Majority decision making and the Graph Model for Conflict Resolution

Majority decision rule in group decision making situations is analyzed within the framework of the Graph Model for Conflict Resolution (GMCR). A group decision making situation and majority decision rule are modeled in a mathematical framework for the analysis of committees with permissible ranges of decision makers (DMs), and stability and unstability of the states in a group decision making situation with majority decision rule are analyzed within the framework of the GMCR. In the analysis, two types of DMs´ preferences toward `no decision,´ that is, the state where nothing is decided in the group decision making situation, are distinguished. Main results are as follows: i) when DMs prefer `no decision´ to the least preferable alternatives, all of twelve possible majority decision are so unstable that they do not satisfy general metarationality. ii) when DMs prefer the least preferable alternatives to `no decision,´ six out of the twelve majority decisions are coalition Nash stable, other three majority decisions are not coalition Nash stable but Nash and sequentially stable, and the other three majority decisions are not sequentially stable but general metarational.