How many ways can an Electoral College tie happen?

POTUS election season is officially upon us and it has gotten me to wondering something. How many ways are there (if any) to make a perfect tie in the Electoral College, 269-269? How would you write an equation/logorithm for it and how would you figure that out on paper?

It's a great problem and well-known in CS circles: Partition Problem on WikiPedia.
There are several algorithms to do it, especially in this case where the sizes of the inputs (state electoral votes) are bounded.

Quote: MathExtremist

It's a great problem and well-known in CS circles: Partition Problem on WikiPedia.
There are several algorithms to do it, especially in this case where the sizes of the inputs (state electoral votes) are bounded.

I'll check it out. I wonder what the odds of it happpening are if say you eliminate all the red/blue states from toss-up based on say how they have voted since say 1996? (ie: always red or blue since then it cannot be a toss-up.)

Yeah AZ, there are some states you should be able to safely 'eliminate' as they are safely red or blue.

When you find a tie scenario, then the next step is to look at Congress as each state delegation gets one vote. :)

Quote: AZDuffman

POTUS election season is officially upon us and it has gotten me to wondering something. How many ways are there (if any) to make a perfect tie in the Electoral College, 269-269? How would you write an equation/logorithm for it and how would you figure that out on paper?

It's important to remember that the election goes to the house not because of a tie, but because no one wins a majority.

The theoretical number of ways to do it is fairly large, but there is still a fair subset which is possible using only battleground states. However, a third party candidate that wins 2 or 3 states could easily deprive someone of the majority. In that case the Republican candidate should win, given their majority in the House.

I remember in 2008, before Obama got his big surge near the end of the campaign, that I found at least four possibilities for a tie using only battleground states.


Presidential of 1968 when Wallace took 5 states, had Nixon lost some of the northeastern states and Michigan (which he would have lost today), it would have still gone to the House even though he had a large plurality of Humphrey.

Trump could be the spoiler in 2012. He could take 1 or 2 states and throw it into the House.

Quote: AZDuffman

I'll check it out. I wonder what the odds of it happpening are if say you eliminate all the red/blue states from toss-up based on say how they have voted since say 1996? (ie: always red or blue since then it cannot be a toss-up.)

The absolute theoretical possible space has to have millions of possibilities to get you a tie of 269-269. For example, you could theoretically win only 11 states and still have 270 electoral votes. If you switch out NJ for VA then you have a 269-269 tie. There are many combinations of smaller states that add up to 13 votes that you could use to replace VA.

1 , California , 55 , 55
2 , Texas , 38 , 93
3 , Florida , 29 , 122
4 , New York , 29 , 151
5 , Pennsylvania , 20 , 171
6 , Illinois , 20 , 191
7 , Ohio , 18 , 209
8 , Georgia , 16 , 225
9 , Michigan , 16 , 241
10 , North Carolina , 15 , 256
11 , New Jersey , 14 , 270

Virginia , 13


It should be fairly easy at this stage in the election to come up with a dozen tie scenarios while still leaving the core states intact.

Obama only lost two of those 11 states in 2008, Texas and Georgia.

Here is my most likely near tie scenario.

The first assumption is that the states that voted against Obama in 2008 will continue to do so in 2012.
= That won McCain 173 electoral votes, but that would be 180 after the 2010 census if 2nd district in Nebraska goes Republican.
The second assumption is that states where Obama received less than 54.25% of the vote will go Republican.
The only exception is Minnesota, which had 54.06% of the vote for Obama in 2008. I assumed they stay with Obama.

29 Florida
18 Ohio
15 North Carolina
11 Indiana
9 Colorado
6 Iowa
1 Nebraska's 2nd district.

This theoretical election results in a near tie, with the Republicans winning 268.

Quote: pacomartin

Here is my most likely near tie scenario.

The first assumption is that the states that voted against Obama in 2008 will continue to do so in 2012.
= That won McCain 173 electoral votes, but that would be 180 after the 2010 census if 2nd district in Nebraska goes Republican.
The second assumption is that states where Obama received less than 54.25% of the vote will go Republican.
The only exception is Minnesota, which had 54.06% of the vote for Obama in 2008. I assumed they stay with Obama.

29 Florida
18 Ohio
15 North Carolina
11 Indiana
9 Colorado
6 Iowa
1 Nebraska's 2nd district.

This theoretical election results in a near tie, with the Republicans winning 268.

IMO, there are a couple of other ways likelier than the NE split again. AZD, you can easily play around at 270towin.com

There's also a lot of legal questioning about whether or not the NEW House or the OLD House would vote (as states' delegations, each getting 1 vote) in the event of no electoral majority. I always thought it was the old (pre-election) House, but some have challenged me and said that only the electoral votes are counted before Christmas, and there is no set time for the House to take their vote, and it might not be immediately. Since the new House is sworn in very quickly after the New Year, it would be very interesting.

Also, I think you are close to Romney's path to victory, but I'd replace the Western States with VA and NH, which would give him 270 without the NE-split, and give us the 269-269 tie with it:

Romney wins with McCain PLUS FL/OH/NC/VA/IN/NH (and the extra NE vote). A very reasonable path to victory (all but NH were won by Bush 43 twice) that I'm sure is part of his strategy.

Personally I think Romney has a better chance of stealing a vote in Maine than Obama does in winning a vote in Nebraska again, but both would make ties even more plausible.

Quote: cclub79

Romney wins with McCain PLUS FL/OH/NC/VA/IN/NH (and the extra NE vote). A very reasonable path to victory (all but NH were won by Bush 43 twice) that I'm sure is part of his strategy.

The LA Times listed their choice (based on Gallup Poll) for the 12 battleground states. What is interesting about this list of 12 is it includes Arizona and Georgia which were lost by Obama in 2008. I personally find it hard to believe that Obama will win states in 2012 that he lost in 2008.

I am also surprised that Indiana, New Hampshire and Minnesota are not on the list.

Quote: LA Times

Obama's Gallup numbers show 12 states in play in 2012

The battlegrounds, which also appear on lists drawn up by strategists in both parties, are

three perennial swing states,
Florida (29), Ohio (18) and Pennsylvania (20);

Iowa (6);

three in the South,
Virginia (13), North Carolina (15) and Georgia (16);

and five states in the West, Oregon (7) plus a grouping in the interior West made up of
Nevada (6), Arizona (11), New Mexico (5) and Colorado (9).
For those states, Obama would have to depend on a large Latino turnout.

The Southern states would require a heavy turnout among blacks plus support from moderate-to-liberal suburban whites.

Quote: pacomartin

The LA Times listed their choice (based on Gallup Poll) for the 12 battleground states. What is interesting about this list of 12 is it includes Arizona and Georgia which were lost by Obama in 2008. I personally find it hard to believe that Obama will win states in 2012 that he lost in 2008.

I am also surprised that Indiana, New Hampshire and Minnesota are not on the list.

Quote: LA Times

Obama's Gallup numbers show 12 states in play in 2012

The battlegrounds, which also appear on lists drawn up by strategists in both parties, are

three perennial swing states,
Florida (29), Ohio (18) and Pennsylvania (20);

Iowa (6);

three in the South,
Virginia (13), North Carolina (15) and Georgia (16);

and five states in the West, Oregon (7) plus a grouping in the interior West made up of
Nevada (6), Arizona (11), New Mexico (5) and Colorado (9).
For those states, Obama would have to depend on a large Latino turnout.

The Southern states would require a heavy turnout among blacks plus support from moderate-to-liberal suburban whites.

Well at least New Hampshire for sure. I could see them figuring Indiana will flip back to Republican, and Minnesota may always be reasonably close, yet a Republican hasn't won it at the Presidential level since 1972! (Longest such drought in the country for the Republicans, save DC). But NH has been a toss-up with Romney/Obama in nearly every poll, with many having Romney leading. I don't see where they could put that if not in a swing state category.

I suspect that President Obama will campaign in the states that he lost in 2008, just because he has enough money, and it looks good. But I doubt that his strategists think he could win any of them. It would seem strange to have a state move in his favor.

The big question would be about the VP candidate. The flashiest thing for Obama would be if Joseph Biden were to retire.

Senator Bob Mendez is (I believe) the only Latino Democratic Senator (but he is divorced)


Representative Charlie Gonzales from San Antonio is probably the leading Latino Democratic Representative


Texas has gone from 32.0% Latino in 2000 to 37.6% in 2010. That would be really unexpected if Obama could win Texas with a Mexican VP candidate.

Sen. Menendez has about a 0% chance of being selected, for many reasons. He is up for re-election himself in '12, and I don't believe NJ has a "run for VP and Senate at the same time" rule, and the Dem convention is after the NJ Primary. Even if he was allowed to run for both, if he left to become VP, Governor Christie (R) would appoint a Republican to his seat, a no-go for the Dems in DC. Some other reasons: He did a mediocre job as the head of the DSCC (lost 7 seats in '10, and only got bailed out by bad R candidates in DE, NV, and probably CO). He is a machine guy who came out of the very corrupt Hudson Co. Democratic Organization. While he has never been convicted of anything, many he has worked for and with are currently serving long prison sentences. He underperformed in his only non-walkover election in 2006, winning by less than any other Democratic Senate incumbent or Democratic-held open seat.

I don't think just putting a Latino on the ticket will give Obama a huge win with that group, but if he wanted to, the best choice would probably be Ken Salazar, former Colorado Senator and current Sec. of the Interior. He's affable, not overtly partisan, and has done well in swingy Colorado. Plus he has experience in the administration, so it would be a natural promotion for someone who's already in the Cabinet meetings and working for and with the White House.

The National Popular Vote bill would guarantee the Presidency to the candidate who receives the most popular votes in all 50 states (and DC).

Every vote, everywhere, would be politically relevant and equal in presidential elections. No more distorting and divisive red and blue state maps. There would no longer be a handful of 'battleground' states where voters and policies are more important than those of the voters in more than 3/4ths of the states that will just be 'spectators' and ignored.

When the bill is enacted by states possessing a majority of the electoral votes– enough electoral votes to elect a President (270 of 538), all the electoral votes from the enacting states would be awarded to the presidential candidate who receives the most popular votes in all 50 states and DC.

The bill uses the power given to each state by the Founding Fathers in the Constitution to change how they award their electoral votes for President. Historically, virtually all of the major changes in the method of electing the President, including ending the requirement that only men who owned substantial property could vote and 48 current state-by-state winner-take-all laws, have come about by state legislative action.

In Gallup polls since 1944, only about 20% of the public has supported the current system of awarding all of a state's electoral votes to the presidential candidate who receives the most votes in each separate state (with about 70% opposed and about 10% undecided). Support for a national popular vote is strong among Republicans, Democrats, and Independent voters, as well as every demographic group in virtually every state surveyed in recent polls in closely divided Battleground states: CO – 68%, FL – 78%, IA 75%, MI – 73%, MO – 70%, NH – 69%, NV – 72%, NM– 76%, NC – 74%, OH – 70%, PA – 78%, VA – 74%, and WI – 71%; in Small states (3 to 5 electoral votes): AK – 70%, DC – 76%, DE – 75%, ID – 77%, ME – 77%, MT – 72%, NE 74%, NH – 69%, NV – 72%, NM – 76%, OK – 81%, RI – 74%, SD – 71%, UT – 70%, VT – 75%, WV – 81%, and WY – 69%; in Southern and Border states: AR – 80%,, KY- 80%, MS – 77%, MO – 70%, NC – 74%, OK – 81%, SC – 71%, TN – 83%, VA – 74%, and WV – 81%; and in other states polled: CA – 70%, CT – 74%, MA – 73%, MN – 75%, NY – 79%, OR – 76%, and WA – 77%. Americans believe that the candidate who receives the most votes should win.

The bill has passed 31 state legislative chambers in 21 small, medium-small, medium, and large states. The bill has been enacted by 9 jurisdictions possessing 132 electoral votes - 49% of the 270 necessary to bring the law into effect.

NationalPopularVote
Follow National Popular Vote on Facebook via nationalpopularvoteinc

Hopefully the National Popular Vote never happens as it would subvert the intent of the constitution. If so many people are in favor of it, ammend the constitution.

Quote: slyther

Hopefully the National Popular Vote never happens as it would subvert the intent of the constitution. If so many people are in favor of it, ammend the constitution.

The Founding Fathers in the Constitution did not require states to allow their citizens to vote for president, much less award all their electoral votes based upon the vote of their citizens.

The presidential election system we have today is not in the Constitution, and enacting National Popular Vote would not need an amendment. State-by-state winner-take-all laws to award Electoral College votes, were eventually enacted by states, using their exclusive power to do so, AFTER the Founding Fathers wrote the Constitution. Now our current system can be changed by state laws again.

Unable to agree on any particular method for selecting presidential electors, the Founding Fathers left the choice of method exclusively to the states in section 1 of Article II of the U.S. Constitution-- "Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors . . ." The U.S. Supreme Court has repeatedly characterized the authority of the state legislatures over the manner of awarding their electoral votes as "plenary" and "exclusive."

The constitution does not prohibit any of the methods that were debated and rejected. Indeed, a majority of the states appointed their presidential electors using two of the rejected methods in the nation's first presidential election in 1789 (i.e., appointment by the legislature and by the governor and his cabinet). Presidential electors were appointed by state legislatures for almost a century.

Neither of the two most important features of the current system of electing the President (namely, universal suffrage, and the 48 state-by-state winner-take-all method) are in the U.S. Constitution. Neither was the choice of the Founders when they went back to their states to organize the nation's first presidential election.

In 1789, in the nation's first election, the people had no vote for President in most states, only men who owned a substantial amount of property could vote, and only three states used the state-by-state winner-take-all method to award electoral votes.

The current 48 state-by-state winner-take-all method (i.e., awarding all of a state's electoral votes to the candidate who receives the most popular votes in a particular state) is not entitled to any special deference based on history or the historical meaning of the words in the U.S. Constitution. It is not mentioned in the U.S. Constitution, the debates of the Constitutional Convention, or the Federalist Papers. The actions taken by the Founding Fathers make it clear that they never gave their imprimatur to the winner-take-all method.

The constitutional wording does not encourage, discourage, require, or prohibit the use of any particular method for awarding the state's electoral votes.

As a result of changes in state laws enacted since 1789, the people have the right to vote for presidential electors in 100% of the states, there are no property requirements for voting in any state, and the state-by-state winner-take-all method is used by 48 of the 50 states. States can, and frequently have, changed their method of awarding electoral votes over the years. Maine and Nebraska do not use the winner-take-all method– a reminder that an amendment to the U.S. Constitution is not required to change the way the President is elected.

The normal process of effecting change in the method of electing the President is specified in the U.S. Constitution, namely action by the state legislatures. This is how the current system was created, and this is the built-in method that the Constitution provides for making changes. The abnormal process is to go outside the Constitution, and amend it.

Quote: kohler

The Founding Fathers in the Constitution did not require states to allow their citizens to vote for president, much less award all their electoral votes based upon the vote of their citizens.

The presidential election system we have today is not in the Constitution, and enacting National Popular Vote would not need an amendment. State-by-state winner-take-all laws to award Electoral College votes, were eventually enacted by states, using their exclusive power to do so, AFTER the Founding Fathers wrote the Constitution. Now our current system can be changed by state laws again.

That statement is true. The states individually determined that they could maximize the attention of the presidential candidates by adopting the winner take all system.

Why not try for a somewhat less radical goal? Consider reducing the number of electoral college votes to the number of representatives. Why should voters in Wyoming see their votes count three times? I think that would be a more attainable goal, then this pipe dream you have.

Quote: MathExtremist

It's a great problem and well-known in CS circles: Partition Problem on WikiPedia.
There are several algorithms to do it, especially in this case where the sizes of the inputs (state electoral votes) are bounded.

I have an integer partition problem in some of my analysis. The Nevada Gaming Commission (NGC) is forbidden by law to publish information that reflects on the performance of an individual casino. However, to satisfy government officials, the public, and people in the business, they publish a great deal of information about a group of casinos.

For instance they are permitted to publish hundreds of statistics that apply to the 4 Casinos in South Shore Lake Tahoe Area. Among the statistics are the "average square footage of a casino" in this group. Believe it or not, they NGC is forbidden by law to even reveal the names of the 4 casinos in this group.

However, it is no big secret as to the names of the casinos in South Shore Lake Tahoe. Using the square footages provided in the database for each casino, you can easily derive the same averages in the abstract. So given that the collective cleared $50m in pit revenue, and $142m in slot revenue, you can make an educated guess as to how the total was split between the four properties.

NAME	PIT+KENO+BINGO	SLOTS	RACE/SPORTS	POKER/PAN	TOTAL
HARVEYS RESORT	22,834	60,683	2,967	2,760	89,244
LAKE TAHOE HORIZON		29,689			29,689
LAKESIDE INN	1,210	14,501	1,600	541	17,852
MONTBLEU	15,000	27,500		2,500	45,000
Total	39,044	132,373	4,567	5,801	181,785
Count	3	4	2	3	4
Average	13,015	33,093	2,284	1,934	45,446

The NGC concludes that pit revenue in South Shore Lake Tahoe is $50.3 million / 13,015 = $1289 per square foot (considerably below the statewide average of $2235 per square foot).

As a first guess, I might assume that the revenue is split up in the same proportion as the square footage (like so).

NAME	PIT+KENO+BINGO	SLOTS	RACE/SPORTS	POKER/PAN	TOTAL
HARVEYS RESORT	$29,423,714	$65,304,016	$2,066,399	$1,266,388	$98,060,517
LAKE TAHOE HORIZON	$0	$31,949,820	$0	$0	$31,949,820
LAKESIDE INN	$1,559,197	$15,605,253	$1,114,337	$248,230	$18,527,017
MONTBLEU	$19,328,883	$29,594,128	$0	$1,147,090	$50,070,101
Total	$50,311,794	$142,453,217	$3,180,736	$2,661,708	$198,607,455

I could try and refine my estimate based on perceived assets of each casino. Lakeside may not even get that much pit game action since it appeals to mostly slot players. Harvey's has smaller betters, but more action based on their wildly popular player's club card.

I also know that Harvey's is the only casino in Lake Tahoe to clear more than $72 million in total gaming revenue. So it is likely that it also took roughly half of the $142m in slot revenue.

The estimate for Lake Tahoe Horizon is undoubtedly way too high. There is a lot of square footage in the casino, but it is barely populated with a mere 200 slot machines. It would be lucky to earn half the estimated amount.
================
Hypothetically, if it wasn't so easy to know a priori which four casinos were in this group, you have an integer partition problem. It is fairly easily solved by writing a computer program to add up the square footage of any four casinos in the statewide database, and testing to see when the average corresponds to the average given in the report.

Since there are 256 casinos statewide, there are combin(256,4)=174,792,640 possibilities (not an overwhelming problem for a small computer).

My problem is that I am trying to find combinations of as many as 32 casinos where
combin(256,32)= 58,244,594,029,230,700,000,000,000,000,000,000,000,000 which is proving a difficult problem even letting the computer run for a week.

I have tried using "a priori" logic to eliminate the most unlikely combinations, and reduce the probability space to something smaller. For example
combin(150,18)=79,802,042,605,894,700,000,000

But the program fails to find a solution.

I may have to use a smarter algorithm than just brute force trial and error.

Quote: pacomartin

Hypothetically, if it wasn't so easy to know a priori which four casinos were in this group, you have an integer partition problem. It is fairly easily solved by writing a computer program to add up the square footage of any four casinos in the statewide database, and testing to see when the average corresponds to the average given in the report.

Since there are 256 casinos statewide, there are combin(256,4)=174,792,640 possibilities (not an overwhelming problem for a small computer).

My problem is that I am trying to find combinations of as many as 32 casinos where
combin(256,32)= 58,244,594,029,230,700,000,000,000,000,000,000,000,000 which is proving a difficult problem even letting the computer run for a week.

I have tried using "a priori" logic to eliminate the most unlikely combinations, and reduce the probability space to something smaller. For example
combin(150,18)=79,802,042,605,894,700,000,000

But the program fails to find a solution.

I may have to use a smarter algorithm than just brute force trial and error.

Work up to the hard subsets, from sparsely populated regions to densely populated ones. Shrink your problem space by slotting known combinations into other buckets first. The four South Lake Tahoe casinos are in South Lake Tahoe, not the Strip, so your space is now 252. Keep doing that for the smallest aggregate group until you get to the ones where you actually need to let the code run, and you should be much lower than 150.

Paco Martin map of a possible tie (#1)

The above website has a way to store potential election possibilities. People can make up their own, and post them on this thread.

It might be easier to think about starting from this tie position, and having Obama win the marginal states. To return to the Obama win status in 2008, you have to give him 7 states + Nebraska lone vote.

NV, CO, FL, VA, NC, IA, IN + (1)NE

So what's up with Santorum? Now he is winning three states at once?

Quote: pacomartin

So what's up with Santorum? Now he is winning three states at once?

Kind of wild. I think Romney ignored the smaller, cacus states here and Rick took them. Many GOP voters, myself included, see Romney as another establishment Dole/McCain and are still not sold. Mitt seems to think the whole thing should have been handed to him, but he is now learning that to be the man you have to bear the man.

Or is that the wrong Rick?

Quote: AZDuffman

Or is that the wrong Rick?

Rick Santorum from Penn Hills (suburb of Pittsburgh). Two term Representative from PA 18th district, and two term United States Senator from Pennsylvania (January 3, 1995 – January 3, 2007).

In the November 7, 2006 election, Santorum lost by over 700,000 votes, receiving 41% of the vote to Casey's 59%, the largest margin of defeat for an incumbent senator since 1980 and the largest losing margin for an incumbent Republican senator ever. So if he wins the candidacy it would be one of the more amazing comebacks in history.

Part of the reason he lost is that Casey was also anti-abortion. Pennsylvania has many abortion single-issue voters, and since there was no choice to be made, the Democratic candidate won. Plus Democrats were dominating in 2006, with widespread dissatisfaction with Republicans.

Catholics remain roughly 25% of the country for most of the last half century since our only Catholic President (JFK). Latino immigrations keeps the Catholic percentage steady.

Rick S. seems to have caught the attention of a lot of Catholics who are particularly displeased with Obama's insistence that the church pay for contraceptives and abortions for their employees.