Assume we have three neighbors Akente, Katerina, and Denise who share a pond. The pond is polluted. There is a filter that could be installed that would clean up the lake. The cost of the filter is equal to $9,000. We are looking at two ways that the filter can be provided. First, the three people can negotiate amongst themselves and come up with an arrangement to pay for the filter. Second, government can have the three people vote on whether or not the filter should be installed. If the vote passes by a majority then each person will pay 1/3^rd of the cost of installing the filter.

Assume that Akente attaches a value of $3,500 to the filter; Katerina attaches a value of $3,200 to the filter; and Denise attaches a value of $1,200 to the filter?

1. Should the filter be installed? Explain.
2. Assume government will let each person vote on whether or not the filter should be installed.If at least two of the three vote yes then government will buy the filter, install it, and charge everyone 1/3^rd of the total cost of the filter. How many people will vote yes? Explain your reasoning.