Actions
Only
Malaria
charity
effective
(25%)
$1,000 to No effect
Malaria
charity
0
$500 to
each
Only
Animal
charity
effective
No effect
0
$1,000 to No effect
Animal
Both
charities
effective
EU
(25%)
(25%)
No effect
0
(25%)
Extend 2
human
lives
Extend 2
human
lives
1.1
2.2
2.2
Improve
Extend 1 Extend 1
100 animal human life human life;
lives
Improve
100 animal
1.1
lives
1.05
1
2.1
Improve
No effect Improve
200 animal
200 animal
DO WE HAVE TO MAXIMISE
EXPECTED UTILITY?
So do we have to maximise
expected utility?
• Economists normally say yes!
– VnM axioms prescribe maximising expected
utility in cases of risk
– Savage axioms prescribe maximising
expected utility in cases of uncertainty
So do we have to maximise
expected utility?
• But most people are risk averse over
utilities and this may be permissible
– Savage / VnM axioms have been challenged
by Buchak (2013) and McClennen (1983)
– Allais paradox clearly shows that most people
are in fact risk averse over utilities
So do we have to maximise
expected utility?
• New decision theories have been proposed
which allow some non-linear weighting of
probabilities, accounting for risk aversion
– Prospect theory (Kahneman & Tversky, 1979)
– Rank-dependent expected utility theory
(Quiggin, 1993)
– Risk-weighted expected utility theory (Buchak,
2013)
So do we have to maximise
expected utility?
• There may be more than one way of
aggregating states so as to achieve the
means to ones ends.
• Attitude to risk is just another subjective
preference. There is no right answer
So do we have to maximise
expected utility?
• Even if this is true for self-interested
preferences, it is not true for altruistic
preferences
THINGS ARE DIFFERENT
WITH ALTRUISTIC
PREFERENCES
Hedge
P1) Malaria is as good as *Malaria*
P2) *Malaria* is better than Both
C) Malaria is better than Both
• What kind of attitude is risk aversion?
• Is it just a subjective preference capturing my own
attitude towards risk?
– If so, it seems inappropriate to determine what to do
for the sake of others based on this.
• Is it rather a view as to what constitutes a morally
better set of state contingent outcomes?
– If so, it seems an indefensible one, given that Malaria
is just as good as *Malaria* from the perspective of all
the potential beneficiaries, and *Malaria* is better
than Both.
Recap
• Maximising expected utility gives us a
reason to donate to only one charity
• Maximising expected utility might not be
required with self-interested preferences
• But there is more reason that it might hold
for altruistic preferences
When would this result not hold?
Empirical
• Not purely altruistic
• Diminishing marginal
returns
• Signalling
• Ineffective donation
might reduce future
desire to give
• Indifference
Philosophical
• Incomparability
• Evidential decision
theory creates quasicoordination problems
• Diminishing marginal
moral value (e.g. moral
satisficing)
QUESTIONS