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---
title: "The Expansion of War"
subtitle: POSC 3610 -- International Conflict
author: Steven V. Miller
institute: Department of Political Science
titlegraphic: /Dropbox/teaching/clemson-academic.png
date:
fontsize: 10pt
output:
beamer_presentation:
template: ~/Dropbox/miscelanea/svm-r-markdown-templates/svm-latex-beamer.tex
latex_engine: xelatex
dev: cairo_pdf
fig_caption: false
slide_level: 3
make149: true
mainfont: "Open Sans"
titlefont: "Titillium Web"
---
```{r setup, include=FALSE, cache=F, message=F, warning=F, results="hide"}
knitr::opts_chunk$set(cache=TRUE)
knitr::opts_chunk$set(fig.path='figs/')
knitr::opts_chunk$set(cache.path='cache/')
knitr::opts_chunk$set(
fig.process = function(x) {
x2 = sub('-\\d+([.][a-z]+)$', '\\1', x)
if (file.rename(x, x2)) x2 else x
}
)
```
```{r loadstuff, include=FALSE}
knitr::opts_chunk$set(cache=TRUE)
options(knitr.kable.NA = '')
library(tidyverse)
library(stevemisc)
library(countrycode)
library(knitr)
# library(kableExtra)
library(stargazer)
```
```{r loaddata, cache=T, eval=T, echo=F, message=F, error=F, warning=F}
MIDA <- read.csv("~/Dropbox/projects/mid-project/gml-mid-data/2.03/gml-mida-2.03.csv") %>% tbl_df()
Wars <- read.csv("~/Dropbox/data/cow/wars/Inter-StateWarData_v4.0.csv") %>% tbl_df()
```
# Introduction
### Question for Today
*What happens when war starts?*
### When War Starts
You'll notice we've talked about causes of war with saying little about war.
- Most our analyses have focused on MID onset.
- We just finished with MID escalation.
In other words: we belabored the first two conflict "phases" without addressing the third.
### A Framework for Studying the Evolution of War
![A Framework for Studying the Evolution of War](stoll-evolution.png)
# Properties of War
## War Expansion
### Not All Wars Look Like WWII
![Not all wars look like World War II](ww2-london.jpg)
### The Football War Might Actually Be Closer to Typical
![Other cases like the Football War stand out here.](football-war.png)
### Are All Wars Comparable?
The disparity leads some to assume they're different phenomena.
- Most classic scholarship cares about "big wars."
- In contrast, more recent scholarship is interested in "small wars."
- Better descriptor: "nonsystemic wars"
### "Born Big?"
Most scholarship assumes these "big wars" are "born big."
- If so, there's nothing left to explain about its evolution.
However, this would be misleading. Examples:
- WWI: started as an Austrian threat to use force against Serbia.
- WWII: started as a British/French threat against Germany re: Poland
- Gulf War I: started as an Iraqi threat to Kuwait re: slant drilling.
There's a corollary issue of selection bias.
- Again: these are *not* typical cases of war.
###
```{r num-participants-war, echo=F, eval=T, fig.width = 14, fig.height = 8.5}
Wars %>%
group_by(WarNum) %>%
summarize(n = n()) %>%
group_by(n) %>%
summarize(warp = n()) %>%
ggplot(.,aes(as.factor(n), warp)) +
geom_bar(stat = "identity", position = "dodge", alpha = I(0.8),color = I("black")) +
theme_steve_web() +
annotate("text", x = 7, y = 5, label = "Seven\nWeeks\nWar") +
annotate("text", x = 9, y = 5, label = "World\nWar\nI") +
annotate("text", x = 11, y = 5, label = "World\nWar\nII") +
annotate("text", x = 10, y = 5, label = "\nKorean\nWar") +
annotate("text", x = 8, y = 5, label = "\nGulf\nWar") +
xlab("Number of Participants in War") + ylab("Count") +
scale_y_continuous(breaks = seq(0, 60, by = 10)) +
labs(title = "Most Wars (60%) are Bilateral",
subtitle = "There is still substantial variation in war expansion even as wars like WWII are outliers.",
caption = "Data: Correlates of War Inter-State War Data (v. 4.0)")
```
### Explaining Expansion
How do we explain the wars that do expand?
- Opportunity/willingness
- Expected utility theory
### Opportunity/Willingness
The opportunity/willingness framework translates well from MID onset to war evolution.
- Problem: how do you measure it?
### Opportunity/Willingness
Siverson and Starr (1991) offer the following measurements.
- Opportunity: warring border states
- measurement: contiguity (broadly defined)
- Willingness: warring alliance partners
- measurement: alliances (vary by type)
###
| **War Involvement** | **No** | **Yes** | **TOTAL** |
|:--------------------|:------:|:-------:|:---------:|
| No | 2,320 | 1,335 | 3,655 |
| Yes | 8 | 86 | 94 |
| Total | 2,328 | 1,421 | 3,749 |
Table: Warring Border States OR Alliance Partners and War Involvement (1816-1965)
*Data come from Siverson and Starr (1991)*
### Limitations With This Approach
This scholarship implicitly treats war as a "disease" you "catch."
- Importantly: war is a choice that state leaders make.
- They make these choices weighing costs and benefits.
## War Expansion by Rational Choice
### War Expansion by Rational Choice
Altfeld and Bueno de Mesquita (1979) use expected utility to model third-party decisions to join war.
### Expected Utility for War
The intuition is simple:
- Joining a war is an expected utility calculation.
- One decision is preferred to the other when the **expected** utility for one is greater than the other.
- Importantly: utility is weighted by probability.
### The Parameters in the Calculations
Let State B's decision for joining an A-C War be modeled with:
- $U_{ba}$ ($U_{bc}$): utility for B of A (or C) winning the war.
- $K_{ba}$ ($K_{bc}$): costs B expects to endure for helping A (or C) win the war.
$\frac{b}{a + b + c}$: probability *B*'s participation matters (as modeled by CINC scores) to the outcome.
### When Does B Prefer to Help A Beat C?
\begin{eqnarray}
(\frac{b}{a + b + c})(U_{ba}) - K_{ba} &>& (\frac{b}{a + b + c})(U_{bc}) - K_{bc} \nonumber \\
(\frac{b}{a + b + c})(U_{ba}) - (\frac{b}{a + b + c})(U_{bc}) &>& K_{ba} - K_{bc} \nonumber \\
(\frac{b}{a + b + c})(U_{ba} - U_{bc}) &>& K_{ba} - K_{bc} \nonumber
\end{eqnarray}
###
| **Actual Choice** | **p(Join Weaker)** | **p(Stay Neutral)** | **p(Join Stronger)** |
|:------------------|:------------------:|:-------------------:|:--------------------:|
| Join Weaker | 16 | 4 | 0 |
| Stay Neutral | 1 | 104 | 3 |
| Join Stronger | 1 | 5 | 10 |
Table: Predicted and Actual Third-Party War Choices (Altfeld and BdM (1979))
<!-- ## War Duration
###
```{r, echo=F, eval=T, fig.width = 14, fig.height = 8.5}
MIDA %>%
filter(hostlev == 5 & mindur != 1) %>%
group_by(mindur) %>%
summarize(n = n()) %>%
mutate(category=cut(mindur, breaks=c(-Inf, 1, 30, 60, 120, 365, 730, 1095, Inf),
labels=c("One-day","2-30\ndays","31-60\ndays", "61-120\ndays",
"121-365\ndays",
"1-2 years", "2-3 years", "Longer than\n3 years"))) %>%
group_by(category) %>%
summarize(n = n()) %>%
mutate(perc = round((n/sum(n))*100, 2),
perc = paste0(perc,"%")) %>%
ggplot(., aes(category, n)) +
geom_bar(stat = "identity", position = "dodge", alpha = I(0.8),color = I("black")) +
theme_steve() +
xlab("Duration Category") + ylab("Count") +
geom_text(aes(label=perc), vjust=-.5, colour="black",
position=position_dodge(.9), size=4) +
labs(title = "Your Typical War Is Going to Last 365 Days or Fewer",
subtitle = "...and still plenty wars last several years.",
caption = "Data: Gibler-Miller-Little MID Data (v. 2.01)")
```
-->
## War Durations
### War Duration
There is considerable interest in how long wars last.
- Longer wars typically indicate substantially higher (broadly defined) costs.
Yet, there's substantial variation among wars.
- Vietnam War lasted more than 10 years.
- The Football War lasted a few days.
- The Six Day War lasted... well, six days.
###
```{r war-duration, echo=F, eval=T, fig.width = 14, fig.height = 8.5}
MIDA %>%
filter(hostlev == 5 & mindur != 1) %>%
group_by(mindur) %>%
summarize(n = n()) %>%
mutate(category=cut(mindur, breaks=c(-Inf, 1, 30, 60, 120, 365, 730, 1095, Inf),
labels=c("One-day","2-30\ndays","31-60\ndays", "61-120\ndays",
"121-365\ndays",
"1-2 years", "2-3 years", "Longer than\n3 years"))) %>%
group_by(category) %>%
summarize(n = n()) %>%
mutate(perc = round((n/sum(n))*100, 2),
perc = paste0(perc,"%")) %>%
ggplot(., aes(category, n)) +
geom_bar(stat = "identity", position = "dodge", alpha = I(0.8),color = I("black")) +
theme_steve_web() +
xlab("Duration Category") + ylab("Count") +
geom_text(aes(label=perc), vjust=-.5, colour="black",
position=position_dodge(.9), size=4) +
labs(title = "Your Typical War Is Going to Last 365 Days or Fewer",
subtitle = "...and still plenty wars last several years.",
caption = "Data: Gibler-Miller-Little MID Data (v. 2.03)")
```
### What Explains War Duration?
Per Bennett and Stam (1996), wars generally last longer when:
- Terrain is "rougher" relative to more "open."
- Power is balanced among disputants.
- More troops are committed to combat zones.
- *Fewer* states are involved.
## War Outcomes
### War Outcomes
Who wins the war? Seems like an important question.
- Like war duration, though, we won't know until war is over.
###
```{r war-outcomes, echo=F, eval=T, fig.width = 14, fig.height = 8.5}
MIDA %>%
filter(hostlev == 5 & mindur != 1) %>%
group_by(outcome) %>%
filter(outcome != 9) %>%
summarize(n = n()) %>%
mutate(category=c("Victory by\nSide A", "Victory by\nSide B",
"Yield by\nSide A", "Yield by\nSide B",
"Stalemate", "Compromise")) %>%
mutate(perc = round((n/sum(n))*100, 2),
perc = paste0(perc,"%")) %>%
ggplot(., aes(category, n)) +
geom_bar(stat = "identity", position = "dodge", alpha = I(0.8),color = I("black")) +
theme_steve_web() +
xlab("Outcome Category") + ylab("Count") +
geom_text(aes(label=perc), vjust=-.5, colour="black",
position=position_dodge(.9), size=4) +
labs(title = "Most Wars End in a Victory for One Side or the Other",
subtitle = "but almost 20% of wars end with no change to the motivating issue that caused the war.",
caption = "Data: Gibler-Miller-Little MID Data (v. 2.01)")
```
### War Outcomes
Initiators generally win their wars.
- Yet there's still substantial variation and even more confusion distinguishing between MID/war initiation.
Conventional wisdom holds power matters most.
- Its likelihood of winning a war should increase monotonically with increases in relative power.
###
```{r traditional-view-power-war, echo=F, eval=T, fig.width = 14, fig.height = 8.5}
x <- seq(0, 1, length.out =100)
tibble(x = x,
awins = x*1,
bwins = (1-x)*1) %>%
ggplot(.,aes(x, awins)) + theme_steve_web() +
geom_path(aes(, awins), color = "#F8766D", size = 1.5) +
geom_path(aes(, bwins), color = "#00BCF4", size=1.5, linetype="dashed") +
ylab("Pr(Win)") + xlab("A's Capabilities Relative to B") +
annotate("text", x = 0, y = .10, label = "Pr(A wins)", family="Open Sans") +
annotate("text", x = 0, y = .90, label = "Pr(B wins)", family = "Open Sans") +
labs(title = "The Traditional View of the Impact of Power on War Outcomes",
subtitle = "Conventional wisdom holds for a linear relationship between power and war outcomes.",
caption = "Stam III, Allan C. 1996. Win, Lose, or Draw: Domestic Politics and the Crucible of War. Ann Arbor, MI: University of Michigan Press")
```
### A Better View of Power and War Outcomes
The conventional wisdom is missing much about the nature of war.
- Wars can (and do) end in stalemates or draws.
- States see benefits and costs associated with continued combat.
- "Costs" can be understood as wherewithal to absorb damage from opponent.
Understanding war as mutual coercion in a cost-benefit analysis better approximates how wars can end.
###
![War as Mutual Coercion via Stam (1996)](quadrant.png)
###
```{r likelihood-war-outcomes, echo=F, eval=T, fig.width = 14, fig.height = 8.5}
x <- seq((pi/4), (2*pi), length.out =100)
tibble(x = x,
awins = sin(x)*(1 - cos(x)),
bwins = cos(x)*(1 - sin(x)),
draw = (1 - cos(x))*(1 - sin(x))) %>%
ggplot(.,aes(x, draw)) + theme_steve_web() +
geom_path(aes(, awins), color = "#F8766D", size = 1.5) +
geom_path(aes(, bwins), color = "#00BCF4", size=1.5, linetype="dashed") +
geom_path(aes(, draw), color = "#7CAE00", size=1.5, linetype = "dotted") +
scale_y_continuous(breaks = NULL) +
ylab("Likelihood of War Outcome") +
xlab("Theta") +
annotate("text", x = 2, y = 1.5, label = "Greatest probability\nfor A to win", family="Open Sans") +
annotate("text", x = 5.75, y = 1.5, label = "Greatest probability\nfor B to win", family="Open Sans") +
annotate("text", x = 5*pi/4, y = 2.5, label = "Greatest probability\nof a draw", family="Open Sans") +
scale_x_continuous(breaks = c(pi/4, pi/2, 3*pi/4,
pi, 5*pi/4, 3*pi/2,
7*pi/4, 2*pi),
labels = c("pi/4", "pi/2", "3pi/4",
"pi", "5pi/4", "3pi/2",
"7pi/4", "2pi")) +
geom_hline(yintercept = 0, linetype = "dashed") +
geom_vline(xintercept = pi/4, linetype = "dashed") +
labs(title = "Likelihood of War Outcomes",
subtitle = "Importantly, the probability of A winning and B winning can both rise at the same time.",
caption="Stam III, Allan C. 1996. Win, Lose, or Draw: Domestic Politics and the Crucible of War. Ann Arbor, MI: University of Michigan Press")
```
###
```{r war-fatalities, echo=F, eval=T, fig.width = 14, fig.height = 8.5}
Wars %>%
group_by(WarNum) %>%
summarize(n = sum(BatDeath)) %>%
mutate(category=cut(n, breaks=c(-Inf, 3000, 10000, 50000, 100000,
1000000, 5000000, 10000000, Inf),
labels=c("1,000-3,000\nFatalities","3,000-10,000\nFatalities",
"10,000-50,000\nFatalities", "50,000-100,0000\nFatalities",
"100,000-1,000,000\nFatalities",
"1,000,000-5,000,000\nFatalities",
"5,000,000-10,000,000\nFatalities",
"More Than 10,000,000\nFatalities"))) %>%
group_by(category) %>%
summarize(n = n()) %>%
mutate(perc = round((n/sum(n))*100, 2),
perc = paste0(perc,"%")) %>%
ggplot(.,aes(category, n)) +
geom_bar(stat = "identity", position = "dodge", alpha = I(0.8),color = I("black")) +
theme_steve_web() +
annotate("text", x = 6, y = 3.5, label = "Vietnam War,\nIran-Iraq War") +
annotate("text", x = 7, y = 3, label = "World\nWar\nI") +
annotate("text", x = 8, y = 3, label = "World\nWar\nII") +
xlab("Number of Estimated Fatalities in Combat") + ylab("Count") +
labs(title = "The Median War Claims Fewer Than 10,000 Fatalities in Combat",
subtitle = "...and, by the grace of god, wars like the world wars are rare events.",
caption = "Data: Correlates of War Inter-State War Data (v. 4.0)")
```
# Conclusion
### Conclusion
Most conflict studies dance around war dynamics but few address it.
- Most analyses are concerned with MID (or war) onset and less properties of the war itself.
Big questions: when does war expand?
- Bilateral wars seldom carry systemic consequences.
- Opportunity/willingness provide some clues.
- Certainly: war expansion is more choice than contagion.
### Conclusion
War is a fatality threshold for which there is substantial variation. Descriptively:
- Most wars last a year or less
- Most wars end in victory, but stalemates are still common.
- Most wars claim fewer than 10,000 fatalities.
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