1. A Spatial Model of Multilateral Negotiations
Kevin L. Cope and James D. Morrow
University of Michigan

2. Multilateral Negotiations
Much of international law is created through multilateral treaties that aspire to universality:
Human rights
International humanitarian law
Trade
Much progress has been made in studying the effects of these treaties, but we know little systematically about the negotiations that create these treaties.

3. Characteristics of multilateral bargaining
Consensus required.
States select into international law through treaty ratification.
Multiple issues to bargain over
Could drop/ignore some parties with following consequences...
Excluded party could add value to the agreement.
The broader/deeper tradeoff

4. Spatial Model of Negotiations
Spatial models allow us to analyze how actors with different positions reconcile their differences to produce a common outcome.
Elections
Legislatures
Bilateral negotiations
Core concepts:
Issues modeled spatially
Ideal points for each actor
Declining utility moving away from ideal point

5. The Game Actors: M States, D-Drafting committee
N-dimensional issue space
Preferences:
D: Ideal point at the origin
States: ideal points xi
Value for the treaty depends on how many states ratify. Each state has weight wi with
𝑊+ 𝑖=1 𝑀 𝑤 𝑖 =1

6. For D, payoff is 𝑢 𝐷 𝑥 = 𝑊+ 𝑖 𝑟𝑎𝑡𝑖𝑓𝑖𝑒𝑠 𝑤 𝑖 − 𝑥 2
𝑢 𝐷 𝑥 = 𝑊+ 𝑖 𝑟𝑎𝑡𝑖𝑓𝑖𝑒𝑠 𝑤 𝑖 − 𝑥 2
For i ϵ M, value ViIN if i ratifies, value ViOUT if i does not, with Δi = ViIN – ViOUT.
Values vary with nature of good produced by treaty and expressive value for ratification.
i’s payoff is
𝑢 𝑖 𝑥 = ∆ 𝑖 𝑊+ 𝑖 𝑟𝑎𝑡𝑖𝑓𝑖𝑒𝑠 𝑤 𝑖 − 𝑥− 𝑥 𝑖 2

7. Time Line of Game:
D proposes treaty x.
All i simultaneously ratify x or not. Payoffs are received.

8. Characterizing the Equilibrium
For K M, define i ϵ M to be favorable under K if
∆ 𝑖 𝑊+ 𝑗∈𝐾 𝑤 𝑗 − 𝑥 𝑖 2 ≥0
and unfavorable under K otherwise.
Coalition K is feasible if all i ϵ K are favorable under K and all i ∉ K are unfavorable.
Coalition K is the base coalition if it is feasible and 𝑤 𝐾 = 𝑖∈𝐾 𝑤 𝑖 is a maximum over all feasible K.

9. Let i be unfavorable under the base coalition
Let i be unfavorable under the base coalition. Define Ω 𝑖 = 1− ∆ 𝑖 𝑊+ 𝑗∈𝐵+𝑖 𝑤 𝑗 𝑥 𝑖 𝑥 𝑖
Choose treaty t ϵ {Ωi,0} to maximize uD(t).
Equilibrium: D proposes t. i ratifies if ui(t) ≥ 0.

10. Here are three actors:
Each has ideal point and indifference curve for what treaties it will accept.
B is favorable and forms the base coalition.
A and C are unfavorable under base coalition.

11. Treaty will be whichever of {0,ΩA,ΩC,ΩAC} maximizes uD(t).

12. What is to Be Done? Finalize proofs.
Use the model to drive the estimation procedure.
Rome Conference is test data.
Much of the data is missing compared to votes and decisions.
Apply procedure to analyze other treaties, particularly human rights treaties.
Substantive questions:
Do conference rules matter?
Variation across treaties
The logic of exclusion and its effect on resulting treaties

13. Extra Slides

14. The Rome Statute
The Rome Statute of 1998 constituted the International Criminal Court and gave it power to prosecute war crimes and crimes against humanity.
Final conference held in Rome during June-July 1998 with 160 states represented.
Plenary sessions collected comments on draft treaty leading to revisions by the Drafting Committee.
Final vote followed by ratification afterwards.

15. ICC created after 60 states ratified the Rome Statute.
124 states are parties to the ICC now.

16. Estimating Ideal Points
We use the negotiating record published by the UN as data course to estimate state ideal points.
Each comment by a state was coded as
Critical of the proposed language
Supportive of the proposed language
No opinion
218 issues were coded; some articles present multiple issues.

17. Bayesian spatial modeling based on item-response theory.
We adapt techniques used for legislatures and courts to estimate ideal points from votes and decisions (Poole and Rosenthal, Martin and Quinn, Voeten).
Bayesian spatial modeling based on item-response theory.
135 states expressed at least one view during negotiations.
Of 29,430 (= 135*218) potential state views , 4364 expressed, most critical.
We recover one dimension from the procedure.

18. Procedure gives distributions for the estimate of each state’s position.

19. Estimated ideal point predicts ratification of the treaty afterwards.
Ratified in blue
Not ratified in red