Question 11.65
35. A corporation has four shareholders and a total of 100 shares. The quota for passing a measure is the votes of shareholders owning 51 or more shares. The number of shares owned by each shareholder is as follows:
| Shareholder | Shares Owned |
|---|---|
| 40 | |
| 26 | |
| 24 | |
| 10 |
There is also an investor, , who is interested in buying shares but does not own any shares at present. Sales of fractional shares are not permitted.
- List the winning coalitions and compute the number of extra votes for each. Make a separate list of the losing coalitions, and compute the number of votes that would be needed to make the coalition winning.
- How many shares can sell to without causing any of the winning coalitions listed in part (a) to lose or any of the losing coalitions in part (a) to win?
- How many shares can sell to without changing the sets of winning or losing coalitions?
- How many shares can sell to without changing the winning coalitions? Because is now a dummy, he must remain a dummy after the trade.
35.
(a) In the following table, all coalitions that include are omitted.
| Winning Coalition | Extra Votes | Losing Coalition | Vote Deficit |
| 15 | 51 | ||
| 13 | 11 | ||
| 39 | 25 | ||
| 25 | 27 | ||
| 49 | 41 | ||
| 23 | 1 | ||
| 9 | 1 | ||
| 15 | |||
| 17 |
(b) can sell zero shares, because if gains just one share, the losing coalition will become a winning coalition.
(c) can sell 13 shares. All winning coalitions that include have enough votes to support that, and the losing coalitions that include would still be losing after the sale. ( is one share short of meeting the quota, but any transfer of shares between and would not affect its total.)
(d) can sell zero shares. If had just one share, the losing coalition would become a winning coalition.