A Nuclear Dilemma

It has been proposed by Kaiser-Hill, the private company hired to operate and cleanup the Rocky Flats Environmental Technology Site, that some of the waste products from the former nuclear weapons plant will be stored in an underground facility to be built in Boulder County. The possible location of this facility (which, based on a number of criteria was reduced to Boulder, Erie, Lyons, and Louisville) was recently voted on by the residents of Boulder County in an unofficial survey. The results of the voters' rank-ordered choices are as follows:

Location Preference Number of Votes
Boulder, Louisville, Erie, Lyons 960
Erie, Louisville, Boulder, Lyons 150
Lyons, Erie, Louisville, Boulder 62,000
Lyons, Erie, Boulder, Louisville 12,000
Louisville, Lyons, Boulder, Erie 620

 

  1. (a) Based on these results, where should the facility be built? Please justify your reasoning. You may want to consult the attached demographic data to inform your decision.

    (b) Use Arrow's Criteria to examine the fairness of the results of this survey and the method you used to arrive at your decision (you may have to make assumptions about the people participating in this survey).

    (c) Based on the results of this survey, speculate on what the results of a similar survey would be if the survey employed an approval voting structure (assume that the same people participate in this approval voting).

     

  2. If the election were restricted to each of the mayors of the cities (towns) in Boulder County having a vote (or number of votes), how would you design a fair voting system (in your examination of the fairness of your system, be sure to address winning coalitions, power, dictators, and dummies)? Refer to the attached demographic data to support your system.

The Discrete Mathematics Project