Reasoning

1
Chapter 12

• Reasoning

2
Human Reasoning
The focus of this chapter will be on human
reasoning, with reasoning thought of as the way
we draw conclusions (or what is sometimes called
beliefs) based on the available
evidence. Integral to this issue is the way in
which we test certain alternative beliefs to
insure that our current belief is, in
fact, justified. As you will see, this process
of arriving at and testing beliefs is not quite
as reasonable as we might often like to
believe it is.
3
Belief Bias (or Confirmation Bias)
One (unreasonable?) characteristic of human
reasoning that effects us in many different
contexts is a bias in our reasoning called belief
bias or confirmation bias. Basically, this bias
can be explained as the tendency to search for
evidence that supports our current beliefs, and
to discount (or to not even seek out) evidence
that does not support our current beliefs. This
tendency might best be illustrated with an
example The numbers 4, 6, 8 conform to some
rule - give me other sets or numbers and ask me
if they conform then tell me the rule.
4
The Inappropriateness of Belief Bias
Generally speaking, this bias to seek out
confirming evidence, and to avoid or ignore
disconfirming evidence, is an extremely poor way
to draw conclusions. This is true because, as
the philosopher named Popper has pointed out,
disconfirming evidence is much more
informative that is confirming evidence
why? While confirming evidence may be
consistent with your current belief, it does not
discriminate between that belief and any
other. In contrast, disconfirming evidence
rules out certain beliefs.
5
The Pervasiveness of Belief Bias
Despite the fact that this belief bias is
generally inappropriate as a means for adopting
beliefs, it does seem to be a very big part of
the way we adopt and sustain our beliefs. You
will see evidence of this in a number of human
reasoning contexts throughout this chapter we
generally want to accept things that fit with our
current belief structure and reject those that
dont. How could we have evolved to this point
with such a faulty reasoning bias in place? Good
question lets keep in fresh as we consider
some reasoning contexts.
6
Logic Reasoning
When we colloquially use words like reasonable,
we generally associate them with logic. That is,
when we say someone is behaving in a reasonable
manner, we mean there is a good logical basis
for their acts. In fact, when philosophers were
trying to formally capture the way in which
humans draw conclusions based on evidence, the
procedure they came up with is that of formal
logic. But, as Spock might question, is human
reasoning truly logical at all? Our discussion
of belief bias suggests not but lets consider
this in more detail.
7
Logic Syllogisms
One way in which formal logical problems are
often presented is via a set of statements called
a syllogism. A syllogism typically includes two
premises, and a conclusion. The task is to decide
if the conclusion is necessarily true given the
premises (and only given the premises). For
example All P are M All S are M Therefore,
all S are P Does this conclusion follow from the
premises?
8
More Syllogism Examples
Are these conclusions valid or invalid
given the premises? Should I put a question
or two like this on the exam?
9
Human Performance with Syllogisms
It turns out the humans are quite pathetic at
coming up with the correct answer when presented
with syllogisms. For example, Chapman Chapman
(1959) gave subjects syllogisms like the one you
just saw, and 81 of the subjects endorsed false
syllogisms as being correct (did you?). Subjects
did better when the syllogisms were spelled out
in concrete terms (as illustrated below), but
only a little better. All Plumbers are
Mortal All Sadists are Mortal Therefore, all
Sadists are Plumbers
10
Belief Bias as a Source of Errors
The errors that humans make when solving
syllogisms arise as the results of several
different factors. One factor that causes errors
is the belief bias we discussed earlier. In the
case of syllogisms, this shows up as a general
bias to accept conclusions that the subject
believes are true, irrespective of whether the
conclusion follows from the premises. All
Slaves work hard. Some Professors wear
jeans. All Students work hard. Some Idiots wear
jeans. Therefore, Therefore, All
Students are Slaves. Some Professors are Idiots.
11
Atmosphere as a Source of Errors
Another factor that has found to be relevant to
the errors humans make with syllogisms is
something termed Atmosphere. As you have
noticed, syllogisms can include words in the
premises such as all or some. It has been
shown that if the premises include the word
all, subjects are more likely to accept
conclusions that include the word all (same
with some). It is as though the wording
used in the premises creates an atmosphere that
makes us more likely to accept conclusions that
have that same wording.
12
Conversion Errors
It also seems as though subjects do not properly
understand the formal rules of logic, and
regularly make conversion errors. That is,
they do things like (1) Interpret all A are B
as also implying that all B are (all
students are human does not logically imply that
all humans are students). (2) Interpret
A or B as implying not both A B when
logically, A or B implies A, B or AandB. (3)
Interpret some F are not G as implying some G
are not F
13
Logic Reasoning Summary
What this all suggests is that humans do not
reason in a logical manner at least if
logical is measured by their ability
to understand syllogism. Instead, they seem to
be illogically influenced by things such as
belief bias, atmosphere effects, and errors of
conversion. But perhaps these errors only
suggest that humans do not think in terms of
syllogistic logic (even though it was meant to
formalize human logic) perhaps in other logic
contexts human reasoning would seem to be more
logical.
14
Conditional Statements
Another context in which human reasoning has been
examined is humans ability to assess the truth
of conditional statements. Conditional
statements are statements of the If X, then
Y type like If I have my parents permission,
then I can take the car out Friday
evening Typical problems involve a conditional
statement followed by some event subjects are
then asked what (if anything) they can conclude,
like If X then not Y .. X? Y? not X? not Y?
15
Human Performance on Conditional Statements
Once again, humans are generally very bad at
drawing valid conclusions from these types of
problems. Once again, they do a little better
when the problems are made concrete rather than
left abstract. And once again they show a belief
bias whereby they are likely to endorse any
problem that has a conclusion in line with
their beliefs, and to reject any problem where
the conclusion goes against their
beliefs. However, a true explanation is a little
more complex. To get their, lets try some
examples ...
16
Vowels and Even Numbers
Which cards would you turn over to test the
following rule if a card has a vowel on one
side, it has an even number on the other ...
Only 4 of human subjects get this problem
completely right can you get it right after
all you have learned?
17
Informative vs. Non-informative
The first is an This card is The third is This
card informative not useful not informative is
informative card because because because
neither because if the if the number neither a an
even nor an letter is a is odd, the vowel
or odd card digit vowel, the rule is invalid.
consonant invalidates the rule is
invalid. invalidates rule
18
OK with Modus Ponens
Most people do correctly pick the A card as one
to be turned over. The need to turn over the A
card reflects a logical rule termed modus ponens,
as embodied in the following abstract form If
P then Q. P is true. Therefore Q must be
true Thus, the A card represents a condition
where P (one side is a vowel) is true, and we
seem to know that in order for the rule to be
true, then Q must be true (there must be an even
number on the other side) via modus ponens.
19
No Good at Modus Tollens
However, subjects do not seem to understand the
other logical rule that must be true for the
conditional statement to hold. This rule is
reflected in the following abstract form If P
then Q. Q is false. Therefore P must also be
false. In the card problem, this could be tested
by examining the 7 card (Q is false) to test
whether P is also false (as would be suggested if
the digit were odd an even digit would be
a violation of modus tollens.
20
Not Just Bad Logic
Thus, it seems as though our reasoning is not
based on formal logical principles in the
conditional situation either. However, it is not
as simple as that because human reasoning in
conditional situations actually becomes better
when we test it with respect to rules that the
subjects are familiar with. For example, try
evaluating the following conditional
statement, then mentally compare your thinking
in this context with your thinking in the more
abstract context whats different?
21
How about this one?
Test the rule If the person is drinking beer,
then they must be over 18 years old - subjects
are about 73 accurate here
Joe is drinking beer
Sarah is 21 years old
Bruce is drinking Coca- Cola
Brenda is 16 years old
Easier, right? Why? More concrete? Or Familiar
with the rule?
22
Try this one ...
If an envelope is sealed, then it has a 50 lire
stamp on it
Subjects familiar with this type of rule find
this problem quite easy those unfamiliar with
the rule find it fairly difficult, despite the
fact that it is a fairly concrete problem. Thus,
familiarity seems the key why?
23
Case-Based Reasoning
Given these sorts of results, several
investigators have claimed that humans do not
convert problems into abstract logical rules but,
rather, we reason by thinking of experiences
relevant to the problem, and then we draw
analogies based on these experiences. This
notion is sometimes called case-based or
instance-based reasoning, and is obviously
related to the notions of relying on instances
when defining concepts. According to this view,
we do well with familiar rules because they call
to mind relevant cases which we can then base our
reasoning on unfamiliar rules provide no cases
and, therefore, poor reasoning.
24
Case-Based versus Logical
At this point it is important to note the change
in thinking that has occurred. The original idea
of logic was to capture human reasoning at
an abstract problem solving level suggesting
that humans reason at the level of abstract
logical rules. The case-based perspective argues
that we are no good when dealing with abstract
cases, because we think and reason in terms of
concrete instances or cases. There is a view
in-between that is also worthy of consideration.
25
Pragmatic Reasoning Schemata
This third view brings back the schemata notion
that we have discussed earlier in the
course. Recall that schemata are assumed to be
derived from experience, and are assumed to
capture those aspects that are redundant,
and therefore highly expected in some given
context. In reasoning contexts therefore, we may
have developed reasoning schemata such as a
cause-and-effect schema, a permission schema, an
obligation schema, etc So, our permission
schema may reflect the notion that If I
have permission to take some action, then I may
take that action.
26
Case-Based versus Reasoning Schema
Like case-based reasoning, the notion of
reasoning schemata assumes that our evaluation
of rules is based on our experiences. However,
the case-based approach assumes we retrieve
certain specific experiences whereas the schema
notion suggests that we retrieve a general
rule-schema that was created based on
pastexperiences (an average of past experiences
a prototype?). Lets examine a little more
data in light of all these options ...
27
The Role of a Rationale
If the form says entering on one side, then the
other side includes cholera among a list of
diseases.
Now let me provide you with a rationale that
should be sufficient to trigger your
permission schema does the problem become
much easier? Schema or Case?
28
Back to Envelopes Stamps
Recall the envelope and stamp problem subjects
were again given this problem, but were first
either told (or not) the rationale that
Unsealed envelopes only cost 40 lire to send
whereas sealed envelopes cost 50 lire. The
result? And in Hong Kong?
29
So, what about Logic?
Basically Spock was (will be?) right humans
do not reason logically. If we did, there would
be no performance differences in the previous
example as all simply involve the if-then
rule. In fact we have repeatedly seen cases
where human behaviour is sensitive to their past
experiences and current beliefs when they
should be based on logical principles. You do
not (naturally) reason logically deal with it!
30
So, what about Case-Based?
Although past experience does indeed impact on
our reasoning, it does not appear that it does so
in the way that the case-based view predicts. If
it did, then familiarity should be the most
important factor familiar situations should
retrieve relevant cases whereas abstract
situations should not. The cholera and envelope
situations should have been just as familiar with
and without the rationale. It seems as if the
rationale was the important factor. In fact, it
seems familiarity may not be needed at all ...
31
Yes, one more example ...
Test - One can only take action A if
precondition P has been fulfilled
This is an abstract rule, but subjects find it
easy to evaluate, presumably because it is
sufficiently specified to call the permission
schema into play making the problem easy
32
Reasoning Summary
All this seems to suggest that human reasoning is
best explained in terms of pragmatic reasoning
schema. If a problem calls one of our schema
into play, we will have an easy time deciding
whether or not the evidence is consistent
with the schema (or which evidence would or would
not be). If the problem does not call one of the
schema into play, we must then reason on the
fly. One would think we might employ logic in
these cases but, instead, it appears we
fall victim to such things as belief bias and the
like.
33
More Chapter 12

• Decision Making

34
Choices, choices
Another issue relevant to human reasoning is one
called decision making. That is, when we are in
a situation where we have several options
available to us, how do we decide which option to
take? gt Buying a car Choosing a therapy
Friday night On what basis do we tend to make
these decisions? Again, we can ask whether our
decision making follows is the result of a
careful decision mechanism that weighs the
various option, or whether our decision making is
not so reasonable
35
Weighing Alternatives
Example Professor or Doctor? The problem with
decisions is that the various choices often are
associated with very different outcomes that are
often very difficult to compare e.g., money
versus time In order to come to a decision, one
must somehow compare these outcomes that, at
some level, are impossible to compare. One must
convert each possible outcome into some
measure of subjective worth. How?
36
Utility Theory
One rationale way to make decisions is embodied
in a theory called utility theory. The general
idea here is that, when considering a possible
decision, one looks at the cost and benefits of
making that decision in light of that persons
goals. The outcome is termed expected utility
and can be defined as Expected Utility
P(particular outcome) x utility(outcome) Utility
itself is assumed to be some subjective
assessment of worth for some people, money
might have high utility for others, free time
might rank higher.
37
Utility Theory and Human Decisions
There are definitely times when we humans do make
decisions on the basis of utility
theory. However, there is also evidence of
situations where we do not seem to be maximizing
utility and, instead, are influenced by various
factors that have nothing to do with utility
(shock!). We will consider a number of these
factors then, after doing so, return to a
consideration of a theory for describing
human decision making behaviour.
38
Framing the Outcomes
One factor that has a strong influence on
peoples decision making process is the manner
in which the outcome is framed. Consider the
following
When the question is framed in this manner 72
choose Program A
39
A Slightly Different Frame
If we ask the essentially the same question, but
in a slightly different manner, choices change.
Specifically ...
When framed in this manner, 78 of subjects
choose Program B
40
More Frame Discussion
Note that in these two problems, there really was
no correct answer which likely inflates the
likelihood that subjects will rely on other
information when making their decisions. Nonethel
ess, the example shows that by simply focussing
on how many died, rather than on how many
survived, we can strong effect choices. If
subjects were basing their decisions on a
thorough analysis of costs and benefits, the
wording should not matter but it clearly does.
41
Another Example
18 choose radiation
44 choose radiation
42
Framing the Question
It is not only the way the outcomes are framed
that is important. The framing of the question
also matters. That is, even though we ask
essentially the same question in two different
ways, the answer people will give will depend
on which way we frame the question. For example,
you are on a jury and must decide which of
the following parents to award custody of a child
to which would you choose?
43
Custody Example
44
Custody Example Continued
When the question is asked in the manner just
presented, 64 of subjects decide to award
custody to parent B. However, when subjects were
instead asked To which parent would you deny
sole custody to? they tended to again
pick parent B (55). Why would they award
custody to the parent that they feel is most
worthy of being denied custody? Is certain
evidence weighed differently depending on the way
the question is asked?
45
The Influence of Alternatives
a. 66 b. 34 a. 27 b. 27 c. 46
Why?
46
Another Alternative Example
69 29 2 19 79 2
Again, why?
47
So what about Utility Theory?
These examples show that we do not make decisions
by simply weighing the utility of the choices
why? Perhaps we try to and do actually use
utility as a basis for simple decisions, but that
we have difficulty doing so with more complex
decisions gt see texts discussion on how
pathetic we are with probability Thus, we may
abandon an assessment of utility in
complex situations and rely, instead, on
short-cut strategies such as ...
48
Two Possible Strategies
One such shortcut strategy would be to focus on
finding a satisfactory choice, rather than
finding the optimal choice. Thus, as soon as a
satisfactory choice is found, we go with
it. Another possibility is called elimination
by aspects. According to this view, we
sometimes focus on certain aspects of the
alternatives, and narrow them down by
eliminating alternatives. gt Steves car buying
example I want black sexy fast
convertible reliable
49
Utility vs. Justification
Another possibility is the following again, we
start with the assumption that we are generally
poor at calculating the utility of the
alternatives. Given this Perhaps we look for
some reason for picking on option over the
other, and the reason we focus on depends on
the framing of the question and
alternatives. Re-consider the Asteroid vs. Bravo
car comparison perhaps when the Comet is added,
people see the Asteroid as another good ride car
with much better gas mileage but in the
Clarion context, the Bravo now looks like a nice
compromise.
50
Summary
Although this is a simplification much of the
decision making data can be accounted by the
following When making decisions we look for
the alternative that we can best justify to
others that is, we want to seem rational. In
the case of simple decisions, where we can weigh
the utility of the alternatives, these decisions
will follow utility theory. However, in more
complex decision situations, we will grab on to
some aspect of the decision context that we can
use to rationalize our decision. What that thing
is may depend on the way the decision context is
framed.