The Paradox of Disconnected Coalitions
by
Steven J. Brams
New York University
Coauthors: Michael A. Jones (Montclair State University), D. Marc Kilgour (Wilfrid Laurier University)

The paradox of disconnected coalitions is that "disconnected" coalitions can arise from the "connected" (i.e., single-peaked) preferences of as few as five players. Two models of coalition formation are analyzed in which the paradox can occur, in both of which players coalesce when they find each other mutually acceptable:

• Fallback (FB): Players seek coalition partners by descending lower and lower in their preferences until a majority coalition emerges.

• Build-Up (BU): Same as FB, except that when nonmajority subcoalitions form, they fuse into composite players, and the descent restarts.

FB better reflects the unconstrained, or nonmyopic, possibilities of coalition formation, whereas BU, because all subcoalition members must be included in any majority coalition that forms, restricts combinatorial possibilities considerably and tends to produce larger and less tight majority coalitions.

If player perceptions of the single-peaked ordering are sufficiently similar (spatially single-peaked), the paradox is precluded. But the strange bedfellows frequently observed in legislative coalitions and military alliances suggest that even when players agree on, say, a left-right ordering, their perceptions of exactly where players stand in this ordering may differ substantially. If so, a player may be acceptable to a coalition but may not find every member in it acceptable, causing that player not to join and creating a "hole" in an otherwise connected coalition. Applications of the models are discussed.

Date received: June 20, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafk-24.