EXAMPLE 5 Sharing Diamonds by the Hamilton Method

In Table 14.1 (page 572), we saw that Winnie’s, Louise’s, and Tim’s quotas for the 100 diamonds were 78.26, 17.39, and 4.35, respectively. We will round these quotas so that they sum to 100. To start, we apportion diamonds to Winnie, diamonds to Louise, and diamonds to Tim. This leaves one diamond, which must go to Louise because her fraction, 0.39, is the largest. The final apportionment is 78 diamonds for Winnie, 18 diamonds for Louise, and 4 diamonds for Tim. Winnie will want to veto this apportionment.