Problem of the Week: Pacifican Suffrage
In the U.S., the Electoral College is used in presidential elections. Each state is awarded a number of electors equal to the number of representatives (based on population) and senators (2 per state) they have in congress. Since most states award the winner of the popular vote in their state all their state’s electoral votes, the Electoral College acts as a weighted voting system. To explore how the Electoral College works, we'll look at a fictional country "Pacifica" with 4 states: California, British Columbia, Washington, and Oregon. Here is the outcome of a hypothetical election: $$ \begin{array}{r|cccc} \mbox{} & \mbox{California} & \mbox{Washington} & \mbox{British Columbia} & \mbox{Oregon}\\ \hline \mbox{Population (in Millions)} & 39.56 & 7.536 & 4.992 & 4.191\\ \mbox{% Popular Vote for Candidate A} & 60\% & 20\% & 30\% & 20\%\\ \mbox{% Popular Vote for Candidate B} & 40\% & 80\% & 70\% & 80\%\\ \end{array} $$ (a) Suppose the Pacifican House of Representatives has 100 seats to be apportioned out to each state/province. Like the United States, Pacifica also uses the Huntington-Hill method. Use the Huntington-Hill Method to apportion these seats.(b) Like the Electoral College in the U.S., the Pacifican Electoral College has a "winner-take-all" system. In other words, all of a state's/province's electoral votes go the the winner in that state/province. The effect of this is that the Electoral College acts as a weighted voting system. The candidate which receives the majority of electoral votes wins the election. The number of electoral votes a state/province has is its number of seats in the House of Representatives (see part (a)) plus two more for each senator. With the above information, write the Pacifican Electoral College as a weighted voting system of the form $$[q:w_1,w_2,w_3,w_4].$$ (c) Which candidate won the Electoral College vote?
(d) Which candidate won the popular vote?
(e) Calculate the Banzhaf Power Distribution of the weighted voting system you determined in part (c) and compare it to your answers for parts (c) and (d).