Consider a block meeting called after a number of fires have occurred: some with tragic consequences. The last fire consumed three houses because the local hydrant was broken. The neighbors on U Street North East, a relatively long dead-end street bordering a park (see the map in Figure 10), are upset. The street has no hydrant. They are meeting to decide what to do about it. Lobbying the town government regarding the placing of a fire hydrant on the street seems to be winning the day when Tim (who lives about halfway down the long block, at number 10) wonders where they will ask the government to place the hydrant. He also proposes that in front of his house would be as good a place as any. An argument breaks out, as each resident sees an advantage in having the hydrant as near as possible to their house. Where will it be placed?

Understanding how to analyze such a problem will help us figure out the effect of voting rules on the outcomes of group choice.

The above example has some properties that we can sum up. We will relate the geometry of the situation to individual preferences. This will often give us leverage on predicting outcomes.