Epistemic Decision Theory
Hilary Greaves
Faculty of Philosophy, University of Oxford
hilary.greaves@philosophy.ox.ac.uk
I explore the prospects for modelling epistemic rationality (in the probabilist set-
ting) via an epistemic decision theory, in a consequentialist spirit. Previous work
has focused on cases in which the truth-values of the propositions in which the
agent is selecting credences do not depend, either causally or merely evidentially, on
the agent’s choice of credences. Relaxing that restriction leads to a proliferation of
puzzle cases and theories to deal with them, including epistemic analogues of
evidential and causal decision theory, and of the Newcomb Problem and
‘Psychopath Button’ Problem. A variant of causal epistemic decision theory deals
well with most cases. However, there is a recalcitrant class of problem cases for
which no epistemic decision theory seems able to match our intuitive judgements
of epistemic rationality. This lends both precision and credence to the view that
there is a fundamental mismatch between epistemic consequentialism and the in-
tuitive notion of epistemic rationality; the implications for understanding the latter
are briefly discussed.
1. Beyond pure observation: Some puzzle cases
In most epistemological situations, the agent is a pure observer, in the
following two senses. (1) What she believes does not causally influence
the truth of the propositions that her beliefs are about. (2) While one
generally hopes that the agent is more likely to believe that P if P is
true than if P is false, still the fact that S believes that P on the basis of
evidence E is not itself additional evidence in favour of, or against, P.
Interesting epistemological puzzle cases arise when the agent is not
merely an observer: when the truth of the proposition believed does
depend, in some stronger way than in the usual cases, on the extent to
which the agent believes either that very proposition, or some other
proposition. Here are a few such cases.
Promotion:
Alice is up for promotion. Her boss, however, is a deeply insecure type:
he is more likely to promote Alice if she comes across as lacking in
confidence. Furthermore, Alice is useless at play-acting, so she will
come across that way iff she really does have a low degree of belief
Mind, Vol. 122 . 488 . October 2013 ß Greaves 2013
doi:10.1093/mind/fzt090 Advance Access publication 23 December 2013
at Rutgers University on April 28, 2014http://mind.oxfordjournals.org/Downloaded from
that she’s going to get the promotion. Specifically, the chance
1
of
her getting the promotion will be ð1 xÞ, where x is whatever degree
of belief she chooses to have in the proposition P that she will be
promoted. What credence in P is it epistemically rational for Alice to
have?
Presumably, in the Promotion case, there is a unique rationally per-
mitted degree of belief in P: Alice must adopt credence
1
2
in P, because
only in this case will her credences match her beliefs about the chances
once she has updated on the proposition that she will adopt that very
credence in P. (Here and in the following, we assume that the agent is
aware of the specification of his or her case.)
Leap:
Bob stands on the brink of a chasm, summoning up the courage to
try and leap across it. Confidence helps him in such situations:
specifically, for any value of x between 0 and 1, if Bob attempted
to leap across the chasm while having degree of belief x that he
would succeed, his chance of success would then be x. What cre-
dence in success is it epistemically rational for Bob to have?
One feels pulled in two directions. On the one hand: adopting an
extremal credence (0 or 1) will lead to a perfect match between
one’s credence and the truth, whereas a non-extremal credence will
lead to only imperfect match. But on the other: whatever credence one
adopts (extremal or otherwise), one’s credences will match the
chances: they will be the right credences to have given the then-
chances. Is any degree of belief in success epistemically rationally per-
missible, or only an extremal credence?
Embezzlement:
One of Charlie’s colleagues is accused of embezzling funds. Charlie
happens to have conclusive evidence that her colleague is guilty. She
is to be interviewed by the disciplinary tribunal. But Charlie’s col-
league has had an opportunity to randomize the content of several
1
Here and throughout the paper, I employ a relatively permissive notion of chance. On a
more restrictive notion it might turn out, for instance, that for every degree of belief Alice
might have, whether or not Alice would get the promotion if she entered the interview with
that degree of belief was already fixed by the present microphysical state of the universe, hence
the relevant chance would be either 0 or 1. Some of my analyses (specifically, some of those
based on causal epistemic decision theory) would change if I used this more restrictive notion,
but probably not in ways that would ultimately be of interest for the purposes of this paper.
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otherwise informative files (files, let us say, that the tribunal will want to
examine if Charlie gives a damning testimony). Further, in so far as the
colleague thinks that Charlie believes him guilty, he will have done so.
Specifically, if x is the colleague’s prediction for Charlie’s degree of
belief that he’s guilty, then there is a chance x that he has set in
motion a process by which each proposition originally in the files is
replaced by its own negation if a fair coin lands Heads, and is left
unaltered if the coin lands Tails. The colleague is a very reliable pre-
dictor of Charlie’s doxastic states. After such randomization (if any
occurred), Charlie has now read the files; they (now) purport to testify
to the truth of n propositions P
1
, … , P
n
. Charlie’s credence in each of
the propositions P
i
, conditional on the proposition that the files have
been randomized, is
1
2
; her credence in each P
i
conditional on the prop-
osition that the files have not been randomized is 1. What credence is it
epistemically rational for Charlie to have in the proposition G that her
colleague is guilty and in the propositions P
i
that the files purport to
testify to the truth of ?
One again feels pulled in two directions. On the one hand: Charlie has
conclusive evidence that her colleague is guilty, so, presumably, she
should retain her degree of belief 1 in the proposition G that he is
guilty. But if she does, then her colleague will almost certainly have
predicted that she would do this, hence will almost certainly have
randomized the files, in which case Charlie should adopt credence
1
2
in each P
i
; this is the best she can do, but she knows that her degree of
belief is then bound to be ‘one half away from the truth’ for each P
i
,as
the truth-value can only be 1 or 0. If, on the other hand, Charlie moves
to degree of belief 0 in G, then her colleague will almost certainly have
predicted that, and so he will almost certainly have left the files alone;
in that case, by trusting the testimony of the files vis-a
`
-vis the P
i
s,
Charlie can do very well in terms of getting the truth-values of the P
i
s
correct. Agents who disrespect their evidence concerning G in cases
like this will tend to have more beliefs that are closer to the truth —
does epistemic rationality, therefore, recommend joining them?
Arrogance:
Dennis is wondering whether or not he is arrogant. He takes a low
(resp. a high) degree of belief that one is arrogant to be evidence for
the proposition that one in fact is (resp. is not) arrogant: specifically,
his credence in the proposition A that he is arrogant, conditional on
the proposition that he will end up with credence x in A, is 1 x, for
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all x 2½0,1. What credence is it epistemically rational for Dennis to
have in the proposition A that he is arrogant?
Again there seems to be a unique rationally permitted credence:
Dennis must have credence
1
2
in A, but for a slightly different reason
than in Promotion: only if his final credence in A is
1
2
can that final
credence equal his conditional initial credence in A, conditional on the
proposition that his final credence takes that particular value.
Imps:
Emily is taking a walk through the Garden of Epistemic Imps. A
child plays on the grass in front of her. In a nearby summerhouse
are n further children, each of whom may or may not come out to
play in a minute. They are able to read Emily ’s mind, and their
algorithm for deciding whether to play outdoors is as follows. If she
forms degree of belief 0 that there is now a child before her, they will
come out to play. If she forms degree of belief 1 that there is a child
before her, they will roll a fair die, and come out to play iff the
outcome is an even number. More generally, the summerhouse chil-
dren will play with chance 1
1
2
q ðC
0
Þ
, where qðC
0
Þ is the degree of
belief Emily adopts in the proposition ð C
0
Þ that there is now a child
before her. Emily’s epistemic decision is the choice of credences in
the proposition C
0
that there is now a child before her, and, for each
j ¼ 1, … , n, the proposition C
j
that the jth summerhouse child will
be outdoors in a few minutes’ time.
Again one is torn. On the one hand: Emily has conclusive evidence
that there is now a child before her, so presumably she should retain
her degree of belief 1 in the proposition C
0
that indeed there is. In that
case, there will be a chance of
1
2
of each summerhouse child coming
out to play, so she should have credence
1
2
in each C
i
; this is the best
she can do, but she knows that her degree of belief is then bound to be
‘one half away from the truth’ for each C
i
, as the truth-value can only
be 1 or 0. On the other hand, if Emily can just persuade herself to
ignore her evidence for C
0
, and adopt (at the other extreme) credence
0 in C
0
, then, by adopting degree of belief 1 in each C
j
(j = 1,…,10),
she can guarantee a perfect match to the remaining truths. Is it epis-
temically rational to accept this ‘epistemic bribe’?
One might have strong intuitions about what epistemic rationality
recommends for each of these cases. Straw polls, however, suggest that
not all of the intuitions in question are universally shared. And
whether they are shared or not, it would be illuminating to have a
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more precise theoretical framework within which to reason about such
cases. Enter the epistemic consequentialists.
2. Epistemic consequentialism
Epistemic consequentialism is the analogue of prudential or ethical
consequentialism in the epistemic domain. Epistemic consequential-
ists recognise a notion of epistemic value, analogous to utility or ethical
value: a state of affairs is one of high epistemic value for a given agent
just in case it is a state of affairs in which there is a good degree of
fit between that agent’s beliefs and the truth. Where prudential
(respectively, ethical) consequentialists evaluate acts such as carrying
umbrellas (resp. lying) for prudential rationality (resp. moral recti-
tude), the epistemic consequentialist evaluates ‘epistemic acts’ — acts
such as believing or ‘accepting’ particular propositions, or adopting
particular credence functions — for epistemical rationality or irration-
ality. Such acts count as epistemically rational to the extent to which
they do, or could reasonably be expected to, bring about states of high
epistemic value. (The issue of whether or not they are under voluntary
control is orthogonal to that of their epistemic rationality.)
As in the prudential and ethical domains, there is a compelling
independent motivation for epistemic consequentialism (independ-
ent, that is, of consequentialism’s promise to help with theorizing
about problem cases such as those above): it would seem paradoxical
for epistemic rationality to forbid an epistemic act that would lead, or
would reasonably be expected to lead, to more epistemic good than
any permitted act.
In the prudential and ethical domains, consequentialist ideas are
nicely precisified by decision theory, in which the notion of good
being pursued is captured by a utility function (or value function)
that assigns higher numbers to preferred (or better) outcomes. This
suggests the project of developing an analogous epistemic decision
theory, to precisify epistemic consequentialism. This would be a
theory in which an epistemic utility function makes quantitative the
extent to which the agent has ‘achieved a state of high epistemic
value’, and according to which, in any given epistemic predicament,
the epistemically rational (epistemic) ‘act’ is the one that ‘tends to
maximize epistemic utility ’.
The scare quotes enclose phrases that we have thus far deliberately
left vague: epistemic decision theory comes in several varieties,
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