Paradoxes and Puzzles of War

Key Problems in Conflict Studies

I. Paradoxes of WarA. Why do people choose sub-optimal

outcomes?1. War is sub-optimal

a. Bargaining without war: Side A and Side B are arguing over something. Expressing each side’s share as a percentage, A gets x of the disputed resources or territory and B gets 1-x. So A’s share plus B’s share = 1, or 100%. This is called Pareto Optimality (nothing is left on the table).

b. Compare to War

Each side has a chance of winning and losing. One side’s chance of winning is the other side’s chance of losing.

Winner gets everything (100% of disputed resources), loser gets nothing (0%)

Both sides suffer costs (economic, social, military, etc.)

The Math: A Simple Proof

Represent A’s probability of winning as p. Then B’s probability of winning is 1-p.

A’s payoff for war = p*1 + (1-p)*0 – CostsA Simplify: p - CostsA

B’s payoff for war = (1-p)*1+p*0 – CostsB Simplify: 1- p - CostsB

The total return on war is (p-CostsA) + (1-p-CostsB) = p – CostsA + 1 – p – CostsB = 1 – CostsA – Costs B

Since bargaining gives a total return of 1 and 1 > 1 – CostsA – CostsB war is inefficient. Not Pareto Optimal.

2. The Paradox

No matter what the outcome is to a war, the two sides could always have found some agreement that BOTH would have preferred to war – IF both of them agreed on how the war was likely to turn out.

Example: Both sides in a war would ALWAYS be better off by simply adopting the war’s outcome (other than the actual fighting part) as a pre-war bargain.

So why do people fight?

B. The “Para Bellum” Puzzle

1. Arms races are supposed to deter aggression: “If you want peace, prepare for war”

a. Problem: If you want war, you also prepare for warb. Implication: If rivals prepare for war we don’t know

whether they want peace or war

2. Paradox: If we also prepare for war, we give rivals an incentive to strike first (before our arms buildup takes effect) force choice between “continue costly arms race” and “war”

3. Key puzzle: Do “power politics” strategies for avoiding war increase or decrease the risk of war?

C. The Paradox of Deterrence

1. Deterrence requires threat and restrainta. Successful deterrence requires a clear, credible, and

overwhelming threat that will be carried out if a line is crossedb. Successful deterrence also requires restraint, the belief that

the deterring state will refrain from carrying out the threat if the line is not crossed

2. Credibility means rational to carry out the threat (i.e. it produces more benefits than costs)

3. Problem: As it becomes more cost-beneficial to use force, use of force is more likely

4. Paradox: Measures to reinforce threat undermine restraint, undermining deterrence. Rational deterrence relies on being seen as irrational in some way.

D. The Puzzle of Peace

1. War happens…

2. …but usually it doesn’t! Probability any two countries are at war in any year = 1 in 1000.

a. Implication: I can predict war or peace with 99.9% accuracy by just saying “no war this year.”

b. Most countries and peoples spend far more time at peace than at war.

3. The puzzle: Explanations of how war is possible must also explain why it is so rare!

E. The Puzzle of War Termination

1. Wars start – presumably there is a reason for this

2. But the same wars end – and almost all interstate wars and many civil wars end WITHOUT a “fight to the finish”

3. Why do the same people who decide to start a war decide to stop fighting before the bitter end?

II. Models, Ideologies, and Theories

What’s the difference?

Ideologies Models

II. Models, Ideologies, and Theories

What’s the difference?

Ideologies Models

Domain Values Facts

II. Models, Ideologies, and Theories

What’s the difference?

Ideologies Models

Domain Values Facts

About the past… Evaluation Description

II. Models, Ideologies, and Theories

What’s the difference?

Ideologies Models

Domain Values Facts

About the past… Evaluation Description

About the present or future…

Prescription Prediction

II. Models, Ideologies, and Theories

What’s the difference?

Ideologies Models

Domain Values Facts

About the past… Evaluation Description

About the present or future…

Prescription Prediction

When assumptions clearly stated…

Normative Theory

Empirical Theory

III. Empirical Puzzles, Empirical Theories

A. Empirical propositions1. Descriptive (one variable at a time)

2. Causal (two variables are related)a. Independent variable = the cause

b. Dependent variable = what we’re trying to predict

B. Paradoxes of war as empirical problems1. What variables predict conflict onset?

2. What variables predict conflict escalation?

3. What variables predict conflict termination?

C. One basic model:Opportunity and Willingness

1. Key Actors = Leaders of States2. Goals = Stay in Office, Improve Policy, Personal

Gain3. World System, Internal Politics = Constraint on

Leaders4. Menu Analogy

a. Some items aren’t on the menu (no opportunity) b. Some items are on the menu but not desirable (no

willingness) – possibly because leaders misunderstand their consequences!

c. Item chosen = preferred, available dish (both opportunity and willingness)

5. Example: Saddam Hussein

Menu• Kick the US out and execute traitors who

thought about surrender• As above, but then invade the US to preempt

future attacks• Surrender and go into exile

• Delay US forces while searching for a way out of the war

5. Example: Saddam Hussein

Menu• Kick the US out and execute traitors who

thought about surrender• As above, but then invade the US to preempt

future attacks• Surrender and go into exile

• Delay US forces while searching for a way out of the war

5. Example: Saddam Hussein

Menu• Kick the US out and execute traitors who

thought about surrender• As above, but then invade the US to preempt

future attacks• Surrender and go into exile

• Delay US forces while searching for a way out of the war

IV. The Level-of-Analysis Problem

System

Region

Dyad

State

Bureaucratic

Group

Individual

A. Levels of Analysis

B. What’s the Problem?

1. Problem: Testing Hypotheses at the Wrong Level of Analysis

a. Fallacy of Equivocation: Using the Same Word to Mean Two Different Things

“Balance of Power” – Does this mean all states are equal (system level), that two states are balanced with each other (dyad level), or that a leader is committed to preserving a balance of power (individual level)?

b. Applying findings at one level to another: Possible but not straightforward

2. Example: Do Alliances Cause War?

The World at Time 1 The World at Time 2

2. Example: Do Alliances Cause War?

The World at Time 1 The World at Time 2

WORLD-SYSTEM

Time 1 Time 2

% Allied

% at War

2. Example: Do Alliances Cause War?

The World at Time 1 The World at Time 2

WORLD-SYSTEM

Time 1 Time 2

% Allied 0% 60%% at War 0% 40%

2. Example: Do Alliances Cause War?

The World at Time 1 The World at Time 2

WORLD-SYSTEM

Time 1 Time 2

% Allied 0% 60%% at War 0% 40%

STATE-YEARS

Not Allied Allied

Peace

War

2. Example: Do Alliances Cause War?

The World at Time 1 The World at Time 2

WORLD-SYSTEM

Time 1 Time 2

% Allied 0% 60%% at War 0% 40%

STATE-YEARS

Not Allied Allied

Peace 5 3War 2 0

2. Example: Do Alliances Cause War?

The World at Time 1 The World at Time 2

Answer: It depends on the level of analysis!

•A system with more alliances is more war prone

•A state in an alliance is less likely to fight a war

3. Applying Findings at One Level to Another

a. Aggregation: Building up from lower levels. Results may be unexpected!

b. Example: The “Democratic Peace” hypothesisi. Democracies Don’t Fight Each Other

ii. Autocracies are Less Likely to Fight Each Other Than Average

iii. Democracies Do Seem to Fight Just as Often as Autocracies

c. Question: Is more democracy in the world a good thing if we want to avoid war?

Democratic Peace Example

#D

AA

DD

DA

# of Wars

Risk for Autocratic dyads is 1% Risk for Democratic dyads is 0% Risk for Mixed Dyads is 2%

Democratic Peace Example

#D

AA

DD

DA

# of Wars

0 10 0 0 .1

Risk for Autocratic dyads is 1% Risk for Democratic dyads is 0% Risk for Mixed Dyads is 2%

Democratic Peace Example

#D

AA

DD

DA

# of Wars

0 10 0 0 .1

1 6 0 4 .14

Risk for Autocratic dyads is 1% Risk for Democratic dyads is 0% Risk for Mixed Dyads is 2%

Democratic Peace Example

#D

AA

DD

DA

# of Wars

0 10 0 0 .1

1 6 0 4 .14

2 3 1 6 .15

Risk for Autocratic dyads is 1% Risk for Democratic dyads is 0% Risk for Mixed Dyads is 2%

Democratic Peace Example

#D

AA

DD

DA

# of Wars

0 10 0 0 .1

1 6 0 4 .14

2 3 1 6 .15

3 1 3 6 .13

Risk for Autocratic dyads is 1% Risk for Democratic dyads is 0% Risk for Mixed Dyads is 2%

Democratic Peace Example

#D

AA

DD

DA

# of Wars

0 10 0 0 .1

1 6 0 4 .14

2 3 1 6 .15

3 1 3 6 .13

4 0 6 4 .08

Risk for Autocratic dyads is 1% Risk for Democratic dyads is 0% Risk for Mixed Dyads is 2%

Democratic Peace Example

#D

AA

DD

DA

# of Wars

0 10 0 0 .1

1 6 0 4 .14

2 3 1 6 .15

3 1 3 6 .13

4 0 6 4 .08

5 0 10 0 0Risk for Autocratic dyads is 1% Risk for Democratic dyads is 0% Risk for Mixed Dyads is 2%

Democratic Peace Example Solution: Relationship is nonlinear – Adding

democracies to a world of dictatorships increases war risk until critical point reached. After that point, more democracy means less war.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 1 2 3 4 5

AverageNumber ofWars

V. Implications

A. War and Peace are choices: Leaders must select them from a range of options

B. Keys to the puzzle:1. How does the international environment

constrain opportunities for peace or war?

2. How does the internal structure of a state constrain opportunities for peace or war?

3. How do leaders choose from their “menus for choice?”