superprismatic Posted May 17, 2011 Report Share Posted May 17, 2011 We get rid of the condition that all voters must vote, which was in the Electoral College Puzzle, to make this new puzzle. Everything else is the same. In this new version you can assume as few or as many votes as you like in any state, up to its population. How does this change the answer? I restate the problem with this new change in bold: We all know that it is possible for a presidential candidate to win the U.S. presidency with fewer voters voting for him than for his opponents. That's what this puzzle is all about. In case you need a refresher, here's how the process works: Each state (as well as Washington D.C.) has a number of electoral votes (EVs). The candidate with the most votes in that state (or D.C.) gets all of its electoral votes1. The candidate who gets at least 270 EVs wins. Assuming this process, that the number of voters in each state is its entire population, and that not all voters need to actually vote, what is the fewest number of voters which a winning candidate can have voting for him? 1Footnote: Two states, Nevada and Maine, can split their votes amongst the candidates. For the purpose of this puzzle, assume that they can't. Assume the numbers, below, which will be used for the 2012 election: STATE EV POPULATION ----------------------------- California 55 37253956 Texas 38 25145561 New York 29 19378102 Florida 29 18801310 Illinois 20 12830632 Pennsylvania 20 12702379 Ohio 18 11536504 Michigan 16 9883640 Georgia 16 9687653 North Carolina 15 9535483 New Jersey 14 8791894 Virginia 13 8001024 Washington 12 6724540 Massachusetts 11 6547629 Indiana 11 6483802 Arizona 11 6392017 Tennessee 11 6346105 Missouri 10 5988927 Maryland 10 5773552 Wisconsin 10 5686986 Minnesota 10 5303925 Colorado 9 5029196 Alabama 9 4779736 South Carolina 9 4625364 Louisiana 8 4533372 Kentucky 8 4339367 Oregon 7 3831074 Oklahoma 7 3751351 Connecticut 7 3574097 Iowa 6 3046355 Mississippi 6 2967297 Arkansas 6 2915918 Kansas 6 2853118 Utah 6 2763885 Nevada 6 2700551 New Mexico 5 2059179 West Virginia 5 1852994 Nebraska 5 1826341 Idaho 4 1567582 Hawaii 4 1360301 Maine 4 1328361 New Hampshire 4 1316470 Rhode Island 4 1052567 Montana 3 989415 Delaware 3 900877 South Dakota 3 814180 Alaska 3 710231 North Dakota 3 672591 Vermont 3 625741 Washington D.C. 3 601723 Wyoming 3 563626 ----------------------------- 50 States+D.C. 538 308748481 [/code] Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 17, 2011 Report Share Posted May 17, 2011 11 If he carries California 55 Texas 38 New York 29 Florida 29 Illinois 20 Pennsylvania 20 Ohio 18 Michigan 16 Georgia 16 North Carolina 15 New Jersey 14 by 1-0 and if he gets 0 votes from all other states Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 17, 2011 Report Share Posted May 17, 2011 Only 11, the 11 states with the most EVs as then the other candidate can get every single other vote. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 17, 2011 Report Share Posted May 17, 2011 11 If he carries California 55 Texas 38 New York 29 Florida 29 Illinois 20 Pennsylvania 20 Ohio 18 Michigan 16 Georgia 16 North Carolina 15 New Jersey 14 by 1-0 and if he gets 0 votes from all other states or she... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 17, 2011 Report Share Posted May 17, 2011 (edited) In the worst case scenario where only 1 person votes (for Candidate A) from each of the 11 High-EV states and everyone votes (for Candidate B) in each of the remaining 40 Low-EV states (plus D.C.), we have: 11 / 133201378 = .000008% of the voting population choosing the winner. Edited May 17, 2011 by JDave Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 17, 2011 Report Share Posted May 17, 2011 So, interesting twist on this one, what is the most number of votes one could lose by and still win the election. Simplest case is take the solution given with 11 states being required and assume everyone in the other states votes for the other guy but that isn't optimial. What is? and can you prove it? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 17, 2011 Report Share Posted May 17, 2011 (edited) So, interesting twist on this one, what is the most number of votes one could lose by and still win the election. Simplest case is take the solution given with 11 states being required and assume everyone in the other states votes for the other guy but that isn't optimial. What is? and can you prove it? I don't get what you're asking for... nm, I get it. Hmm, I'll think about this one a bit. Edited May 17, 2011 by maurice Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 17, 2011 Report Share Posted May 17, 2011 Correction to the footnote: The two states are NEBRASKA and Maine that have legislated a difference to the 'winner-take-all' Electoral votes. Let's not forget that at least 270 votes (the Electoral College majority) need be won. ...what is the fewest number of voters which a winning candidate can have voting for him? The minimum number of Popular votes won can be... 0, with 270 as the minimum number of Electoral College votes. In most States, if not all States, the Electors in the Electoral College may be appointed by their State Legislature. Of the several possible cases where this can occur, one would be where no voter in the general populace of the State cast a vote for a valid Candidate in the Presidential Election. Thus, a Presidential Candidate need not get any of the popular votes. Basically, the only requirement would be for the Candidate to receive a majority of the votes of the Electoral College. As the majority of Electors in this problem is set at 270, the minimum number of votes the Presidential Candidate needs to win is 270 Electoral votes and 0 Popular votes. Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted May 17, 2011 Author Report Share Posted May 17, 2011 (edited) Correction to the footnote: The two states are NEBRASKA and Maine that have legislated a difference to the 'winner-take-all' Electoral votes. Let's not forget that at least 270 votes (the Electoral College majority) need be won. The minimum number of Popular votes won can be... 0, with 270 as the minimum number of Electoral College votes. In most States, if not all States, the Electors in the Electoral College may be appointed by their State Legislature. Of the several possible cases where this can occur, one would be where no voter in the general populace of the State cast a vote for a valid Candidate in the Presidential Election. Thus, a Presidential Candidate need not get any of the popular votes. Basically, the only requirement would be for the Candidate to receive a majority of the votes of the Electoral College. As the majority of Electors in this problem is set at 270, the minimum number of votes the Presidential Candidate needs to win is 270 Electoral votes and 0 Popular votes. Thanks for the NEBRASKA correction (I got the N right!). The US constitution gives the state legislatures the power to appoint electors. As such, they may not voluntarily give up this constitutional power. However, all state legislatures have decided to go with their constituents votes as far as electors are concerned. But they can change their minds at any time, even after the popular election -- Florida was about to do this in 2000 when the Supreme Court ruling made this moot. As far as the OP is concerned, I said "Assuming this process...." which referred to the popular vote to choose electors. Edited May 17, 2011 by superprismatic Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 18, 2011 Report Share Posted May 18, 2011 Thanks for the NEBRASKA correction (I got the N right!). The US constitution gives the state legislatures the power to appoint electors. As such, they may not voluntarily give up this constitutional power. However, all state legislatures have decided to go with their constituents votes as far as electors are concerned. But they can change their minds at any time, even after the popular election -- Florida was about to do this in 2000 when the Supreme Court ruling made this moot. As far as the OP is concerned, I said "Assuming this process...." which referred to the popular vote to choose electors. If, for some reason, the Electoral College does not cast any ballots, the U.S. House of Representatives elects the President. The minimum number of Representatives voting for the President-elect would need be 26. Thus, 0 Popular votes, 0 Electoral votes and 26 Representative votes for the low number of 26 votes. If the House deadlocks, the Vice-President, elected in this case by the Senate, becomes the Acting President. If both House and Senate deadlock, the Speaker of the House becomes the Acting President. 0 Popular votes, 0 Electoral votes, 0 Representative votes, 0 Senate votes = 0 votes (an absolute minimum). If the President-Elect is elected by means of the Popular vote, this would be 11 [as others have indicated in earlier posts] plus the 270 votes required by the Electoral College for a total of 281 minimum votes.. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 24, 2011 Report Share Posted August 24, 2011 (edited) So, interesting twist on this one, what is the most number of votes one could lose by and still win the election. Simplest case is take the solution given with 11 states being required and assume everyone in the other states votes for the other guy but that isn't optimial. What is? and can you prove it? I can't prove it but I get - 174,012,615 votes lose CA, TX, NY, FL, IL, PA, OH, MI, GA, MI, NJ, and VA all at 0 votes to the total population. win all the other states 1-0. 270 electoral votes Edited August 24, 2011 by smoth333 Quote Link to comment Share on other sites More sharing options...
Question
superprismatic
We get rid of the condition that all
voters must vote, which was in the
Electoral College Puzzle, to
make this new puzzle. Everything else
is the same. In this new version you
can assume as few or as many votes
as you like in any state, up to its
population. How does this change the
answer?
I restate the problem with this new
change in bold:
We all know that it is possible for a
presidential candidate to win the U.S.
presidency with fewer voters voting
for him than for his opponents.
That's what this puzzle is all about.
In case you need a refresher, here's
how the process works: Each state
(as well as Washington D.C.) has a
number of electoral votes (EVs).
The candidate with the most votes in
that state (or D.C.) gets all of its
electoral votes1. The candidate who
gets at least 270 EVs wins.
Assuming this process, that the
number of voters in each state is
its entire population, and that not
all voters need to actually vote,
what is the fewest number of voters
which a winning candidate can have
voting for him?
1Footnote: Two states, Nevada and
Maine, can split their votes amongst
the candidates. For the purpose of
this puzzle, assume that they can't.
Assume the numbers, below, which
will be used for the 2012 election:
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