T7 Slides

Andreas Flache

Manu Muñoz-Herrera

Test Exam - SolutionsTutorial Week 7 - Application of Theories

Block A 2012/2013

http://manumunozh.wix.com/apptheories



Structure

✤ Quick review

✤ YOU propose an answer

✤ We compare answers

Q1. Critical Tests

✤ When you have two competing explanations of the same phenomenon make use of a critical test:

✤ Derive from both underlying theories predictions for the same situation, so that only the predictions of one theory can be right (contradicting predictions).

✤ test them

✤ Q1. Two theories have been proposed to explain residential segregation in cities. Theory 1 assumes that individuals prefer to live together with a majority of neighbors of their own ethnic group. Theory 2 assumes that members of the ethnic minority have lower incomes and therefore are more likely to live in neighborhoods with cheaper housing. Describe a critical test to empirically distinguish these two explanations. Explain why this is a critical test.

What is your answer?

We observe a social phenomenon: Residential Segregation

What should we see?

If T1 (homophily) is true, there is majority of one group or the other in each neighborhood. The reason is that individuals who are in the minority would prefer to live elsewhere and therefore leave the neighborhood (or do not enter).

If T2 (income inequality) is true, there is a majority of “whites” is expensive neighborhoods and a majority of “blacks” in cheaper neighborhoods. The reason is that most blacks cannot afford housing in the expensive neighborhoods and that generally prefer better (more expensive) housing if they can afford it.

How can we test (critically) the competing explanations?

Compare (Q1) - 1

Experiment - Mixing houses: In a neighborhood where rents are low and “blacks” are a majority, build expensive houses. The two theories have contradicting predictions for this experiment and both predictions can be tested

T1: Predicts that only blacks with higher incomes will move to these new houses, because they can afford them and will prefer to be with a majority of their own. “Whites” on the contrary, will not move into the new houses because they rather be with a majority of their own kind - only “blacks” move in.

T2: Predicts that both blacks and whites with higher incomes move into the new houses and the neighborhood composition will not have an effect on their choices - both “blacks” and “whites” move in.

Compare (Q1) - 2

Valid reasoning for each of the two theories why it predicts segregation.

Valid reasoning for each of the two theories what it predicts for the critical experiment.

Predictions are contradictory

Predictions are testable

Criteria (Q1)

Q2. Argument Validity

✤ Explanation is formed by the explanandum (the thing that is to be explained) and the explanans (the things used to explain).

✤ The explanandum must be a logical consequence of the explanans

✤ The explanans must contain at least one general law and one singular statements (necessary to derive the explanandum)

✤ The explanans must have empirical content

✤ All statements of the explanans must be true


If citizens are satisfied with the government, then they will not vote

In 2012, American citizens will be satisfied with the government

--------------------------------------------------------------------------------

In 2012, American citizens will be politically inactive

✤ Q2. Decide whether the following argument is valid. Explain briefly why you arrived at your conclusion:

Compare (Q2) - 1

If citizens are satisfied with the government (S), then they will not vote (N) General Law

In 2012, American citizens (t) will be citizens satisfied with the government (S) Condition

In 2012, American citizens (t) will be politically inactive (I) Explanandum

All S* is N

t is S

------------

t is I*

The explanandum does not follow logically from the explanans

We do not need the explanans to obtain the explanandum

We can test validity (star test)

All statements are wffs (+)

There is only one star on the right hand side (+)

N is not starred (-)

The argument is not valid

Compare (Q2) - 2

How about implicit assumptions? - This is not a necessary part of the answer

Politically inactive citizens (I) reject political mechanisms (R)

The rejection of political mechanisms (R) is expressed when citizens who do not vote (N)

Citizens who do not vote (N) are politically inactive citizens (I)

All S* is N

All N* is I

t is S

------------

t is I*

The argument is valid

( but it is not the original argument)All N is I

Compare (Q2) - 3

Criteria (Q2)

Explain what “validity of an argument” means.

Show why this argument is not valid given your explanation (here: conclusion does not follow from premises)

You can use syllogistic logic and the star test, but this was not asked here

If you do not use this, you have to explain in your own words clearly why the conclusion does not follow from the premises.

Q3. Propositional Logic

✤ Propositional Logic - single objects

✤ Propositions are statements which are either true or false - not valid or invalid

✤ Propositions can be combined to form new propositions - using operators

✤ Operators define the truth-value of the combined propositions based on the truth-values of the propositions that it consists of

✤ We make use of truth tables


Rules of inference 1: Hypothetical syllogism

Example:

If Popper is a sociologist (p), then he is a Marxist (q).

If Popper is a Marxist (q), then he hates capitalism (r)

If Popper is a sociologist (p), then he hates capitalism (r).

General form:

p⊃q

q⊃r

p⊃r

✤ Q3. Demonstrate that the following argument is valid, using a truth table. Explain why your truth table demonstrates that the argument is valid.

Compare (Q3) - 1

p q r p⊃q q⊃r (p⊃q).(q⊃r) p⊃r ((p⊃q).(q⊃r))⊃(p⊃r)

1 1 1 1 1 1 1 1

1 1 0 1 0 0 0 1

1 0 1 0 1 0 1 1

1 0 0 0 1 0 0 1

0 1 1 1 1 1 1 1

0 1 0 1 0 0 1 1

0 0 1 1 1 1 1 1

0 0 0 1 1 1 1 1

Compare (Q3) - 2

✤ The task is to demonstrate that the hypothetical syllogism is valid: Is ((p⊃q)·(q⊃r))⊃(p⊃r) valid?

✤ The implication of p and q is false only if p is true and q is false

✤ We make use of a truth table

✤ Why truth table: Because it shows that for every combination of p.q,r, it is true that the conclusion of this reasoning(p⊃r) is an implication of (follows logically from) the conjunction of the premises (which is ((p⊃q)·(q⊃r)) )

Q4. Syllogistic Logic

Syllogistic Logic - domains objects

We study the implication of general statements (wffs)

There are five words (All, No, Some, Is, Not)

There are 8 possible forms of wffs

We make use of the Star Test and Venn-Diagrams to test validity of the arguments


All hominids have a tailHumans are hominids---------------------------No human has a tail

No X is Yz isX------------Z is

Some L is Mg is not L----------------g is not M

a b c

✤ Q4. Below, you find a list of syllogisms. Demonstrate whether they are valid or not, using the star test and a Venn-diagram. If necessary, translate the statements

All hominids (H) have tail (T)Humans (U) are hominids (H)---------------------------No human (U) has tail (T)

Start Test

All H* is TAll U* is H-------------No U is T

H

TU

Venn-D.

All are wffs T is not * No * right side

Conclusion needs to be drawn There cannot be a U with no T


Compare (Q4) - 1

Start Test

X

YZ

Venn-D.

Not all statements are wffs Z is not * Z is not in the premises The conclusion is not a wff

The argument is not validNo X is Yz isX------------Z is

No X* is Y*z is X------------All Z is

z

Compare (Q4) - 2

Start Test Venn-D.

M is not * g can be an M although all

premises are true it is not clear where to draw g


Some L is Mg is not L----------------g is not M

Some L is Mg is not L*----------------g is not M

Compare (Q4) - 3

L

Mx

Q5. Empirical Content

✤ Recall: explanations must be empirically testable

✤ Theories should be as informative as possible

✤ The set of objects in the if part should be larger (general), and the set of objects in the then part should be smaller (specific).

✤ The empirical content of a statement is higher the more possible states there are which would falsify the statement. One way to achieve this:

✤ More states: if part contains a disjunction

✤ More states: then part contains a conjunction


A. If citizens are dissatisfied with the living conditions in their country, then they will vote for conservative partiesB. If citizens are dissatisfied with the living conditions in their country and if they are religious, then they will vote for conservative parties

A. People who do not vote will participate in demonstrations or sign a petition.B. People who vote will participate in demonstrations.

a

b

✤ Q5. Below you find 2 boxes which contain pairs of statements. Decide for each pair which statement has more empirical content. Sketch why.

Compare (Q5) - 1

A. If citizens are dissatisfied with the living conditions in their country, then they will vote for conservative partiesB. If citizens are dissatisfied with the living conditions in their country and if they are religious, then they will vote for conservative parties

There is a conjunction in the if part of statement B The informational content of statement B is smaller than of A

because due to the conjunction, the set of objects referred to in the if part of B is only a subset of those referred to in A (not all citizens – but only the religious ones)

A has more empirical content

Compare (Q5) - 2

A has more empirical content

Dissatisfied Citizens

Religious

Voting for conservative

parties

A

B

Compare (Q5) - 3

A is about non voters and B about voters - we do not know if the two set are of the same size (which is larger)

There is a disjunction in the then part of A There are less states that can be falsified in the then

part of B

We cannot answer the question

A. People who do not vote will participate in demonstrations or sign a petition.B. People who vote will participate in demonstrations.

Compare (Q5) - 4

Non votersDemonstrate

A

Voters

Sign a

petition

A

B

We cannot answer the question

Q6. Social Phenomena & Individual Behavior✤ Micro-level explanations provide information that might be

overlooked if only macro-relationships are considered

✤ Explain the macro-to-micro relationship (bridge assumption)

✤ Explain the theory of action

✤ Explain the micro-to-macro relationship (transformation assumption)

✤ Assess validity for all!

✤ Explanations lead to predictions (Advice)

✤ Consider the ceteris paribus assumptions


✤ Q6. Read the following article. The author argues that the quality of teaching in the US can be raised by giving teachers more autonomy. Both variables “quality of teaching in the US” and “autonomy given to teachers” are collective phenomena. Develop an explanation of this relationship based on assumptions about individual behavior. You can use arguments of the author and/or include own assumptions.

✤ a. Draw a “Coleman-boat” of your theory

✤ b. Make explicit all bridge assumptions, the theory of action of your theory, and the transformation assumptions you make. Justify these assumptions, using general theories or empirical background knowledge. Demonstrate that your arguments are valid

✤ c. Do you think that the advice to increase teachers’ autonomy is valid? explain your answer.

a. Draw a “Coleman-boat” of your theory

mac

ro le

vel

Autonomy given to teachers

Quality of teaching

indi

v. l

evel Perception of safety

for choosing the best teaching

method

Choice of best teaching

techniques

Compare (Q6) - 1

Compare (Q6) - 2


Quality of teaching

Perception of safety for choosing the best

teaching method

Choice of best teaching

techniques

b. Make explicit all bridge assumptions, the theory of action of your theory, and the transformation assumptions you make.

+ Justify these assumptions, using general theories or empirical background knowledge.

+ Demonstrate that your arguments are valid

Bridge Assumption

T. of Action - RCT

Transf. Assumption


Perception of safety for choosing the best teaching method

Bridge Assumption: If teachers have more autonomy, they perceive that it is safer for them to choose themselves the best teaching techniques.

The higher the autonomy given to teachers (I) the less likely they will feel obliged to choose teaching techniques to make the principal happy (R)

The less obliged teachers feel to chooses teaching techniques to make the principal happy (R) the more likely teachers perceive safety for choosing the best teaching techniques (B)

--------------------------------------------------------------------------------

The higher the autonomy given to teachers (I) the more likely teachers perceive safety for choosing the best teaching techniques (B)

Compare (Q6) - 3

All I* is R

All R* is B

------------

All I is B*

All statements are wffs All capital letters are * once There is one * on the right



Bridge Assumption: If teachers have more autonomy, they perceive that it is safer for them to choose themselves the best teaching techniques.

Compare (Q6) - 4


Choice of best teaching techniques

The higher the autonomy given to teachers (I) the more likely teachers perceive safety for choosing the best teaching techniques (B)

The higher teachers’ perception of safety for choosing the best teaching techniques (B), the more likely teachers will choose the best teaching techniques (T)

--------------------------------------------------------------------------------

The higher the autonomy given to teachers (I), the more likely teachers will choose the best teaching techniques (T)

T. of Action: If teachers perceive that it is safer for them to choose themselves the best teaching techniques, it is more likely they will choose them.

Compare (Q6) - 5

All I* is B

All B* is T

------------

All I is T*




T. of Action: If teachers perceive that it is safer for them to choose themselves the best teaching techniques, it is more likely they will choose them.

Compare (Q6) - 6

Transf. Assumption: An increase in the use of the best teaching techniques increases the quality of teaching in the classroom

Quality of teaching


The higher the autonomy given to teachers (I), the more likely teachers will choose the best teaching techniques (T)

the more likely teachers will choose the best teaching techniques (T), the higher the quality of teaching in the classroom (Q)

--------------------------------------------------------------------------------

The higher the autonomy given to teachers (I), the higher the quality of teaching in the classroom (Q)

Compare (Q6) - 7

All I* is T

All T* is Q

------------

All I is Q*


Transf. Assumption: An increase in the use of the best teaching techniques increases the quality of teaching in the classroom

Quality of teaching


Compare (Q6) - 8

c. Do you think that the advice to increase teachers’ autonomy is valid? explain your answer.

The advice is valid, as it has been shown in the arguments of points a and b. Nonetheless, there are problems that might arise given the ceteris paribus assumptions of the explanations and the advice.

It is assumed that if given safety about keeping their jobs (autonomy), teachers will always use the best teaching techniques. This implies that they know them - how about teachers that are not well trained?

Even if assumed that all teachers know what are the best teaching techniques, their implementation has no cost (requires the same effort than using traditional techniques)- how about lazy teachers?

Compare (Q6) - 9

Definitions of concepts

Multiple choice

Matching

Good luck in the exam!

Other types of questions

Technology

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