Forecasting with One-Dimensional Rational Choice Models

1. Forecasting with One-Dimensional Rational Choice Models From Voting Theorems to Expected Utility Models

2. I. A non-strategic model of choice • Black’s Median Voter Theorem (1948) • Assumptions • Single Dimension (important one!) • “Single-peaked” preferences

3. Single-peaked preferences? • Red: Yes • Blue: Yes • Green: No! • When are single-peaked preferences an appropriate assumption?

4. I. A non-strategic model of choice • Black’s Median Voter Theorem (1948) • Assumptions • Single Dimension (important one!) • “Single-peaked” preferences • Majority rule (more on this later…) • Odd number of decision-makers (trivial) • Conclusion: No other position can beat that of the median voter

5. Example • Who is the median voter? • What is the median voter’s position? • Don’t confuse median voter with moderate policy!

6. B. Expanding the model 1. We can eliminate assumptions (c) and (d) by adding power (aka potential influence) to the model. • Majority rule just becomes a special case when power is equal (one person, one vote). • But how do we find the “median voter” now?

7. Example • Who is the weighted median voter? • Sum power, then divide by 2: • 20+100+100+50+50+100+10 = 430 • Divide by 2 = 215 • From either end, where does cumulative power reach 215?

8. 2. Salience • We can further refine the prediction by taking into account that some actors have other items on their agendas • What proportion of their power (potential influence) are actors willing to spend on this issue? • General finding in politics: small, narrowly-focused groups often outperform large ones with broad goals

9. Example • Who is the weightedmedian voter now? • Need to find the median point of power * salience: Multiply, sum, then divide by 2:

10. Actual Influence = Potential Influence * Salience

11. Actual Influence = Potential Influence * Salience

12. 142 / 2 = 71. Who’s the WMV?

13. 142 / 2 = 71. Who’s the WMV?

14. C. Limitations of the Weighted Median Voter model • Limited to one dimension (by assumption) • Assumes sincere voting – but what if being a winner is its own reward? “If you can’t beat ‘em, join ‘em.” This condition violates the single-issue assumption of Black… • Neglects coercion – What if actors are able to bully others into taking insincere positions? • Outcome is ambiguous -- The “vote” is an outcome, but does it result from acceptance by the players or war between them?

15. II. Adding Game Theory • Rational choice: preferences are connected and transitive • Expected utility: decision-makers base decisions on expected (rather than actual) payoffs • Rational expected utility maximizers interacting = a game. Each player plays best by anticipating behavior of opponent. Equilibrium = all are playing best given others’ play

16. D. Strategies: Two basic choices • What position to take (sincere or some alternative position) • Whether to threaten conflict against some or all participants by making demands/offers to them

17. E. Information • Information is imperfect: actors make their offers simultaneously (like in the PD) • Information is also incomplete: actors don’t know each other’s “true” preferences, so they have to have some rule for estimating them

18. F. Summary • Actors believe that if everyone acts sincerely and refrains from coercion, the weighted median voter’s position (WMV) will prevail • Actors do not know if others are making sincere proposals or will refrain from coercion (threats may or may not be credible) • Actors therefore make offers to each other designed to shift the expected outcome in their favor and/or to ensure they are part of the winning coalition

19. III. Solving the game • Dealing with incomplete information (private knowledge) – players use Bayes’ Rule (a probability function) to estimate opponents’ true positions from their previous behavior

20. B. Banks monotonicity theorem • Theorem: When information is incomplete (players have private information about their true expectations regarding conflict) then players who privately desire conflict (expect its utility to be high) will take more extreme bargaining positions

21. 2. Implications • Together with Bayes’ Rule, this means we expect players who have taken positions far from the weighted mean to be willing to fight • Bueno de Mesquita calls these players “risk-acceptant” since they are obviously willing to gamble on getting “all or nothing” -- the conflict lottery of p(win = 1)+(1-p)(lose = 0)-c -- rather than taking a compromise position likely to get them something

22. C. Time 1. Why it is needed: Bayes’ Rule is about probabilities. But real preferences are 100% true. This means mistakes can be made. • How can we allow players to correct others’ misconceptions?

23. Example WMV = D What if A is not truly conflict-seeking?

24. What if we are wrong about…A? • There is a simple solution: A can shift positions to match the winning position (currently 70), thereby accepting the balance of power • Other players see this and conclude A is conflict-averse • But B and C are now more isolated, changing the expected utility of conflict for them. • Shows the need for multiple rounds, so players have the chance to avoid conflicts they believe they cannot win

25. Example

26. 2. Discounting • All else being equal, I would rather get my way sooner rather than later • This means that if we are very close to a deal, I will probably just give in or offer to split the difference to avoid dragging things out • Discounting is important to prevent the model from continuing to infinity (the value of getting your way an infinite number of periods later is zero)

27. D. Solution Process 1. Start with data on (public) position, estimated power (potential influence), and salience. 2. First round: • Everyone sees the WMV as being the outcome if nothing changes and everyone fights for his/her position • Each player makes its best offer (or no offer) to each player: I’ll come to position X if you will too • Risk-acceptant players are more likely to demand a move near their own position • Players near the WMV are probably very risk-averse! This creates opportunities for bullying…

28. 3. Subsequent Rounds • Players continue to shift position, thereby sorting themselves out by their true risk propensity • Players often receive multiple offers and must choose between them (or reject all of them) • Note that the winning position can shift each round, since a shift by the WMV shift alters winning position and shifts “across” the WMV alters the identity of the median voter. • Many players start to converge on a few positions: the current winning position and a few alternatives where coalitions can form

29. 4. When does it end? • Obvious ending: no player makes an offer, because each player is currently playing his/her best strategy given others’ strategy choices (equilibrium) • Can also cut it off at some arbitrary point known to the players in advance (the discount factor)

30. 5. What are the results? • Of course, there is a forecast • The model also shows players who refuse to accept the winning position (conflict) • In addition, the model allows “what if” analysis, i.e. “What if A initially took a position of 60?” This is what makes Bueno de Mesquita money as a consultant…

31. IV. Refining and Using the Model • Alternative decision rules: supermajorities, veto players, etc All that is required is an estimate of the status quo position. Status quo becomes the expected winning position if no supermajority is reached, or if veto player rejects settlement. Just replace projected winning position each round with the new rule.

32. B. Using the model to forecast • Pick an issue. Note the importance of reducing the issue to a one-dimensional scale. • Identify the stakeholders (players) • Create the issue scale, taking into account the space between each position • Find players’ positions, power (influence), and salience  interviews or research needed • Note veto players • Type the data in Excel and save as tab-delimited text (.txt), using Bueno de Mesquita’s Zimbabwe data as an example • Input the data and run the model • Interpret the results

33. C. Scenario Analysis Compares “base case” to alternatives Example: Compare “base case” outcome to outcome that could be reached if one of the factions changes its policyor salience.

34. Example: Besançon (2003) Used the model to predict results of 2002-2003 Round Table talks in Northern Ireland. Key issue = disarmament of militias Advised the Northern Ireland Women’s Coalition (NIWC) on ways to make progress on the disarmament issue (NIWC wanted complete disarmament)

36. Base Case: 75 (not bad, but not 100 either)

37. NIWC takes a different position and devotes more of its resources to the issue

38. NIWC forms a coalition with PUP

39. D. Buenode Mesquita answers questions Daily Show appearance Interview with questions

40. V. Other scholars’ use of the EUM: Did it work for them? • James and Lusztig (2000 using 1999 data): Forecasting elements of an FTAA • Congress will grant the President fast-track authority, but with more limits than those Clinton requested in 1997. 2002: Congress grants even greater authority to Bush (> 100). • The FTAA will be formed de novo, rather than simply extended southward from NAFTA – but will still be dominated by the US. FTAA never formed, largely being replaced by agreements with individual countries or groups (CAFTA-DR).

41. B. Stokman and Thomson (1998 using 1997 data): The UK and the EMU Forecasts Labour rejection of EMU even after election victory and previous statements of support Labour rejected the EMU after winning elections

43. C. International Interactions Special Issue (Vol. 23, No. 1-2, 1997)

44. VI. Assessing Model Accuracy • Must distinguish between different versions of the model: bargaining-free (weighted median voter or WMV), EUM (single issue with risk profiles), and PG (next session) • CIA study (in Feder 2002): 80 issues, more than 20 countries  90% accuracy for WMV model

45. From Feder (2002) • “During my government career, I used Bueno de Mesquita’s voting model on more than 1200 issues in more than 75 countries. Between 1982 and 1986, issues forecasted included the following (Feder 1995, p. 283): • What policy is Egypt likely to adopt toward Israel? • How fully will France participate in the Strategic Defense Initiative? • What is the Philippines likely to do about US bases? • What policy will Beijing adopt toward Taiwan’s role in the Asian Development Bank?”

46. C. European Community Decision-Making (Ed. Bueno de Mesquita and Stokman, 1994) Compared “conflict model” (EUM) to “exchange model” of Stokman (decision-makers trade positions when expected utility is positive), other models Model was accurate 97% of the time (but other models based on expert inputs also did quite well – especially the exchange model)

47. D. Red Flag Over Hong Kong (1995) 11 of 12 forecasts were accurate (exception was land valuation) Key predictions were about social and political rights (namely, that China would not respect Hong Kong’s special status)

48. E. Ray and Russett (1996): Largely focuses on EUM 1988 Prediction of defeat for Ortega in 1990 Nicaraguan elections (unclear if correct successor identified) Feb 1989: Prediction of hard-line crackdown in China (pre-Tiananmen Square) 1989: Predicted “key features” of 1991 Cambodia Peace Accords 1991: Predicted admission of two Koreas to UN, failure of anti-Gorbachev coup Other forecasts: oil prices, conditions of trade agreements, funding for family planning programs

49. F. Labor Negotiations in the Netherlands (Rojer 1999)