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.