Suppose there are a set of n precincts P1 . . . Pn with m voters in each precinct. Each voter supports one of two possible political parties. (In this country, only 2 political parties exist). We are required to carve the precincts into two electoral districts which each have exactly n/2 precincts. We know exactly how many voters in each precinct support each party. The goal is to strategically assign the precincts to the two districts. Describe an algorithm which determines whether it is possible to define the two districts in such a way that the same political party holds the majority in both districts. Assume n is even. Example: Consider n = 4, with the voters distributed as in the table. In this case. By grouping precincts 1 and 3 into a district and precincts 2 and 4 into a district, the Repulsive party will have a majority in both districts. Though, by total count, the Repulsive party only has a tiny advantage over the Demonic party (205 to 195).
Suppose there are a set of n precincts P1 . . . Pn with m voters in each precinct. Each voter supports
one of two possible political parties. (In this country, only 2 political parties exist).
We are required to carve the precincts into two electoral districts which each have exactly n/2 precincts.
We know exactly how many voters in each precinct support each party. The goal is to strategically
assign the precincts to the two districts.
Describe an
such a way that the same political party holds the majority in both districts. Assume n is even.
Example: Consider n = 4, with the voters distributed as in the table.
In this case. By grouping precincts 1 and 3 into a district and precincts 2 and 4 into a district, the
Repulsive party will have a majority in both districts. Though, by total count, the Repulsive party only
has a tiny advantage over the Demonic party (205 to 195).
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