Formal Models in Political Science Symbols, Proofs, Models, and
Theories Slide 2 I. Models and Theories A. Focus: Empirical,
Normative, or Both? Max Weber: Distinction between fact and value.
While we cannot escape our values, we can study the empirical world
scientifically within those value systems. (Research best means for
accomplishing the end). Others disagree, but the distinction
endures in science. Slide 3 I. Models and Theories A. Focus:
Empirical, Normative, or Both? B. Rough definitions, with a focus
on empirical models. Theories: Sets of assumptions about how the
world works (or should work), along with their associated
implications. Slide 4 Lave and March (1975) on theories: The
essence of theorizing is that you start with an observation, and
then imagine the observation as the outcome of a (hidden) process.
Slide 5 I. Models and Theories A. Focus: Empirical, Normative, or
Both? B. Rough definitions, with a focus on empirical models.
Theories: Sets of assumptions about how the world works (or should
work), along with their associated implications. Models: Generally
narrower than theories because they seek to be more specific and to
trim elements of reality in favor of simplicity These are just
rules of thumb. Both words refer to ways of systematically thinking
about the world Slide 6 C. Why do we need models? 1. Allow us to
reason from what we do know to some things we dont. Counter-
intuitive hypotheses are especially prized since they represent
potential new knowledge. Slide 7 Slide 8 C. Why do we need models?
1. Allow us to reason from what we do know to some things we dont.
Counter- intuitive hypotheses are especially prized since they
represent potential new knowledge. 2. The world is too complex to
comprehend without simplification. The only accurate map of Killeen
is.Killeen itself (or a 1:1 scale map). Even large maps omit data
that is below their resolution. Slide 9 C. Why do we need models?
3. Much is unobservable, so we need to construct models of what is
happening behind the scenes 4. Weber argues for the use of ideal
types that only exist in the abstract (e.g. the rational voter)
without understanding (modeling) the ideal type, we cannot know
if/when/which voters behave irrationally. No abstract ideal types =
no conclusions about reality. Slide 10 D. What makes a model
formal? Contains the following elements (from Morgan): Slide 11 A
simple formal model: Slide 12 Slide 13 Recent examples of formal
models Study: Faria and Arce. 2012. A Vintage Model of Terrorist
Organizations. Journal of Conflict Resolution 56 (May): 629-650.
Model: Conclusions: Terrorist groups disintegrate unless they
recruit at higher levels than present membership (grow or perish).
Governments should therefore follow a strategy of impatience
against these groups. Slide 14 Recent examples of formal models
Study: Kyle Mattes. 2012. What Happens When a Candidate Doesnt
Bark? Journal of Politics 74 (April): 369-382. Model: Conclusions:
There is an optimal mix of positive and negative campaign
advertising for each candidate in an election, and as voters become
more capable of integrating new information into their assessment
of candidates, then the proportion of negative ads decreases. Slide
15 Recent examples of formal models Study: Kyle Mattes. 2012. What
Happens When a Candidate Doesnt Bark? Journal of Politics 74
(April): 369-382. Model: Conclusions: There is an optimal mix of
positive and negative campaign advertising for each candidate in an
election, and as voters become more capable of integrating new
information into their assessment of candidates, then the
proportion of negative ads decreases. Slide 16 Ronen Bar-El, Kobi
Kagan, and Asher Tishler, JCR, Aug 2010 Demonstrates that given
typical assumptions about forward-planning, countries that plan
defense spending years into the future actually perform more poorly
than those who simply plan from year to year advice to defense
planners Slide 17 Jean-Paul Azam and Vronique Thelen, JCR, June
2010 Finds that the supply of terrorist attacks against a country
increases as it practices more military intervention and decreases
as it dispenses more foreign aid aid makes a better anti-terrorism
policy for a state than military intervention Slide 18 Gartzke,
Erik and Hewitt, J. Joseph International Interactions, Vol 2, 2010
Conclusion: Capitalism produces interstate peace through free
markets, economic development, and interest similarity Slide 19
Slide 20 E. Why formal models? 1. Force a more disciplined form of
argument need to prove that hypotheses actually do follow from the
theory before one tests them! 2. Counterintuitive findings
following common sense doesnt tell us more than we already know
(the goal of science). 3. Often argued to be less subjective or
more objective than informal models. Its hard to care passionately
about the value of alpha. Slide 21 II. What is Science? We need to
know because we dont want to get stuck doing pseudoscience. Slide
22 II. What is Science? We need to know because we dont want to get
stuck doing pseudoscience. My approach: Recount the philosophy of
science in order to discover rules for Separating science from
pseudo-science Comparing two scientific theories or explanations
Slide 23 Huntington on political development: pseudoscience?
Political Order in Changing Societies Argued that modernization and
prosperity would not bring democracy, but would instead increase
social change which would produce violence if not controlled by an
elite. Only after an autocratic government had led the country
through development could democracy be safely introduced (as the
rate of social change slowed). Slide 24 The infamous equations Note
that the form is a/b=c, c/d=e, e/f=g Slide 25 Replies by
Mathematician Koblintz Huntington never bothers to inform the
reader in what sense these are equations. It is doubtful that any
of the terms (a) - (g) can be measured and assigned a single
numerical value. What are the units of measurement? Will Huntington
allow us to operate with these equations using the well-known
techniques of ninth grade algebra? If so, we could infer, for
instance, that a = b * c = b * d * e = b * d * f * g i.e., that
social mobilization is equal to economic development times mobility
opportunities times political institutionalization times political
instability! Slide 26 Koblintzs Verdict: Mathematical verbiage is
being used like a witch doctor's incantation, to install a sense of
awe and reverence in the gullible and poorly educated. A woman I
know was assigned an article by Huntington for her graduate seminar
on historical methodology. The article summarized his work on
modernization and cited these equations. When she criticized the
use of the equations, pointing out the absurdities that follow if
one takes them seriously, both the professors and the other
graduate students demurred. For one, they had some difficulty
following her application of ninth grade algebra. Moreover, they
were not used to questioning an eminent authority figure who could
argue using equations. Slide 27 Result: NAS membership FAIL Not
Huntington Slide 28 III. History of Science A. Ancient Science
1.Aristotle believes that nature is real and must be studied, using
a deductive method 2.Rejection of experiment goal is to understand
what is natural and changing nature is not natural 3.Method = Look
for categories in nature and deduce essence of things. a.Example:
Aristotle notes that female animals have fewer teeth femaleness.
Extrapolates to humans without examining women (who have same
number of teeth as men) b.Another example: Since earth is center of
universe, objects naturally attempt to return there (i.e. fall).
The heavier an object is, the more it desires to be in its natural
state (i.e. it falls faster which is false) Slide 29 4. Ptolemy:
Facts models, not the other way around Example: use math to
estimate positions of the planets, not to describe their real
motion. Justification = many models describe identical data
(apparent motion of planets) Slide 30 B. The Enlightenment:
Essentialism Rejected 1. Rediscovery of ancient texts reveals
ancients didnt know all the answers (example: Ptolemys orbits arent
accurate) 2. Belief in progress As economic growth and technology
advanced, people came to believe that we would know more in the
future (vs. wisdom of the ancients) Slide 31 3. The Copernican
Revolution a. Heliocentrism: Copernicus argued that planets
revolved around the sun simpler system than Ptolemy, but not
(initially) better at predicting planets positions Slide 32 b.
Scientists compare models: Cumulative knowledge i. Observations
undermine idea of heavenly spheres Tycho Brahe observes comet
passing through planetary orbits ii. Galileo observes phases of
Venus (predicted by Copernican model but not by Ptolemaic model)
and moons of Jupiter (not everything revolves around Earth) iii.
Kepler discovers that geometry (ellipse) describes planetary motion
(theory: sun/God animates the universe) iv. Newton theorizes that
simple mathematical laws of gravity might explain Keplers model of
planetary motion Slide 33 C. Logical Positivism 1. Positivism: 19
th -Century idea that scientific knowledge is the only authentic
knowledge. 2. Logical positivism (early 20 th century): Only
statements proven true through logic (deduction) or observation
(induction) are to be accepted. Fact vs. value distinction. 3.
Process: a.Induction: Prove statements true through observation,
then b.Deduction: combine these statements to make new predictions
Slide 34 Slide 35 4. Problems of Logical Positivism a. Gdels
incompleteness theorems (Chapter 9) i.Every system of logic
(axiomatic system) capable of reproducing the rules of arithmetic
can be faced with statements that cannot be evaluated, i.e. This
statement is false. If true If false Gdel showed that this is a
problem with any such system, not just English (he used systems of
arithmetic operating on the set of natural numbers) ii.Because of
this, no useful system of logic is capable of determining its own
consistency. That is, you cannot prove that your axioms will never
contradict each other. Gdel ended the idea of building a complete
deductive guide to the world (incomplete ones are still possible).
Slide 36 b. The Inductive Fallacy Fed at 9 AM everyday for the past
few months Will always get fed at 9 AM Christmas at 9 AM Slide 37
Inductive Fallacy (continued) How many functions (explanations)
will perfectly explain the data? An infinite number, making
dramatically different predictions Slide 38 Slide 39 c. The
Demarcation Problem in Logical Positivism Empirical observation and
attempts at confirmation dont separate science and pseudo-science.
Why not? Slide 40 Who uses empirical methods? Astrologers: Mass of
horoscopes, biographies, star charts Slide 41 Who uses empirical
methods? Astrologers: Mass of horoscopes, biographies, star charts
Phrenologists: Thousands of skull measurements Slide 42 Who uses
empirical methods? Astrologers: Mass of horoscopes, biographies,
star charts Phrenologists: Thousands of skull measurements
Scientific racists: One recent author tabulates 620 separate
studies of average IQ from 100 different countries with a total
sample size of 813,778 to confirm hypotheses of racial differences
Homeopaths, who make selective use of articles supporting their
theories and ignore the thousands that dont Slide 43 C.
Falsificationism 1. Karl Popper: Stop trying to confirm theories
and try falsifying them instead. I cannot prove all sheep are
white, but I sure as heck can disprove it. 2. Method: Make novel
predictions with theory that prove the theory false if they fail to
occur (critical experiments) 3. Result: Scientific theories are
never proven true. Science consists of conjectures (theories which
havent failed yet) and refutations (those which have failed) Slide
44 4. The Demarcation Problem and Falsificationism a. Allows us to
reject astrology, etc as pseudo- science: Astrologers rarely make
testable predictions, and dont give up astrology when they fail b.
Popper argues that Marxism and Freudianism are both pseudo-science
(example of false consciousness in Marxism) enough ifs, ands, and
buts allow them to explain anything after the fact, but predict
nothing novel c. Many physicists consider string theory to be a
huge step forward.while others call it pseudoscience. Why? Slide 45
Slide 46 5. Problems of Falsificationism a. The ceteris paribus
Clause Theories are tested all else being equal but it never is.
Popper called abandoning a theory after one bad experiment nave
falsificationism. b. Virtually all useful scientific theories had
anomalies when first stated (Copernicus, plate tectonics, etc)
strict falsificationism is a recipe for ignorance c. Poppers
solution: require a replacement theory that explains everything the
old one did, plus something else, before abandoning old theory (may
mean we retain pseudoscience) Slide 47 D. Social Models of Science
1. Kuhns Paradigm Shifts a.Idea: Science is a social activity that
proceeds under a paradigm of unquestioned assumptions about the
world and a set of problems considered to be critical (value
decision) b.Every interesting theory has anomalies things that seem
inconsistent with the theory. c.Normal science is puzzle-solving;
unexplained anomalies are simply assumed to be unsolved puzzles
scientists usually suppress novel explanations if they can retain
their paradigms (Tycho Brahe believed in an earth-centered
universe, plate tectonics was rejected for decades, etc) Slide 48
d. Scientific Revolutions When enough anomalies start piling up
(especially ones that get in the way of practical uses of science),
new explanations begin to receive a hearing At some point, the new
explanation becomes the expected explanation a new paradigm Note
that this is a social process we cannot be sure the new paradigm is
any better or more accurate than the old one. Its justdifferent.
Slide 49 Slide 50 2. Lakatos: Research Programs a. Goal: Retain
idea of falsification while acknowledging that scientists do not
actually reject theories when anomalies are found b. Objections to
Kuhn: i.Kuhn offers no way of comparing paradigms but science often
looks like it has progressed over the past centuries ii.Most fields
have multiple paradigms at the same time Slide 51 c. The
Methodology of Scientific Research Programs i. Research programs
rely on multiple theories to identify problems and solve puzzles
ii. Each scientific research program has a hard core of
unquestioned assumptions and a protective belt of auxiliary
hypotheses (i.e. attempts to save the program from falsification)
iii. Evaluation: Look for progressive research programs (making new
predictions and discoveries) and reject degenerative ones (simply
adding to the protective belt without offering new knowledge) Slide
52 Example: Neptune Astronomers discovered that the orbit of Uranus
didnt match Newtons predictions They did NOT give up Newtonian
physics They DID add a new item to the protective belt: something
else must be perturbing the orbit of Uranus This turned out to be
Neptune: Progressive change to research program What ifno Neptune?
Could hypothesize that some unobservable force acts only on Uranus
no new predictions = degenerative shift Slide 53 Degenerative
Programs Slide 54 d. The Demarcation Problem in Research Programs
How do we know pseudoscience? It critiques science without offering
an alternative set of predictions It continually invents new
hypotheses that explain its previous failures but do NOT make new,
falsifiable predictions Slide 55 E. Conclusion: Standards for
Evaluating Science 1. Every model must be tested against another
model a.Simplest model = random chance (systematic studies of
astrology usually show it fails this test) b.It takes a model to
beat a model Where an existing theory outperforms chance, critics
are obligated to suggest a better explanation for the facts Slide
56 2. What makes one explanation better than another? a.
Progressive vs. degenerative research programs A theory or set of
theories that keeps making novel, falsifiable predictions beats one
that keeps adding new assumptions just to explain what we already
know or generates untestable hypotheses b. Utility Since we cannot
be sure theories are True or False (ceteris paribus problem) they
need to be useful. Preference for parsimonious theories using
observable variables. Slide 57 IV. Evaluating Models: Truth,
Beauty, and Justice? Combines division of Lave and March (1975)
with insights from philosophers of science. Slide 58 A. Truth.or
truth? My take: Truth is unattainable through science No
comprehensive set of axioms can be used to deduce its own
consistency, thank you very much Kurt Gdel No real solution to the
induction problem, which was the other scientific route to Truth.
However Slide 59 truth still has a meaning Since research programs
are measured according to progress Does the evidence for the theory
currently outweigh the evidence against it? Does the theory explain
more over time particularly by generating novel, falsifiable
hypotheses? Is the theory internally valid, i.e. do its conclusions
(hypotheses) follow from its axioms? Be sure its not a circular
model Are there critical experiments which can pit the theory
against its competitors? Remember from Popper that it takes a
theory to beat a theory. Slide 60 B.Beauty Parsimony: Explain as
much as possible with as little as possible Simplicity: Small
number of assumptions means we dont have to give as much to the
author Fertility: Large number of testable hypotheses per
assumption Surprise: The model should generate predictions not
immediately obvious from its assumptions. Slide 61 Example: An
Alliance Model 1. Friends of my friends are my friends 2. Friends
of my enemies are my enemies 3. Enemies of my friends are my
enemies 4. Enemies of my enemies are my friends 5. Every country
has an opinion on other countries In a system of 50 countries,
there are 562,949,953,421,312 possible alliance networks that meet
these criteria. BUT Slide 62 Example: An Alliance Model 1. Friends
of my friends are my friends 2. Friends of my enemies are my
enemies 3. Enemies of my friends are my enemies 4. Enemies of my
enemies are my friends 5. Every country has an opinion on other
countries In a system of 50 countries, there are
562,949,953,421,312 possible alliance networks that meet these
criteria. BUT ALL OF THEM are BIPOLAR (the world is divided into
two and only two groups)! Well, one exception: everyone can be
friends. Slide 63 B.Beauty Parsimony: Explain as much as possible
with as little as possible Simplicity: Small number of assumptions
means we dont have to give as much to the author Fertility: Large
number of testable hypotheses per assumption Surprise: The model
should generate predictions not immediately obvious from its
assumptions. Ease of Application? Slide 64 C.Justice? Are the
assumptions themselves biased? Derivations will share those biases.
If accepted, as true what is legitimized? If beautiful, what tool
have we created? How will it be used? Slide 65 D. Putting it all
together Theories should be useful That means they should make
usable (falsifiable) predictions (truth) That means they need to be
usable lower information requirements and lower complexity makes a
model more useful (Beauty) That means we should have a use for them
which we can ethically justify (Justice) Slide 66 V. The Dominance
of Rational Choice: Why? Individual Choice Inter- dependent Choice
Aggregate Choice Institutions Problem:Decision to go see My
American Cousin Decision of two states to go to war Decision to
select a class President Decision to form a coalition government
Level of Analysis IndividualDyad or Group Group or System Rules of
the System Theory Decision Theory (parametric) Game Theory
(strategic interaction) Social Choice (aggregate outcomes) Spatial
Models (core of possible outcomes) Models/ Forms Utility
FunctionsGame Trees / Matrices Equilibrium Analysis Structure-
Induced Equilibrium, Voting Models Slide 67 VI. Understanding the
Language Go through the handout and keep it handy when you
read.
