The general problem: what is the least fraction of the national popular vote with which a presidential candidate may win the Electoral College? Complications like unfaithful or defecting electors, the partisan influence of election officials, and intervention by the Supremes are not considered here. We just look at the worst possibilities of Electoral College math, assuming only two candidates and the state voting populations in the 2000 election.
The general question of 'How skewed...' is probably NP-complete, but it might submit to solution(s) using the Metropolis algorithm or the like.
Exhausting the possibilities of state election outcomes would have taken about 3 years on the author's 450 MHz machine. But we fragmented the problem and three contributors completed it using five machines in one year, less three weeks. [From 24 July 2004 to 3 July 2005.]
Many Gore voters in 2000 felt that their votes were somehow diminished. Not entirely disenfranchised, like some who went to the polls in Florida and found that their names had been purged from the voter registration lists, but just a little bit disenfranchised. I have tried to quantify this feeling by computing the relative worth of a Gore vote so as to make a tie of the popular vote. In Case 1 (the actual outcome) a Gore vote was worth 98.93% of a Bush vote. This fractional vote measure captures the idea of 'skew' in the Electoral College/winner-take-all process so well that I carried it into the extreme cases.
The 'skew' reported below is the margin by which the Electoral College winner loses the national popular vote.
Final conclusion: 22.1110% of the voting population might have properly elected a US president who lost the national popular vote by 56,590,057. (See Case 6 below.)
We computed every possible outcome of the states' popular votes which could produce the worst national skew. There are 2.2+ quadrillion possibilities, and we divided this outcome space into 2252 work units, each of one trillion possible worst-skew outcomes. Each work unit is called an ESP block. [ESP is the abbreviation for Electoral Skew Project.]
Project status: 100.0% of the 2252 ESP blocks [work units] have been completed by 3 contributors (a/o 3 July 2005).
How skewed can a US presidential election get?
In all the cases below Mr. Bush wins the electoral vote
but loses the popular vote. [Nader votes are not
considered here; they would just make it worse anyway.]
Case 1 - Actual result in 2000
Bush: 50456002 (271): one voter, one vote - 49.7320% of voters, States: 30
Gore: 50999897 (267): one voter, 0.9893 vote
Skew: 543895 Total votes: 101455899
Bush states: WY SD ND MT AK NH NV ID WV UT NE AR KS MS SC OK KY CO AZ LA AL TN MO IN VA GA NC OH FL TX
Case 2 - Gore gets all votes in states he won in 2000.
Bush: 27773625 (271): one voter, one vote - 27.3751% of voters, States: 30
Gore: 73682274 (267): one voter, 0.3769 vote
Skew: 45908649 Total votes: 101455899
Bush states: WY SD ND MT AK NH NV ID WV UT NE AR KS MS SC OK KY CO AZ LA AL TN MO IN VA GA NC OH FL TX
Case 3 - Gore gets all votes in states he won in 2000
- and excess Bush votes in states Gore lost.
Bush: 24805910 (271): one voter, one vote - 24.4499% of voters, States: 30
Gore: 76649989 (267): one voter, 0.3236 vote
Skew: 51844079 Total votes: 101455899
Bush states: WY SD ND MT AK NH NV ID WV UT NE AR KS MS SC OK KY CO AZ LA AL TN MO IN VA GA NC OH FL TX
Case 4 - Bush gets bare plurality in smallest electoral states
- Gore gets all other popular votes
Bush: 24229729 (281): one voter, one vote - 23.8820% of voters, States: 41
Gore: 77226170 (257): one voter, 0.3138 vote
Skew: 52996441 Total votes: 101455899
Bush states: WY VT SD ND MT DC DE AK RI NH NV ME ID HI WV UT NM NE AR KS OR MS IA SC OK KY CT CO AZ LA AL MN MD WI WA TN MO MA IN VA GA
Case 4a - Bush gets bare plurality in smallest plurality states
- Gore gets all other popular votes
Bush: 24229729 (281): one voter, one vote - 23.8820% of voters, States: 41
Gore: 77226170 (257): one voter, 0.3138 vote
Skew: 52996441 Total votes: 101455899
Bush states: WY VT SD ND MT DC DE AK RI NH NV ME ID HI WV UT NM NE AR KS OR MS IA SC OK KY CT CO AZ LA AL MN MD WI WA TN MO MA IN VA GA
Case 5 - Bush gets bare plurality in largest electoral states
- Gore gets all other popular votes
Bush: 27766235 (270): one voter, one vote - 27.3678% of voters, States: 11
Gore: 73689664 (268): one voter, 0.3768 vote
Skew: 45923429 Total votes: 101455899
Bush states: CA NY TX FL PA IL OH MI NJ NC GA
Case 6 - The worst skew found - [by Contributor 146]
- Bush gets bare plurality in his states
- Gore gets all other popular votes
Bush: 22432921 (270): one voter, one vote - 22.1110% of voters, States: 34
Gore: 79022978 (268): one voter, 0.2839 vote
Skew: 56590057 Total votes: 101455899
(Outcome number: 1,407,690,025,730,047)
Bush states: WY VT SD ND MT DC DE AK RI NH NV ME ID HI WV UT NM NE AR KS MS IA SC OK KY CT CO AZ AL MD TN IN TX CA