Alliance incentives under the D’Hondt method

• An example of alliance (coalition) that leads to unlimited seat gains is shown.
• The necessary and sufficient condition for the lack of successful alliances is discovered.
• The configuration of the alliance-proof set is described.
• A game-theoretical approach for alliance formation is applied.

This paper studies the incentives for alliance (coalition) formation. It provides an example of an alliance that leads to unlimited seat gains. A full description of a set that guarantees the lack of successful alliance is found. The probability of the lack of successful alliances is evaluated. A game-theoretical approach for alliance formation is applied.