[superprismatic]

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 all

voters 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]

[Guest]

I can't do it right now, but...

divide the electoral votes of each state by the population of that state.

If the ratio is high compared to ratios of other states, add half of that state's population (rounded up) to the number of votes the candidate needs. repeat until the candidate has 270 electoral votes.

note: at the very end it is important to notice that putting the number of electoral votes over 270 is wasteful and that should affect which states you choose.

If I get a chance, I'll do it later.

I like the problem, btw. interesting both mathematically and practically.

Edited May 16, 2011 by magician

[k-man]

The candidate will need to receive a total of 67367941 votes. He/she will need to get the majority of votes in the following states:

State		Votes needed

Wyoming        	281814

Washington D.C.	300862

Vermont        	312871

North Dakota   	336296

Alaska         	355116

Rhode Island   	526284

South Dakota   	407091

Delaware       	450439

New Hampshire  	658236

Montana        	494708

Maine          	664181

Hawaii         	680151

Nebraska       	913171

West Virginia  	926498

Idaho          	783792

New Mexico     	1029590

Nevada         	1350276

Utah           	1381943

Kansas         	1426560

Arkansas       	1457960

Mississippi    	1483649

Iowa           	1523178

Connecticut    	1787049

South Carolina 	2312683

Minnesota      	2651963

Alabama        	2389869

Oklahoma       	1875676

Kentucky       	2169684

Oregon         	1915538

Colorado       	2514599

Washington     	3362271

Louisiana      	2266687

Wisconsin      	2843494

Tennessee      	3173053

Maryland       	2886777

Arizona        	3196009

Indiana        	3241902

Massachusetts  	3273815

Missouri       	2994464

North Carolina 	4767742

[superprismatic]

The candidate will need to receive a total of 67367941 votes. He/she will need to get the majority of votes in the following states:

Wyoming         281814
Washington D.C. 300862
Vermont         312871
North Dakota    336296
Alaska          355116
Rhode Island    526284
South Dakota    407091
Delaware        450439
New Hampshire   658236
Montana         494708
Maine           664181
Hawaii          680151
Nebraska        913171
West Virginia   926498
Idaho           783792
New Mexico      1029590
Nevada          1350276
Utah            1381943
Kansas          1426560
Arkansas        1457960
Mississippi     1483649
Iowa            1523178
Connecticut     1787049
South Carolina  2312683
Minnesota       2651963
Alabama         2389869
Oklahoma        1875676
Kentucky        2169684
Oregon          1915538
Colorado        2514599
Washington      3362271
Louisiana       2266687
Wisconsin       2843494
Tennessee       3173053
Maryland        2886777
Arizona         3196009
Indiana         3241902
Massachusetts   3273815
Missouri        2994464
North Carolina  4767742

State		Votes needed

But that's only 21.8% of the votes! If I were the only other candidate, I'd be hopping mad! I'd have lost even though I got 78.2% of the vote! Methinks there's something amiss here!

[Guest]

You win with 271 ev and total votes of 67,444,026

The states are every state with fewer than 13 ev, and also Georgia. I did not see any combo that could give exactly 270 without increasing the number of votes. I determined this by first determining the number of voters to win a state as 50% plus 1 or plus 1/2, whichever put it over 50%. I then divided that by the ev to determine voters per ev and sorted that from fewest to highest, and then added all the ev to get to 270 or higher. It took 40 states, and left out all the high ev states which also have high voter to ev ratios.

Looking at K-Man I see I should have switched NC in for GA. So close!

This is based on there only being 2 candidates. In reality there are more than 2 candidates and so a state often is won with less than 50% of the votes. With no indication of just how low we can go with the % to win a state, I assumed over 50% to win a state.

Super, welcome to the ev system. You are right, you could lose even with 78% of the votes.

Edited May 17, 2011 by Nana7

[Auramyna]

That's the same way I would have figured it out.

Re- inequality in Population/EV, It goes from 677344/EV for California to 187875/EV for Wyoming. (3.6 times less influence for each Californian.) And the average for the whole country is 573881. So the lower pop states are getting a lot more influence than the larger ones.

Then let's just say, for arguments sake, that Wyoming had a low turnout on voting day, each voter is influencing an even larger fraction of each Electoral Vote.

Any system where someone can lose even with 78% of the votes, unarguably needs to be looked at and revised a little! And let's remember: if the smaller states have a lower turnout percentage-wise than the larger states, a candidate could win with even less than 22% of the vote! Of course this would only work if the smaller states were voting for the less popular candidate.

There are many political wisecracks I could make here but I don't want to start a debate. So all I will say is I'm glad I live in Australia!

Edited May 17, 2011 by Auramyna

[Guest]

Take the case of a 3 way race that is close in 40 states but not in the other 10. It is possible for person A to win 270 ev with just 14.5% of the total, 44,911,969 votes. Say that person B picks up another 2 million in CA but no votes in any of the other 9 states, to end with 0 ev but 15.1% 46,911,929 which is more than person A. And person C has 268 ev, 70.3% and 216,924,583 votes. So not only does the ev winner not have the most votes, but is actually in third place. It is even possible for persons B and C to have just over 1/3 and 1/2 the total overall vote and both still lose to person A who has less than 1/6 the total.

[Guest]

270

The election for President and Vice President is not a direct election by United States citizens. Citizens vote for electors, representing a state, who are the authorized constitutional participants in a presidential election. In early U.S. history, some state laws delegated the choice of electors to the state legislature. Electors are free to vote for anyone eligible to be President, but in practice pledge to vote for specific candidates and voters cast ballots for favored presidential and vice presidential candidates by voting for correspondingly pledged electors.

Assuming those electors went south of their promise and vote someone else

Very few

As nana has alrdy mentioned, a 3 way fight. eg: Where there are 2 equally good moderate party and 1 radical party, with a population of 6000 moderates and 4000 radical. With the 2 moderate fighting for tat 6000 votes(3000 3000), the radical can safely win the election with his minority votes. translate this throughout the country, and we will have a new president whom most of us didnt vote for. And if you extrapolate the trend to infinity moderate parties, all equally good, then we might really have the 1st president to be voted in by 0.00001%

[superprismatic]

Nice, quick work, guys. Especially to magician who got the technique and k-man who was the first to get the correct answer.

[fabpig]

What surprises me is the huge discrepancy in the population per EV over the states. We have a similar "first past the post" system - but we vote for a party rather than an individual - with each of our "constituencies" sending 1 member to parliament: there are (apprx) 650 MPs so each constituency has about 100,000 poplulation. Every so often ,there is a review of the constituency populations, and if needs be the constituency boundaries are altered to give a fairer representation (doesn't happen very often).

As we're more of a 3 party state than US, the 3rd party (Liberal Democrats) have been complaining for the last umpteen years that the number of MPs that they send to London does not reflect the number of votes that they receive nationwide, and that some sort of Proportional Representation would be fairer. SO.......the last election gave no party overall majority, and so the Lib Dems formed a coalition with the Tory party with the proviso that there be a referendum on electoral reform. We've just had that referendum and it was rejected out-of-hand by the BrItish public!

I understand that Australia currently use an electoral system similar to the one rejected over here: that it's pretty-well hated countrywide and they want a quick return to first past the post. WombatBreath will be able to tell you more than I can.

Sorry if that's a bit -off-topic, but something I found interesting and hoped you might.

[Guest]

I think it's not a hard puzzle with the following steps:

1. figure out those states with the highest EV to population ratio.

2. among those states, find the best combination to let the candidate just enough to win with the least votes.

Thx for your puzzle. But I'm too lazy to solve it. Pls let me know if my method is not correct