L4 Slides

Application of Theories

Lecture week 4: How to criticize a theory/explanation?

Andreas Flache

Manu Muñoz-Herrera

Tuesday March 5, 2013

Aims of the lecture

•  What defines a good explanation?

•  How to find out whether a theory/explanation is good?

•  How to formulate informative theories/hypotheses?

•  What to do with wrong explanations/theories?

What is a good explanation?

A good explanation is an explanation where all conditions of adequacy are met (Hempel / Oppenheim, week 2)

Condition 1: The explanandum must be a logical consequence of the explanans.

Condition 2: The explanans must contain at least one general law and at least one singular statement.

Condition 3: The explanans must have empirical content.

Condition 4: All statements of the explanans must be true.

Stop and Think…


…

think about how “condition 4” relates to what Popper (reading this week) is saying about the difference of “verifiability” and “falsifiability” as criteria for good theories! (pp. 40)


Compare this to Popper (p 32) “testing the internal consistency of theories”

(First line “along which the testing of theories could be carried out” – out of four)


Henri Tajfel (1919 – 1982)

John C. Turner

•  Example: Social Identity Theory by Tajfel and Turner (1986)

•  Very successful social psychological approach to stereotyping, intergroup competition, intergroup conflict, and political protest

•  Core claim: People seek to optimize their social identity (= part of identity that is derived from group memberships)

•  The pure categorization into in- and outgroups triggers comparison between groups and motivates individuals to act in such a way that they perceive their ingroups as “better”.

Feb, 2011

•  Quotes from Tajfel and Turner (1986):

Is it really possible to derive the propositions on the right from those on the left?

Premises / “Explanans” Conclusions (“explanandum”)

All individuals (I) enhance (=maintain) their self-image (=concept=esteem) (C).

all I is C

Problem 1:

This is the definition of “social identity”:

Does this imply the following?

One way how individuals enhance their self-image (C) is to enhance their social identity (S).

some C is S

All Individuals (I) enhance their social identity (S) all I is S

all I is C

Is this a valid argument?

some C is S

all I is S

*

*

I

C S Ñ Ñ

What is wrong?

There are I which are not S. Furthermore, if we exclude the upper cross, then all premises are true but no I is S.

In other words:

The “self-concept” consists of several parts and “social identity” is only one part. Accordingly, there might be other ways of achieving a positive self-concept besides achieving a positive social identity.

Testing whether a syllogism is valid: The star test

The star test consist of three steps: Step 1: Find the “distributed letters”

A letter is distributed if it occurs just after “all” or anywhere after “no” or “not” e.g. all A is B no A is B x is A x is not y

Step 2: Star premise letters which are distributed and conclusion letters which are not distributed

e.g. all A is B

some C is A

some C is B

*

* *

Step 3: Decide: A syllogism is valid if and only if every capital letter is starred exactly once

and

if there is exactly one star on the right hand side.

*

* *

e.g. all A is B

some C is A

some C is B

Each capital letter is stared exactly once and there is exactly one star at the right hand side (see the B).

Thus, this syllogism is valid

all C is S

all I is C

all I is S

What could we do to make the argument valid?

Possibility 1: assume that the only way to achieve a positive self-concept is to achieve a positive social identity

In other words, we assume that all C is S.

* *

*

all I is C

some C is S

all I is S

*

* This is valid

I

C S

All possible parts of I are S. This shows that the argument is valid.

What could we do to make the argument valid?

Possibility 1: assume that the only way to achieve a positive self-concept is to achieve a positive social identity.

We have shown that this would work, however,

is this a plausible assumption?

Possibility 2: Make explicit all potential ways to achieve a positive self-concept and include assumptions about conditions under which individuals will prefer certain strategies.

This is a lot of work mainly because this requires a theory of decision making (when to chose which alternative). However, before this is not done, it is very difficult to test SIT.

(Think of Popper’s criterion of “falsifiability”)

•  Problem 2:

Does this imply the following?

What is wrong?

Variables of the explanandum do not appear in the explanans. This is impossible.

Does not appear in explanans

This is hidden in “comparison” between groups


Both must actually be required to logically derive the explanandum.


Example taken from Opp and Gern’s explanation of the protests in Eastern Germany (1993: 661):

This argument is not based on a general law. The prediction is induced from observations of other protests, an endeavor that is impossible without a (implicit) law. Karl-Dieter Opp

(*1937)

explanans

explanandum


Compare this and condition 2 to Popper’s (p 32) “determining whether it [the theory] has the character of an empirical or scientific theory” and (p.40) “a system [is] empirical or scientific only if it is capable of being tested by experience”

(Second line “along which the testing of theories could be carried out” – out of four)


•  In other words, our theories must be testable. It must be possible to derive at least one testable statement from the theory.

•  The most straightforward way to make a theory testable is to find a way to measure the variables in its premises (e.g. X and Y in “all X are Y”) and investigate whether there is the proposed relationship.

•  This would mean that you directly test the assumptions of the theory. BUT…

•  Social scientific theories often include concepts which are very difficult to measure for two reasons:

A: The concept is not defined properly.

B: The concept is latent in the sense that it can not be observed directly.

How to define a concept?

A definition is a passage that explains the meaning of a concept which is to be obscure (called definiendum), by the use of terms with a clear meaning (called definiens).

Two kinds of definitions:

- intensional definitions: specifies all necessary and sufficient conditions for an object to be considered a member of a set e.g.: “A sociologist is a scientist who studies human societies.”

- extensional definitions: lists all members of a set e.g.: “Sociologists are Durkheim, Marx, Weber, and Parsons. This is a complete list.”

Common problems with definitions

- Circular definitions: e.g.: define the concept sociologist: “A sociologist is a scientist who studies sociology.” define the concept sociology: “Sociology is what sociologists do”

- Definiens is obscure: e.g. define the concept sociologist: “A sociologist is a scientist who studies social facts” the concept “social fact” needs to be defined too.

- Definition based on examples and counter examples: e.g. define the concept sociologist: “Scientists like Emile Durkheim are sociologists” Durkheim was male, French, and well dressed. Thus, “the inspector” from “Pink Panther” is a sociologist too

The inspector

Example: the definition of “social identity”

This is the definition of “social identity”:

This definition suggests that all humans have a “self-image” and that a human’s self-image is influenced by multiple characteristics (categories).

The part of the “self-image” that is based on social categories to which the individual perceives himself as belonging is called “social identity.”

Open questions:

a) What is a “self-image”?

b) What are “social categories”?

c) When does an individual “perceive to belong to” a social category

What is a “self-image”?

Unfortunately, this is not clear. Self-image might refer to an individual’s description of herself (I am a female farmer) or her evaluation of herself (I hate myself) or both.

However, Tajfel and Turner refer to the self-image also as the “self- concept” and hold that individual’s seek to achieve a “positive self- concept”. This suggests that self-image refers to evaluations.

Thus, we might define “self-image” as an individual’s evaluation of herself.

This implies that “social-identity” refers to the part of an individual’s self-evaluation which is based on social categories to which the individual feels to belong.

It is still left open what a defines a category as “social”…

The process of clarifying the meaning of a concept is called “explication”.

Another big problem is that many concepts of our theories are not directly observable

For instance, opinions, preferences, motives, perceptions, personality traits, utility and fears can not be directly measured. Also an individual’s social identity is not observable.

Does this imply that theories which contain such concepts do not have empirical content?

NO!!!

Many concepts may not be directly observable but their antecedents and consequences may be. Thus, statements that include latent variables can be tested indirectly.

For instance, social identity theory holds that individuals have a negative social identity when groups to which they feel to belong have a low status (antecedent). Plus, when social identity is negative, then individuals tend to act aggressively towards outgroups (consequence). Group status and aggressive behavior can be measured and, thus, allow to derive (indirectly) testable statements from SIT.

Indirect tests are standard also in the natural sciences:

For instance, the temperature of an object is defined as the “speed of the particles that an object contains”.

Thus, let us measure the body temperature of a human. Can we measure the “speed of the particles the body contains”?

No. Instead, we measure the volume of objects that are near to the body and have the same temperature, using (mercury) thermometers.

In sum, also theories which contain unclear concepts and concepts which are not directly observable have empirical content. However, this requires additional assumptions and operationalization.

The third condition of adequacy holds that we want empirical content. However, we want a lot of empirical content.

The empirical content of a statement is the higher the more possible states there are which would falsify the statement.

minimal empirical content

maximal empirical

content statements which are always true (tautological)

statements which are always false (contradictory)

"All bachelors are not married." "James is a vegetarian and eats steaks."

Empirical content scale

Statements should have a high informational content. However, informational content should not be maximal.

Empirical content of implications

For example, which of the following statements has a higher empirical content?

A: If a person is frustrated or hurt then she will be aggressive.

B: If a person is frustrated and hurt then she will be aggressive.

The empirical content of a statement is the higher the more possible states there are which would falsify the statement.

Thus, we need to study under which conditions the statements are false.

A and B are implications, statements which are false when the if-part is true and the then-part is false.

A: If a person is frustrated or hurt then she will be aggressive.

B: If a person is frustrated and hurt then she will be aggressive.

This is a disjunction

1 1 1 0

p v q 1 1 0 0

1 0 1 0

p q There are three possible

states where the if-part is true

This is a conjunction

1 0 0 0

p · q 1 1 0 0

1 0 1 0

p q

There is only one possible state where the if-part is true

1 0 0 0

p · q 1 1 0 0

1 0 1 0

p q

Second example: Which of the following statements has a higher empirical content?

C: If a person is frustrated then she will be aggressive or sad.

D: If a person is frustrated then she will be aggressive and sad.

This is a disjunction

1 1 1 0

p v q 1 1 0 0

1 0 1 0

p q There is one possible state where the if-part is false

This is a conjunction

There is only one possible state where the if-part is true

In sum, the empirical content of a statement is higher if there are more possible states that would falsify it.

Implications are false when if-part is true and the then-part is false.

More possible states when if-part contains

disjunction then conjunction

More possible states when if-part contains

conjunction then disjunction

The empirical content of an implication is higher when the if-part contains a disjunction and when the then-part contains a conjunction.

Example: The empirical content of social identity theory This is the core claim of SIT:

We have just seen that it makes a big difference whether there is an “and” or an “or”. This is a not a strong formulation of a theory.

Note that the theory implies only “or” in the “then part”, the alternative with less empirical content.

Empirical content and generality of concepts

Relations between humans

Social relations

friendships

Friendships between students

Friendships between first-years

We can define concepts with different generality.

e.g. define the concept: “network tie”

dyads Relations between

humans

Social relations friendships

Friendships between students

Friendships between first-years

Specifying:

•  Include more characteristics in the definition of the concept

•  Fewer objects fall under the concept

Generalize:

•  Abstract from details

•  More objects fall under the concept

Example: All sociologists (S) are good statisticians (G). (all S is M)

Comparing empirical content of implications

S =df. Everybody with a university

degree in Sociology

S =df. Everybody with at least a

Doctor’s degree in Sociology

G =df. Everybody who can interpret

a regression

G =df. everybody who can explain

what a regression is

3

4

1

2

4 (3) has more empirical content than 2 (1)

4 (2) has more empirical content than 3 (1)


…

think about how “condition 4” relates to what Popper (reading this week) is saying about the difference of “verifiability” and “falsifiability” as criteria for good theories! (pp. 40)

Completeness: for any two lotteries, either BA BA =, BAor

Transitivity: if BA CBand CA, then

A core assumption of RCT is that individuals maximize utility

Von Neuman and Morgenstern showed that expected utility maximization is based on the following assumptions. Thus when you assume this decision rule, then you implicitly also assume the following:

Oskar Morgenstern 1902-1977

Austrian economist co-founder of Game Theory

John von Neumann 1903-1957 Hungarian mathematician co-founder of Game Theory

Continuity: if CBA , then there is a probability p between 0 and 1 such that the lottery CppA )1( −+ is equally preferred to B.

Interdependence: if BA = XppBXppA )1()1( −+=−+, then

Note that there are alternative axiomatizations (see e.g. SEU-theory by Savage)

The theory of rational action is a good example of a wrong theory

Daniel Kahnemann 1934

Israeli psychologist 2002: Nobel price in economics

Amos Tversky 1937-1996 Israeli psychologist Coauthor of Kahnemann

Condition 1: Imagine that the US is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the program are as follows:

A) If program A is adopted, 200 people will be saved

B) If Program B is adopted, there is a one-third probability that 600 people will be saved and a two-third probability that no people will be saved.

Which of the two programs would you favor?

72% of the subjects chose A (N=152)

A famous experiment:

Condition 2: Imagine that the US is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the program are as follows:

C) If program C is adopted, 400 people will die

D) If Program D is adopted, there is a one-third probability that nobody will die and a two-third probability that 600 people will die.

Which of the two programs would you favor?

78% of the subjects chose D (N=155)

The decision problems are identical. Still, the different framing (save lifes vs. loose them) of the effects leads to different decisions. Kahnemann and Tversky concluded that “there is more risk seeking in the second version of the problem than there is risk aversion in the first.” (Kahnemann & Tversky 2000: p.5 )

The framing effect Kahneman and Tversky demonstrated contradicts the idea that humans form decisions based on utility maximization. Their results contradict the assumption of completeness. In other words, the theory of rational action is wrong.

According to the fourth condition of adequacy, explanations which assume utility maximization are not adequate.

Thus, should we abandon the theory of rational action?

Yes, we should if we had a better theory of action. “Better” on all accounts that matter: fertility, simplicity, surprise. As long as we do not have a better theory, we will have to elaborate the theory of rational action.

Current research focuses on elaborating the theory of rational action:

- different decision rules (bounded rationality)

- social preferences (fairness)

- include further assumptions about the perception of risks

The assignment

You can download the assignment from Nestor

L4 Slides

Spiritual

social identity s

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esteem c

valid argument

argument valid

social identity theory

definition of social