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Formal Models in Political Science Symbols, Proofs, Models, and Theories.

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1 Formal Models in Political Science Symbols, Proofs, Models, and Theories

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.

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.

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.

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

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.

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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.

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.

10 D. What makes a model formal? Contains the following elements (from Morgan):

11 A simple formal model:

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13 Recent examples of formal models Study: Faria and Arce A Vintage Model of Terrorist Organizations. Journal of Conflict Resolution 56 (May): 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.

14 Recent examples of formal models Study: Kyle Mattes What Happens When a Candidate Doesnt Bark? Journal of Politics 74 (April): 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.

15 Recent examples of formal models Study: Kyle Mattes What Happens When a Candidate Doesnt Bark? Journal of Politics 74 (April): 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.

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

17 Jean-Paul Azam and Véronique 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

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

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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.

21 II. What is Science? We need to know because we dont want to get stuck doing pseudoscience.

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

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).

24 The infamous equations Note that the form is a/b=c, c/d=e, e/f=g

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!

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.

27 Result: NAS membership FAIL Not Huntington

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)

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)

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)

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

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

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

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35 4. Problems of Logical Positivism a. Gödels 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… Gödel 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. Gödel ended the idea of building a complete deductive guide to the world (incomplete ones are still possible).

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

37 Inductive Fallacy (continued) How many functions (explanations) will perfectly explain the data? An infinite number, making dramatically different predictions

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39 c. The Demarcation Problem in Logical Positivism Empirical observation and attempts at confirmation dont separate science and pseudo-science. Why not?

40 Who uses empirical methods? Astrologers: Mass of horoscopes, biographies, star charts

41 Who uses empirical methods? Astrologers: Mass of horoscopes, biographies, star charts Phrenologists: Thousands of skull measurements

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

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)

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?

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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 naïve 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…)

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)

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 just…different.

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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

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)

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 if…no Neptune? Could hypothesize that some unobservable force acts only on Uranus no new predictions = degenerative shift

53 Degenerative Programs

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

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

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.

57 IV. Evaluating Models: Truth, Beauty, and Justice? Combines division of Lave and March (1975) with insights from philosophers of science.

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 Gödel No real solution to the induction problem, which was the other scientific route to Truth. However…

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.

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.

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…

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.

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?

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?

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)

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

67 VI. Understanding the Language Go through the handout and keep it handy when you read.


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