Forecasting with One-Dimensional Rational

Choice Models

From Voting Theorems to Expected Utility Models

I. A non-strategic model of choice

A. Black’s Median Voter Theorem (1948)1. Assumptions

a. Single Dimension (important one!)

b. “Single-peaked” preferences

Single-peaked preferences?

Red: Yes Blue: Yes Green: No!

When are single-peaked preferences an appropriate assumption?

I. A non-strategic model of choice

A. Black’s Median Voter Theorem (1948)1. Assumptions

a. Single Dimension (important one!)

b. “Single-peaked” preferences

c. Majority rule (more on this later…)

d. Odd number of decision-makers (trivial)

2. Conclusion: No other position can beat that of the median voter

Example

Who is the median voter?

What is the median voter’s position?

Don’t confuse median voter with moderate policy!

Actor Position

A 0

B 10

C 20

D 70

E 70

F 80

G 100

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?

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?

Actor Position Power

A 0 20

B 10 100

C 20 100

D 70 50

E 70 50

F 80 100

G 100 10

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

Example

Who is the weighted median voter now?

Need to find the median point of power * salience: Multiply, sum, then divide by 2:

Actor Pos. Power Salience

A 0 20 60%

B 10 100 25%

C 20 100 25%

D 70 50 20%

E 70 50 20%

F 80 100 50%

G 100 10 100%

Actual Influence = Potential Influence * Salience

Actor Pos. Power Salience EFFECT

A 0 20 60% 12

B 10 100 25% 25

C 20 100 25% 25

D 70 50 20% 10

E 70 50 20% 10

F 80 100 50% 50

G 100 10 100% 10

Actual Influence = Potential Influence * SalienceActor Pos. Power Salience EFFECT

A 0 20 60% 12

B 10 100 25% 25

C 20 100 25% 25

D 70 50 20% 10

E 70 50 20% 10

F 80 100 50% 50

G 100 10 100% 10

SUM 142

142 / 2 = 71. Who’s the WMV?Actor Pos. Power Salience EFFECT

A 0 20 60% 12

B 10 100 25% 25

C 20 100 25% 25

D 70 50 20% 10

E 70 50 20% 10

F 80 100 50% 40

G 100 10 100% 10

SUM 142

142 / 2 = 71. Who’s the WMV?Actor Pos. Power Salience EFFECT

A 0 20 60% 12

B 10 100 25% 25

C 20 100 25% 25

D 70 50 20% 10

E 70 50 20% 10

F 80 100 50% 40

G 100 10 100% 10

SUM 142

C. Limitations of the Weighted Median Voter model

1. Limited to one dimension (by assumption)

2. 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…

3. Neglects coercion – What if actors are able to bully others into taking insincere positions?

4. Outcome is ambiguous -- The “vote” is an outcome, but does it result from acceptance by the players or war between them?

II. Adding Game Theory

A. Rational choice: preferences are connected and transitive

B. Expected utility: decision-makers base decisions on expected (rather than actual) payoffs

C. Rational expected utility maximizers interacting = a game. Each player plays best by anticipating behavior of opponent. Equilibrium = all are playing best given others’ play

D. Strategies: Two basic choices

1. What position to take (sincere or some alternative position)

2. Whether to threaten conflict against some or all participants by making demands/offers to them

E. Information

1. Information is imperfect: actors make their offers simultaneously (like in the PD)

2. Information is also incomplete: actors don’t know each other’s “true” preferences, so they have to have some rule for estimating them

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

III. Solving the game

A. Dealing with incomplete information (private knowledge) – players use Bayes’ Rule (a probability function) to estimate opponents’ true positions from their previous behavior

B. Banks monotonicity theorem

1.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

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

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?

ExampleActor Pos.

A 0

B 10

C 20

D 70

E 70

F 80

G 100

SUM

WMV = D

What if A is not truly conflict-seeking?

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

ExampleActor Round 1 Round 2 Round 3

A 0 70 70

B 10 10 10

C 20 20 50

D 70 70 50

E 70 70 50

F 80 80 80

G 100 100 100

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)

D. Solution Process1. 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…

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

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)

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…

IV. Refining and Using the Model

A. 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.

B. Using the model to forecast1. Pick an issue. Note the importance of reducing

the issue to a one-dimensional scale. 2. Identify the stakeholders (players)3. Create the issue scale, taking into account the

space between each position4. Find players’ positions, power (influence), and

salience interviews or research needed5. Note veto players6. Type the data in Excel and save as tab-delimited

text (.txt), using Bueno de Mesquita’s Zimbabwe data as an example

7. Input the data and run the model8. Interpret the results

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 policy or salience.

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)

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

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

NIWC forms a coalition with PUP

D. Bueno de Mesquita answers questions

Daily Show appearance Interview with questions

V. Other scholars’ use of the EUM: Did it work for them?

A. James and Lusztig (2000 using 1999 data): Forecasting elements of an FTAA

1. 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).

2. 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).

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

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

Issue 1996 Forecast Since 1996

1st Chechnya War No peace agreement Peace agreement reached 1996, treaty signed 1997.

Russian Economic Reforms Yeltsin key to continued economic liberalization

Yeltsin re-elected, so hypothesis not tested.

NAFTA Mexican trucks will be largely barred from US roads (88 of 100)

Mexican trucks “confined to border zones where they must offload goods to be carried by US companies”

Quebec No constitutional accord, conflict (secession)

No constitutional accord, no secession

Chinese economic reforms Descriptive Untestable

Jerusalem’s status No settlement No settlement

Bosnia peace accords US necessary for peace. Pullout before peace secured war

US pulls out in 2004. No test of hypothesis.

VI. Assessing Model Accuracy

A. 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)

B. CIA study (in Feder 2002): 80 issues, more than 20 countries 90% accuracy for WMV model

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?”

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)

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)

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

F. Labor Negotiations in the Netherlands (Rojer 1999)