EXAMPLE 19 Minimal Winning Coalitions in the Four-Shareholder Corporation
Example 6 (page 470) was about the Shapley-Shubik index of the corporation with four shareholders, . it uses the voting system , and Table 11.7 lists the winning coalitions and their extra votes.
The minimal winning coalitions are those in which each voter is a critical voter: ,, and . These minimal winning coalitions are displayed in Figure 11.1.
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Table 11.11: TABLE 11.7 Winning Coalitions in the Four-Shareholder Corporation
| Winning Coalition | Extra Votes | Critical Voters |
|---|---|---|
| Grand coalition | 49 | None |
| 46 | ||
| 48 | A | |
| 47 | ||
| 0 | ||
| 1 | ||
| 0 |
Figure 11.1: Figure 11.1 Each oval surrounds a minimal winning coalition for the four-shareholder corporation.