In the coalition CDE it is obvious that party D is redundant, but Axelrod states that it is necessary to make the coalition connected.

6) Policy-viable coalitions:

The focus of this theory is only on policy preferences, assuming that parties do not care about holding office. In this case power resides in the legislature rather than the cabinet. The most important party in the legislature is the “core” party because it is the median member of the parliament. It can actually dictate policy since the parties on its neither side have the majority to enact a policy against its will. A policy-viable coalition is one that cannot be defeated by those in the legislature who prefer different policies. If parties care only about policy, no majority can rationally agree to shift the policy position away from that of the median party. Therefore the “core” party can prevail even if it controls much less than a parliamentary majority and it should always be in the governing coalition. The problem with the theories explained above is that they always predict a minimal winning coalition of a different kind. Only Axelrod’s coalitions may be larger. This is based on majoritarian assumptions and is in conflict with all the minority and oversized cabinets in parliamentary democracies. Michael Laver and Norman Schofield classify 196 cabinets formed when there is no a majority party in the parliament in twelve European multiparty democracies from 1945 to 1987. Only 77 of them were minimal winning, 46 were oversized and 73 were minority cabinets. How can this be explained?

Incentives for formation of minority cabinets:

Minority governments are generally less stable and less effective than majority cabinets, but still are quite common in well-functioning democracies such as Denmark, Norway, Sweden, (alternating with single-party majority governments) as well as in Canada and Ireland, which were influenced by British parliamentary tradition and also in France, Italy and Spain. 1. Strom reasons that even if it is correct to assume that parties aim at holding power positions it does not mean that they would want to enter cabinets at all times. Sometimes it might be electorally advantageous for them to leave the government responsibility in the hands of the others. Thus they would remain with the possibility to acquire power position in the future. If many powers expect electoral gains from not participating in the cabinet, this creates a high probability that minority cabinets will be formed.
2. Several institutional features may favor the formation of a minority cabinet. An example is if a new cabinet can take office without the need for a parliamentary vote formally electing or approving it.