Becoming President with 22% of the Votes

Political pundits talk about the possibility of winning the Presidential election with less votes than your opponent. Assuming only two candidates what is the lowest percentage of votes you could get and still win the election? In the case where everyone votes this becomes an interesting question. In America some states have a higher ratio of people to electoral college votes than others. If the ones that are preferentially treated banded together a small percentage of people could decide the election.

In my last post I created a program to work out in an overly complicated way what was the least amount of land a president could be elected from in the US. In this post I want to figure out the best states to win to get you 270+ electoral college seats using the smallest number of voters.

I got the estimated population in July 2011 from the census website here. Using this data in the glpk program below and got the result shown in this map. If everyone voted and the people who get the most power in votes all voted one way then the states on the winning side would have 135936335 voters to get 270 electoral college seats. The total population is 311591917 so 43.67% of the population

The winner would win 40 districts of the 51 states+dc and lose Virginia, Georgia, New Jersey, Michigan, Ohio, Illinois, Pennsylvania, Florida, New York, Texas, California.*

Now if the candidate in these states just squeaked a win by one vote and got zero votes in all the other states that means in a two party election you could win an election, where everyone voted, with under 22% of the vote. If you think of this happening in a senate election where each state has 2 senators (and DC none) then you could control 80% of the senate with under 22% of the vote.

There are all sorts of other questions similar to this. What is the smallest block where all the states touch? What is the shortest distance between all her state capitals a winner could have? I think some analysis that included Senate and Congress seats could be interesting. If you have any ideas please comment. * Thanks to Hakan Kjellerstrand who pointed out here I had read the solution file wrong and North Carolina was not present.

/* sets */
set STATES;
set NEED;

/* parameters */
param VotesTable {i in STATES, j in NEED};
param Pop {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} Pop[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 Pop:=
Alabama 4802740
Alaska 722718
Arizona 6482505
Arkansas 2937979
California 37691912
Colorado 5116796
Connecticut 3580709
Delaware 907135
"District of Columbia" 617996
Florida 19057542
Georgia 9815210
Hawaii 1374810
Idaho 1584985
Illinois 12869257
Indiana 6516922
Iowa 3062309
Kansas 2871238
Kentucky 4369356
Louisiana 4574836
Maine 1328188
Maryland 5828289
Massachusetts 6587536
Michigan 9876187
Minnesota 5344861
Mississippi 2978512
Missouri 6010688
Montana 998199
Nebraska 1842641
Nevada 2723322
"New Hampshire" 1318194
"New Jersey" 8821155
"New Mexico" 2082224
"New York" 19465197
"North Carolina" 9656401
"North Dakota" 683932
Ohio 11544951
Oklahoma 3791508
Oregon 3871859
Pennsylvania 12742886
"Rhode Island" 1051302
"South Carolina" 4679230
"South Dakota" 824082
Tennessee 6403353
Texas 25674681
Utah 2817222
Vermont 626431
Virginia 8096604
Washington 6830038
"West Virginia" 1855364
Wisconsin 5711767
Wyoming 568158;

param Need:=
Votes        270;

end;