Today’s objectives

 

  1. Define: concept of “victory” in war
    1. Is “military victory” possible?
    2. What is alternative?
  2. Review: bargaining model of war
    1. How bargaining failures lead to war
    2. How war is a continuation of bargaining process
  3. Consider: competing explanations of military effectiveness
    1. Numerical preponderance
    2. Technology
    3. Force employment

War is Bargaining by Other Means

 

Definitions  

 

  1. Victory in war
    1. attainment of political aims for which one went to war
    2. can be obtained through force or coercive diplomacy
  2. Military victory
    1. imposition of political terms by rendering one’s enemy incapable of resistance
    2. can be obtained only through force

 

Is this victory?

Is Military Victory Possible?

 

 

 

Pure “military victories” almost never happen

  1. Strategic level
    1. extremely rare for losing army to be fully (or even mostly) destroyed in war
  2. Tactical level
    1. military formations are almost never fully annihilated in combat

Ending war is a choice

  • abstain/exit from combat
    or
  • continue to fight


 

 

Not happening

Personnel losses in interstate wars since 1816

 

Total casualties per war


 

War winners vs. losers

Almost all wars end before belligerents exhaust military potential

  • loss rates higher for median war loser than for winner, but…
  • most belligerents since 1816 lost less than 10% of armed forces
  • median war participant lost 4.5% of overall force strength

Personnel losses in conventional ground battles since 1939

 

Casualties per battle


 

War winners vs. losers

Most battles end before belligerents exhaust military potential

  • high losses more common in battles than in wars, but…
  • median battle participant lost only 14% of available forces
  • loss rates not (strongly) predictive of strategic-level outcomes

Bargaining While Fighting

 

Bargaining model of war

  1. Almost all military outcomes, at all levels of war, are choices that reflect (tacit) bargaining
  2. War begins if sides can’t reach deal
  3. Fighting reveals information about capabilities & resolve, updating perceptions of bargaining leverage
  4. War ends when these perceptions converge, and yield agreement on terms of deal

Purpose of violence

  1. Establish credibility of threats
  2. … not to neutralize enemy’s capacity to resist


 

 

 

How it starts/ends

Illustration: Sides A (blue) and B (red) are bargaining over a disputed territory.

They can resolve this dispute peacefully or through war.

 

Let’s make a deal!

  • blue area is the proportion of land that side A expects to win through war
  • red area is the proportion of land that B expects to win through war
  • gray area represents the cost of war (e.g. land destroyed, people killed)

Pre-War Bargaining

Suppose A makes an ultimatum (take-it-or-leave-it offer) to B

  1. If B accepts the offer, B receives red area, and A keeps remaining blue area

 

What B would get from A’s offer

  1. If B rejects the offer, a war will start, in which B expects to get this area in red
    (land and other booty won through war, minus costs)

 

What B expects to get from war

Will B accept A’s offer, or go to war? It depends on which of these is bigger:

 

 

A’s offer?

 

 

 

 

 

or

Spoils of war?

 

  • if B expects to get better deal from war than from A’s offer, B will choose war

Is there an offer that both A and B would prefer to war?

  • yes, if the offer falls inside the bargaining range

 

Bargaining range

 

Puzzle: If bargaining range exists, then two sides can always settle the dispute peacefully. Settlement will reflect balance of power. But wars still occur. Why?

Fearon (1995) offers three main explanations for why war may still occur:

 

  1. commitment problems: states worry that future shifts in relative power may allow opponent to make new demands
  2. issue indivisibility: some resources are not subject to compromise
    (e.g. sacred religious sites)
  3. incomplete information: states may have incentives to misrepresent their true costs of war (e.g. secrecy around military capabilities)

Intra-War Bargaining

War begins when side A and side B cannot find a negotiated settlement that both prefer to war (e.g. due to incomplete information about relative military capabilities)

 

Over time, fighting reveals new information (“enemy is stronger than I thought”)

Expectations on day 1 of war

Expectations on day 100 of war

War ends when beliefs converge about likely outcome of war, sides make a deal
(“I can’t take any more of this. even a bad deal is better than more war. let’s talk”)

War is bargaining by other means

  • physical combat changes the sides’ understanding of their bargaining leverage
  • this new understanding yields a new negotiated agreement on settlement terms

 

A’s original offer

A’s revised offer

How to gain bargaining leverage: win battles! (but how does one do that?)

Military Effectiveness

Predictors of victory and defeat in battle

Numerical preponderance Technology Force employment Geography Information
force strength offense-defense balance doctrine distance surprise
mobilization base targeting selection strategy terrain intelligence
industrial capacity force structure training climate OPSEC
natural resources communication officer quality roads censorship
replacement of losses logistics operational art fortifications propaganda

Numerical and Technological Preponderance

Numerical preponderance

  1. Force strength
    1. which side has numerical superiority?
  2. Mobilization base
    1. which side has more resources available to meet foreseeable wartime needs?
  3. Industrial capacity
    1. which side can produce at scale, with surge capacity?
  4. Natural resources
    1. which side has access to more raw materials?
  5. Replacement of losses
    1. which side can more easily recover from attrition?


 

 

Biggest army wins

Technology

  1. Offense-defense balance
    1. does available technology favor attacker or defender?
  2. Target selection
    1. which side can engage enemy targets with greater accuracy and precision?
  3. Force structure
    1. which side has optimal force mix (e.g. level of mechanization, tooth-to-tail ratio) for its mission?
  4. Communication
    1. which side can more efficiently share information, coordinate actions?
  5. Logistics
    1. which side can deploy troops and deliver supplies cheaper & faster?


 

 

 

Army with best tech wins

Operations Research Corner

Illustration of Numerical Preponderance: Lanchester’s Model of Direct Fire

  1. Assumptions
    1. each side is visible to the other
    2. each combatant on each side is able to fire on any opposing individual
    3. loss rate on one side is proportional to number of opponents firing
  2. Formalization
    \(dA/dt=-\alpha_{B} B_t,\quad dB/dt=-\alpha_{A} A_t\)
    where
    1. \(\frac{dA}{dt}, \frac{dB}{dt}\) are rates of attrition in A’s and B’s forces over time (\(t\))
    2. \(\alpha_{A}, \alpha_{B}\) are A’s and B’s rates of fire
    3. \(A_t, B_t\) are A’s and B’s force strength on the battlefield at time \(t\)
  3. Solution
    1. by integrating with respect to time, we get the following conditions: \[\begin{align*} \alpha_{B} B^2 &< \alpha_{A} A^2\quad \text{(A wins)},\quad \alpha_{B} B^2 > \alpha_{A} A^2\quad \text{(B wins)} \end{align*}\]
    2. this is the “Square Law”: casualty ratio varies inversely to force ratio
      (force outnumbering opponent will have fewer casualties in equilibrium)
  1. Example
    1. if A is twice as numerous as B (\(A=2B\)),
      but B is three times as effective as A (\(\alpha_{B}=3\alpha_{A}\)), A will still win: \[\begin{align*} 3\alpha_{A} B^2 & < \alpha_{A} (2B)^2 \quad \to \quad 3<4 \end{align*}\]
    2. in a direct fire setting, the numerically larger force will prevail

Attrition in the direct fire model

Illustration of Technological Dominance: Lanchester’s Model of Indirect Fire

  1. Assumptions
    1. each side is invisible to the other
    2. each combatant on each side fires into area other side occupies
    3. loss rate on one side is proportional to number of opponents firing
      and number of friendly troops occupying the area under fire
  2. Formalization
    \(dA/dt=-\alpha_{B} B_t A_t,\quad dB/dt=-\alpha_{A} A_t B_t\)
    where
    1. \(\frac{dA}{dt}, \frac{dB}{dt}\) are rates of attrition in A’s and B’s forces over time (\(t\))
    2. \(\alpha_{A}, \alpha_{B}\) are A’s and B’s rates of fire
    3. \(A_t, B_t\) are A’s and B’s force strength on the battlefield at time \(t\)
  3. Solution
    1. by integrating with respect to time, we get the following conditions: \[\begin{align*} \alpha_{B} B &< \alpha_{A} A\quad \text{(A wins)},\quad \alpha_{B} B > \alpha_{A} A\quad \text{(B wins)} \end{align*}\]
    2. this is the “Linear Law”: casualty ratio varies inversely to relative rates of fire (force outgunning opponent has fewer casualties in equilibrium)
  1. Example
    1. if A is twice as numerous as B (\(A=2B\)),
      but B is three times as effective as A (\(\alpha_{B}=3\alpha_{A}\)), B will now win: \[\begin{align*} 3\alpha_{A} B & > \alpha_{A} (2B) \quad \to \quad 3>2 \end{align*}\]
    2. in an indirect fire setting, technology matters more than numbers

Attrition in the indirect fire model

 

 

Key assumptions Lanchester is making

 

  1. Forces are within weapons range of each other
  2. Effects of weapons rounds are independent
  3. Fire is uniformly distributed across enemy targets
    (or area)
  4. Rates of fire are constant over time
  5. No reinforcements

 

What do you find problematic about these assumptions?

 

What’s missing from these models?


Direct fire

Indirect fire

Force Employment

Force employment

  1. Doctrine
    1. which side is more prepared for expected type of combat?
  2. Strategy
    1. which side has smarter/clearer vision for how to win war?
  3. Training
    1. are troops ready and able to implement the chosen strategy?
  4. Officer & NCO quality
    1. are small team leaders capable of independent decisions?
    2. how well is discipline maintained?
    3. are senior leaders capable of managing large-scale maneuvers?
  5. Operational art
    1. which side can best integrate ends, means?


 

 

 

Most skilled army wins

Example: “Modern System” (Biddle, 2004)

  1. Key elements:
    1. cover and concealment
    2. dispersion
    3. small unit independent maneuver
    4. combined arms warfare
  2. Goal: reduce exposure to firepower

But this is very hard to do!

  1. Requirements:
    1. independent decision-making by 1,000s of junior officers
    2. tight coordination and synchronization between dispersed, moving units
    3. mastery of multiple, dissimilar weapons types
    4. trust (hard for superiors to monitor and control juniors’ behavior)


 

 

 

The modern battlefield

Back to the Negotiating Table

 

If ending war is a choice, what drives this choice?

  1. Convergence of beliefs about who would win a fight to the finish
    1. choice is shaped not only by brute force destructive potential
      (“can we destroy them?”)
    2. but also by resolve and commitment to stakes
      (“is it worth it?”)
    3. example: U.S. in Afghanistan
  2. Wars do not end in stalemate
    1. stalemate creates uncertainty over who would prevail in long run
    2. this makes bargains harder to reach (at least in short term)
    3. negotiated settlement becomes possible when one side is unable and unwilling to maintain stalemate


 

 

 

 

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