I checked this allocation with the GLPK program below. I used the electoral votes listed here and the state areas listed on wikipedia This gets 270 votes with an area of 1625012km². US states + DC is an area of 9826630km² so 16.54% of the US could win an election.
The states are Delaware, District of Columbia, Hawaii, New Hampshire, Rhode Island, Connecticut, Maryland, Indiana, Massachusetts, Virginia, New Jersey, North Carolina, Ohio, Illinois, Pennsylvania, Florida, New York, California. My map is here
Matthew Yglesias' map is the same so he did find the optimal solution by hand.
/*code to find the least land area to get 270 votes. Run with 'glpsol -m election.mod -o out' */ /* sets */ set STATES; set NEED; /* parameters */ param VotesTable {i in STATES, j in NEED}; param Cost {i in STATES}; param Need {j in NEED}; /* decision variables: x1: alabama, x2: , x3: , x4: x51: Wyoming*/ var x {i in STATES} binary >= 0; /* objective function */ minimize z: sum{i in STATES} Cost[i]*x[i]; /* Constraints */ s.t. const{j in NEED} : sum{i in STATES} VotesTable[i,j]*x[i] >= Need[j]; /* data section */ data; set STATES := Alaska Delaware "District of Columbia" Montana "North Dakota" "South Dakota" Vermont Wyoming Hawaii Idaho Maine "New Hampshire" "Rhode Island" Nebraska Nevada "New Mexico" Utah "West Virginia" Arkansas Kansas Mississippi Connecticut Iowa Oklahoma Oregon Kentucky "South Carolina" Alabama Colorado Louisiana Arizona Maryland Minnesota Wisconsin Indiana Missouri Tennessee Washington Massachusetts Virginia Georgia "New Jersey" "North Carolina" Michigan Ohio Illinois Pennsylvania Florida "New York" Texas California; set NEED := Votes; param VotesTable: Votes:= Alabama 9 Alaska 3 Arizona 11 Arkansas 6 California 55 Colorado 9 Connecticut 7 Delaware 3 "District of Columbia" 3 Florida 29 Georgia 16 Hawaii 4 Idaho 4 Illinois 20 Indiana 11 Iowa 6 Kansas 6 Kentucky 8 Louisiana 8 Maine 4 Maryland 10 Massachusetts 11 Michigan 16 Minnesota 10 Mississippi 6 Missouri 10 Montana 3 Nebraska 5 Nevada 6 "New Hampshire" 4 "New Jersey" 14 "New Mexico" 5 "New York" 29 "North Carolina" 15 "North Dakota" 3 Ohio 18 Oklahoma 7 Oregon 7 Pennsylvania 20 "Rhode Island" 4 "South Carolina" 9 "South Dakota" 3 Tennessee 11 Texas 38 Utah 6 Vermont 3 Virginia 13 Washington 12 "West Virginia" 5 Wisconsin 10 Wyoming 3; param Cost:= Alabama 135765 Alaska 1717854 Arizona 295254 Arkansas 137732 California 423970 Colorado 269601 Connecticut 14357 Delaware 6447 "District of Columbia" 177 Florida 170304 Georgia 153909 Hawaii 28311 Idaho 216446 Illinois 149998 Indiana 94321 Iowa 145743 Kansas 213096 Kentucky 104659 Louisiana 134264 Maine 91646 Maryland 32133 Massachusetts 27336 Michigan 250494 Minnesota 225171 Mississippi 125434 Missouri 180533 Montana 380838 Nebraska 200345 Nevada 286351 "New Hampshire" 24216 "New Jersey" 22588 "New Mexico" 314915 "New York" 141299 "North Carolina" 139389 "North Dakota" 183112 Ohio 116096 Oklahoma 181035 Oregon 254805 Pennsylvania 119283 "Rhode Island" 4002 "South Carolina" 82932 "South Dakota" 199731 Tennessee 109151 Texas 695621 Utah 219887 Vermont 24901 Virginia 110785 Washington 184665 "West Virginia" 62755 Wisconsin 169639 Wyoming 253336; param Need:= Votes 270; end;
2 comments:
Ugh, rucksack problems... They always hurt my head.
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