7.10.2008

Tipping Point v2.0

As I've hinted a couple of times, we now have a new version of the model running, which attempts to account for the interrelationships between polling movement in different states. Before I can work up the energy to fully describe that, let me first tell you about the new Tipping-Point States metric that I've developed to accompany it.

A Tipping-Point state is now defined as a states that would be most likely to alter the outcome of a close election if it were decided differently. More specifically, a Tipping-Point State is among the closest states –- taken alone or in combination –- that would give the losing candidate at least 270 electoral votes if transferred to him from the winner’s column, with no wasted electoral votes.

Let me give you a couple of examples. First, 2004, which is an easy one. The closest states won by Bush were New Mexico and Iowa. However, these would not have given John Kerry enough electoral votes even if he had won them. So the third-closest state, Ohio, was the lone Tipping-Point State for that election, since it would have gotten Kerry to 270 all on its own.

Now a somewhat more complicated example: 1960. Richard Nixon was 51 electoral votes shy of winning that election. The closest Kennedy states were as follows:

Hawaii (3)       -0.06%
Illinois (27) -0.19%
Missouri (13) -0.52%
New Mexico (4) -0.74%
New Jersey (16) -0.80%
So, we start with a 51-EV gap and begin whittling those numbers down for Nixon. Giving him Hawaii makes it 48, Illinois makes it 21, Missouri cuts Kennedy's lead to 8, and New Mexico to 4. And then we hit New Jersey, which gives Nixon the election. But it also gives him 12 extra electoral votes.

So we go back through the list in reverse order and see if there is any wastage. In this case, there is. If we place New Mexico back in the Kennedy column, Nixon still has 8 electoral votes to spare. In fact, while we must keep Missouri and Illinois, we can also eliminate Hawaii. So the Tipping-Point states for Nixon in 1960 were Illinois, Missouri, and New Jersey. This was the most efficient possible combination of states that would give him a winning electoral margin.

But I tried to slip one by you there. What do I mean by a "close election"? I mean one in which the electoral math matters. That was the purpose of the graph that I posted this morning:


The Tipping-Point calculation is weighted across each simulation based on the popular vote result predicted in each election. Specifically, it is weighted according to the probability that a candidate with that popular vote share will lose the Electoral College. So a simulation in which the popular vote is divided exactly evenly will be weighted at .5 -- the highest possible weighting. A simulation in which the popular vote margin is 3 points -- that gives the popular vote leader about a 97 percent chance of winning the election -- will be weighted at a .03. Basically, most of the calculation is derived from elections that are decided by a point or two.

So this definition is rather complicated mathematically -- but at the same time, I think it's more intuitive than the previous version. It's definitely a lot more robust.

The hot-off-the-presses Tipping Point numbers are as follows:



Michigan and Ohio will each prove to be decisive in a close election about 30 percent of the time. After that are Colorado and Virginia, which serve as gateways to their respective regions.

The really interesting thing is to compare the Tipping Point states with and without the intrastate (or should that be interstate?) correlations. A state like North Carolina is punished, for instance, for reasons that most of you can probably figure out. But we'll save that for later.

54 comments

Anonymous said...

Hey, are you holding up your sleeve for the next explanation something like what I was guessing - "paths of conquest" where, based on State Similarities, you show that the route to State A2 passes through A1?

Anonymous said...

shouldn't each state's effect on win margin be doubled in the Nixon example? ie, adding Hawaii to the Nixon column should reduce Kennedy's lead from 51 to 45, as it removed 3 electoral votes from Kennedy AND adds three to Nixon

Anonymous said...

ahh, nevermind, i see what you did there now

rusty said...

Let me take a stab at the North Carolina interstate effect. If North Carolina tips, then Virginia also tips 99% of the time, and if Virginia tips then NC is often not needed because other states, or VA alone, will have provided the winning electoral margin.

Probably wrong, but what the heck.

Anonymous said...

How do you account for interventions? Like say we suddenly find out that O fathered a child out of wedlock, or McC passed a significant lobbying favor?

Modeler said...

Hmm... what about this example. Imagine the loss was by 11 electoral votes. The smallest margins of loss were:

New Mexico (5): -0.4%
New Hampshire (4): -0.5%
Montana (3): -0.6%
Missouri (11) -0.7%

If I understand correctly, in this case the first three states would be tipping point states. However, it seems that it is more likely that the candidate would win Missouri than that the candidate would win all three of the other states.

In that sense, I think there was some merit to your old approach.

The Professor said...

Why not just count it as a tipping point if that single state would have switched the election... the various permutations will sort out the multi-state scenarios right?

Anonymous said...

Rasmussen
North Dakota

Obama - 43
McCain - 43

With leaners
McCain - 47
Obama -46

James said...

@ modeler

New Mexico, New Hampshire and Monanta have a combined 6 congressional seats to Missouri's 9. Since congressional seats are a rough proxy for population.

(3*.004)+(2*.005)+(1*.006)= .028
(9*.007) = .063

So winning Missouri would require a candidate to win over voters totaling approx. 6% of a congressional district (20-25,000 voters assuming 50% turnout). Winning the other three states requires a swing of less than half that many voters.

This method removes the previous bias of the tipping point analysis towards individual large states.

Anonymous said...

Very funny...just yesterday a lot of stressed liberals attacked a reliable pollster as Rasmussen because he is republican...today they consider very much the poll on North Dakota...okay okay Obama can win North Dakota and Montana and Virginia and North Carolina...and Georgia...and Mississippi and Alaska and why not? Utah too! please take a breath...election will be very close and McCain is competitive to win...

Conservative from Italy ( Rome )

Steve said...

Great update. How tough would it be to put up an ROI map for the Senate race? I think that would be really valuable, because it can show readers which Senate races make the most sense to spend money on. The ROI presidential map doesn't give activists any useful information, just insight into campaign decisions.

Tim said...

Rusty, you're right. If NC goes Obama, we're essentially sure that VA has already gone for Obama as well, and furthermore that the election as a whole has tipped so far to Obama that we're confident he's already won it, with or without NC's electoral votes. In other words, by the time Obama wins NC, he's clearly already won the election, thus NC isn't much of a true "tipping point" state. Similar statements apply to other states such as ND, MT, and probably even MO and IN to lesser extents.

Basically, the deeper a state is in McCain territory, the better we can feel about Obama's prospects if he wins it. If Obama wins Texas, for example, or Mississippi, of Georgia, we can feel quite confident that he's already won states with similar demographics that are more favorable to him. The whole premise of this site is comparing states and regions by demographic similarity. Thus, we can get a pretty good sense of what kind of demographic shifts would be required in order for moderately or deeply red states to go for Obama and we can apply them across the board. By the time Obama wins any signifcantly red state, he has already won the election.

Jyrinx said...

It's definitely interstate, not intrastate.

(Sweet! I got to contribute! :-) )

Modeler said...

James,

The problem is the distribution of victories. Consider the following simplified example:

New Mexico (5): -0.5%
New Hampshire (4): -0.5%
Montana (3): -0.5%
Missouri (11) -0.7%

Say the likelihood of flipping any one of the first three states is 40%, and the likelihood of flipping Missouri is only 10%. Given the variance in Nate's model, I suspect these are conservative estimates for the point I'm about to make.

The joint probability of all three small states flipping is 6.4%, making it more likely that Missouri flips.

Now there might be interstate correlation, but Nate hasn't taken that into account yet. Even if there is some correlation, it's generally more likely to get a single big flip than a lot of little ones.

I understand that the tipping point analysis favors large states (it still does). However it's supposed to; the ROI analysis corrects for that.

A Big Fan of 538 said...

I have a few comments. First, about, about weighting by the population/EV probability curve. This analysis is predicated by the assumption that some close states would switch which, I would assume, would change the popular vote and hence the weight.

This also seems to hide interesting cases. This weight heavily favors close races when the popular vote is near tied, but aren't tipping point states more interesting when the vote is not tied. Take FL in 2000. I almost want to know the opposite, how likely is a state is sway an election contrary to the popular vote.

My second issue is that we don't know how likely a "close" election is. By the current definition, Michigan is decisive 30% of the time in close elections. Does this happen 1%, 10% or 25% of all simulations? I relation to my previous point, it seems possible that when the election is close, Michigan is also close because it is correlated, say, with the national polls. However, its also possible (though I have no idea how likely) that a state is correlated such that it is likely to switch the vote when the election is not so close. Since the election is currently looking not so close, this might happen alot more, but be weighted less than Michigan's case simply because you favor tipping near a (less likely) popular vote tie.

To me it seems the the tipping point definition is the probabilty that a given state can change the election. I feel like this has a natural definition: average probabilty of that a state switches times the probability of an simulation where a such a switch changes the election. Of course, this is likely to be a small number because of the second factor, but, like you do implcitly above, you can normalize all the probabilities by their sum.

Sorry for the long critical post, but I really find your site fascinating and I am always wondering about slight changes in the simulation.

A Big Fan of 538 said...

One more question, I am not sure a close election is necessarily a likely to change election. Because the polls already indicate a likely winner, aren't some small changes less likely than others?

The case I am considering is take a hypothetical state where the polling is 54 Obama and 46 McCain and the simulation give the state the result 50.1 Obama 49.9 McCain. Isn't switching in this case much less likely than another state where the polling data is 50 Obama and 50 McCain and the simulation results are identical?

Alex Epstein said...

How does this square with your numbers now? You have Obama 3.4 % ahead in the popular vote, but winning only 69% of the time.

Even if you halve that to 1.7% ahead, he wins over 80% of the time according to your S curve.

John said...

The Professor said...
Why not just count it as a tipping point if that single state would have switched the election... the various permutations will sort out the multi-state scenarios right?

Because then CA will be a tipping point, because it would switch an election.

Zack said...

Re: Alex Epstein

"How does this square with your numbers now? You have Obama 3.4 % ahead in the popular vote, but winning only 69% of the time."

I think you're misinterpreting those percentages. My understanding is that the Popular Vote count reflects the likelihood that a candidate wins, not the actual vote differential.

That means (hypothetically) Obama could win 60% of the simulations and have a 60/40 lead in the count. That doesn't mean that he's going to win by 20 points. It just means that he's winning (by whatever margin) in 60% of Nate's simulations.

That any clearer?

Rasmus said...

"
So winning Missouri would require a candidate to win over voters totaling approx. 6% of a congressional district (20-25,000 voters assuming 50% turnout). Winning the other three states requires a swing of less than half that many voters."

But flipping 100,000 voters in Wyoming with a population of 650,000 or so is much harder then flipping 750,000 in California with a population of 33 million or so.

Alex said...

Zack and Alex:

The popular vote count is the projected vote differential. The reason that you see a lower win% for Obama with the higher differential is because of the inherent uncertainty of the projection. If Obama wins the popular vote by the projected differential (ie if our error -> zero), then we can say that he has a very high probability of winning the election. But since we have rather large error bars on that projection, we can't say he'll win with such certainty.

Stuart said...

Nate, if I understand the model that you're using now correctly, it seems to me that it's not actually a symmetrical measurement between the two candidates.

The numbers right now are an aggregate of both 'states that could flip the election to McCain if he won them' and 'states that could flip the election to Obama if he won them'.

I'd be interested to see what the maps looked like if you ran each of those sets of numbers separately - ie, ran the tipping point algorithm on only simulations where Obama won, and then ran it again on only the simulations where McCain won. I wonder how different they'd be...

James said...

Rasmus

But we're already looking at similar win percentages of around 0-1%. I'm arguing that flipping 1% of Wyoming's voters is as easy PER VOTER as flipping 1% of Californa's voters. So flipping 6,300 voters each in ten states the size of North Dakota (population 640,000) would take about as much effort as flipping 65,000 in a state like Indiana (population 6,350,000). So if you can get to 270 electoral votes by flipping fewer total voters in more smaller states, those should be considered the tipping point states.

Modeler,

I see what you're saying, but right now the win percentages at 538 reflect the uncertainty of determining the exact level of support for a candidate from polls. After the election, we have absolute data on the levels of support.

So you're right that single large state that's been called for McCain based on the projections here is more likely to actually favor Obama than three small ones that have been projected to favor McCain by smaller margins, the analysis changes when you're looking at the actual election results (or even one of Nate's simulated election results) because there's no uncertainty factor, and you can just look at questions like "How many more voters would I have won over in state X is I had spent Y extra dollars or made Z extra campaign stops."

I hope I'm not just speaking in nonsense here.

The Professor said...

John, I agree that CA being a tipping state would be strange, but I was thinking along the point modeler first raised. It seems like the joint probably of many small states switching is less than the probability of a single large state switching (more likely say FL / OH than CA). By looking at just one state the tipping analysis would show which single state, if it had gone the other way, is most likely to reverse the outcome of the election.

The other way (per your point, perhaps better way) to do the analysis is to show which states are most involved in alternative permutations that reverse the outcome; only this is a ton of work. For each iteration of the model, the model would have to do all the joint probability calculations for the various permutations that would reverse that election outcome (it would then choose the most likely one)… Not sure how efficient Nate’s code is that but it seems like the single state analysis could be simpler (if answering a slightly different, and perhaps less interesting question).

Allen said...

I think the whole concept of "tipping point states" may be a fallacy. If the electoral vote count is close, then every close state matters, not just one state that supposedly put the candidate "over the top".

Tax said...

I hate the fact that I'm not smart enough to understand this. It seems pretty cool, but it's like a blind man at an orgy...wait no that's not quite right.

kronius said...

Nate -

I think the problem with your method is that it doesn't account for the probability of a state switching. Modeler raised this issue earlier.

I think there might be a very simple way to measure what you're looking for. Just calculate the % of simulations that state X votes for the winner. That is the measurement of the degree to which state X tips the balance.

Think about it. If a state is in the winner's column in 100% of the simulations, then that state is deciding the outcome of the election. It may have a problem with being affected by the fact that obama has a clear advantage right now, but it would at least be interesting to see what the results of that kind of measurement looked like.

Michael said...

Nate:

Somewhat off-topic from this thread, but I've been reading the "Beyond The Polls" site today. The blogger there, AR, has criticized your methods and results several times. Would you like to comment on his/her methods of analysis?

It seems to me that, in spite of his/her avowed claim of "Challenging the conventional wisdom," AR is actually engages in much more traditional analysis than you do. I would tend to compare to his analysis to a narrative analysis of the likelihood of a batter doing well in a given year based on his past batting averages, prior health, and such. He mentions the "giggle test," which sounds a good deal like managing baseball by hunch (educated guess, if you like), rather than through the use of modern stats like OPS (on-base percentage plus slugging) VORP (value over an average replacement player just brought up from AAA), etc.

His site sure is interesting, but I don't see him going out on a limb on much, whereas you are trying to establish new and more reliable ways to predict the outcomes of elections.

Allen said...

If what you are trying to determine is "states that would be most likely to alter the outcome of a close election", I think the approach taken at http://election-projection.net may be the right one. It looks at how a one percentage point change in the polls for a state would effect the probability of each candidate winning the election. If a one percentage point change in the polls has a larger effect on the probability each candidate wins the election, then the state could be considered "more likely to alter the outcome of a close election".

Modeler said...

James,

You're certainly not speaking nonsense (as far as I'm concerned). If I understand you correctly, you are proposing the following metric:

1) Consider the minimum number of voters that would have needed to change their votes to alter the election.

2) Label the states in which those voters reside "tipping point states."

That would be a cool metric, and it would combine elements from both the Tipping Point and ROI analyses. It might actually favor small states because of the high EV/voter ratios in those states, as you pointed out. If that is Nate's intent, then he should be able to calculate it explicitly using estimated voter turnout. Maybe he can call it ROI v2.0.

However, with "Tipping Point" states I think Nate is trying to get at the combination of states most likely to have have changed the outcome of the election. It would be the the combination for which the losing side can most reasonably say "If we'd only won X, we would have won." In my example, it would be more realistic for them to say that about MO than the NH-MT-NM combo.

Anonymous said...

Good news for Obama in latest Pew Poll.

It shows his supporters are much more likely than McCain to be "strong supporters".

Modeler said...

Continuing this train of thought a little further...

You could actually consider multiple "Minimum tipping combinations" for each run, and weight the states in each combination by the probability that they flip. So in my example, MT, NH, and NM would all have weights of 6.4, and MO would have a weight of 10.

The remaining question is "How do you calculate the probability of a state flipping?" For every state you should have the expected result and the variance. From these you can estimate the probability of the state voting for the losing candidate using an error function.

PReader said...

Rasmussen just posted: Obama 50, McCain 39 in Wisconsin (leaners, O 52, M 42)

http://www.rasmussenreports.com/public_content/politics/election_20082/2008_presidential_election/wisconsin/election_2008_wisconsin_presidential_election

lilnev said...

If NC goes Obama, we're essentially sure that VA has already gone for Obama as well ...

Yes.

... and furthermore that the election as a whole has tipped so far to Obama that we're confident he's already won it, with or without NC's electoral votes.

No. This would suggest that all movement would be felt equally across all states -- we simply line them up a single axis from most Obama-friendly to least, and allow for movement along that axis.

But that misses the whole point of the state correlations. Suppose Obama's support collapses among non-Evangelical white working class voters, but he gains a lot of support among African Americans and white Evangelicals -- he could lose OH, MI, WI, but win VA, NC, and even GA. The first group are demographically similar, and we can expect them to move somewhat together, with OH turning red before WI does. Likewise VA, NC, and GA will likely move together, with VA turning blue first. But the two groups are likely to be relatively uncorrelated with each other.

How to implement this into the model? Currently, for each simulation a random number is generated for national movement (applied to all states) and an independent random movement is applied to each state. Instead, the 50 state terms should have a correlation structure based on their demographic similarities. Transform an independent random vector by a covariance matrix constructed from the distance measures that Nate has computed, I believe.

James said...

Modeler,

I understand what you're saying and at least from the point of view of perceptions you're absolutely right. No one looks back on the 2004 election and says "if only we'd won Iowa, New Mexico, and Colorado." <- though Colorado was less close than Ohio, so by Nate's metric this wouldn't be true anyway.

I think the fundamental difference in how we're looking at this comes down to:

"For every state you should have the expected result and the variance. From these you can estimate the probability of the state voting for the losing candidate using an error function."

The way I'm looking at the most likely way to swing is looking at only the data on how close the states electoral outcome was in that particular simulation. You're looking at the actual outcome and the variance in other simulation (or looking at it another way, you're looking at the formula used to generate the outcome in that particular simulation). With info on the variance you can calculate probabilities. Looking at just the results without the formula, I think the best proxy is number of voters, or alternatively percent margin of victory.

I remain amazed that's it's possible to have such interesting and civil discussions on this site.

jdk said...

1. There really needs to be separate maps one for McCain and one for Obama.

2. I'm still not clear what you are trying to get at. Is it the "Florida, Florida, Florida" of 2000 or the "Ohio, Ohio, Ohio" of 2004?

The problem with that is that it never was FL, FL, FL; it was always TN, TN, TN. And since TN was that close, TN may not have come up by this mathematical definition. But probablistically speaking if you don't win your home state -- you will almost certainly LOSE!

In other words, once TN goes against GORE the odds are so staked against him that needs a miracle to win.

It seems to me the better metric we are after is "battleground". If we look at the current map, what states does McCain have to flip back to red to win: IN 11, VA 13, CO 9, OH 20.

It seems silly to call MI and PA tipping states when they're already tipped!

One thing that your State Similarity thing could have used was to take the Nation as a State and say what States are most similar to it. Maybe you did this but didn't post.

I used a little bit different State Similarity method based on 2004 results and my "special sauce" Ancestry (upon reflection, I certainly don't think geographic lat/long should be used; I have some concerns about overfit you've got quite a few variables, and DC, HI, and UT are just special cases).

In any case, my "closest" States to the Nation are FL, NV, CO IL, VA, MI, MO. Which might be interesting

I think that you have to chop of the tails of safe Dems and safe Reps, and only look at close elections in terms of those states, in other words don't let DC, CA, NY, IL, MA, etc. make things seem closer because the "wasted" margin of victory.

Modeler said...

James,

I agree that you would need to use another approach if you didn't want to calculate the probability of each state flipping. In that case, Nate's approach is probably a reasonable heuristic for determining the states most likely to flip. However Nate has the tools to calculate the probability fairly easily.

If you look for the minimum number of voters that needed to filp, then you get some interesting results. For example, as you mentioned the winning combination in 2004 would have been NM + IA + CO, where flipping 57,785 voters would have done the trick. In OH, 59,388 needed to flip.

It's still hard to say that the NM + IA + CO combo would have had better ROI in 2004, because even if Kerry had managed to flip 60,000 voters in those three states, it would have been hard to make sure they were distributed properly to actually affect all three election outcomes.

jdk,

I really like the idea of using the similarity score to compare states to the nation.

low-tech cyclist said...

Brilliant! I love it!!

In the ROI thread, I'd suggested ditching the landslides, but I'd proposed a simple cutoff point. This is much more elegant.

Very, very nice.

low-tech cyclist said...

Oh yeah - I'm looking forward to seeing how this affects the ROI chart.

Anonymous said...

Nate,

It is a well known fact that, ever since FL became a state, the winner of every presidential election has been the candidate who has won at least two (2) states out of {FL, OH, PA}. There have been no exceptions. None. This predictor is better than the national popular vote.

Furthermore, there is no other group of three states for which the above statement is true. Therefore, in the scenario analysis I would like to see how this plays out in your simulation runs

I broke my right wing said...

Nate,

I would really enjoy seeing the mode shown on the Electoral Vote Distribution chart. I am wondering how sensitive that is to changes in other data, most notably winning percentage (thought I would say EVs didnt you?)

low-tech cyclist said...

Just one question, Nate: aren't the percentages supposed to add up to 100%?

Nate said...

No, they now no longer have to add up to 100 percent. There can now be more than one swing state in a given election.

Allen said...

> "A Tipping-Point state is now defined as a states that would be most likely to alter the outcome of a close election if it were decided differently"

"Likely" is equivalent to a probability, but one thing that the computation of the Tipping Point States would seem to NOT be is a probability. In order to be a probability, it seems to me you would have to take the probability of getting to the base outcome and multiply that by the probability of getting to the "tipped" outcome. Since the base outcomes are all equally likely, the factor that has not been included is the probability that the combination of states that "tip" the election would actually tip it. Furthermore, it seems to me you would have to consider all combinations of states that could tip the election, not just the highest probability state or states. I think what you have come up with may just be a heuristic that roughly corresponds to the "battleground states", but it is not a measure of likelihood.

Paul Bradford said...

Tipping States Through the Years

1960: This is interesting. While, as Nate described in the post, Nixon would have needed IL, MO and NJ to get the requisite 269 electoral votes to win the election outright, Nixon would only have had to flip MO (9,980 vote plurality) and IL (8,858 vote plurality) to prevent Kennedy from winning. Kennedy only won 303 Electoral Votes because 8 MS electors and 6 AL electors supported Harry Byrd for president. If you subtract IL (27) and MO (13) from Kennedy's tally you get 263 which is less than the number needed for a majority.

1968: Humphrey would have had to flip MO(12), NJ(17), OH(26) and IL(26) to raise his electoral tally from 191 to 272. But he could have stopped Nixon if he'd merely flipped MO(20,488 votes), NJ (61,261 votes) and AK (2,189 votes). This is because George Wallace won 46 Electoral Votes.

1976: If Ford had flipped OH(25) and WI (11) he would have won the election. In fact, if he'd flipped OH (11,116 votes) and MS (14,463) he'd have gotten 272 electors and the election.

2000: Duh! Gore needed only 537 votes in Florida to reach 291 Electoral Votes and win the election

2004: 136,483 votes in OH would have given Kerry 272 EV's. Of course, flips in NM (6,047 votes), IA (13,498 votes) and NV (21,567 votes) would have brought him to 269 -- which would have been good enough for a tie.

Isn't it interesting how the same states keep popping up. In the USA, some votes count a lot more than others!

Modeler said...

Paul Bradford,

Interesting data. Thanks.

Richard said...

This is very close to what I was hoping for in the way of a change to the tipping-point state analysis. I would be very interested to see these states broken down among the two candidates. For instance, I suspect that Ohio is much more often a tipping point state for McCain than it is for Obama, since McCain has far fewer paths to victory which don't include Ohio than does Obama. I suspect each candidate's tipping-point state map would look very different.

jdk said...

Nate noted: "The closest Kennedy states were ...
Hawaii, Illinois, Missouri, New Mexico, New Jersey. So, we start with a 51-EV gap and begin whittling .. down. ... But it also gives him 12 extra electoral votes. So we go back through the list in reverse order and see if there is any wastage. ... This was the most efficient possible combination of states that would give him a winning electoral margin."

Why bother with the whole going back through the list. I can see doing that if you have a sample of one, i.e. election is perfectly correct simulation. But you are doing 10,000 simulation. I'm not sure there is a need to look in each simulation for the most efficient combination of tippers. The "tippers" will just emerge in the course of so many sims.

To say that Ohio WAS the tipping point state, I think misses the point that Paul Bradford made @July 10, 2008 9:55 PM. Flipping 40K voters efficiently in NM, IA, NV deny Bush a victory "more efficiently" than flipping 136.5K OH voters.

To summarize, in Version 1.x You looked for what state put the WINNER over the top. But I gather really what we want to know is what states the LOSERs needed to flip in a simulation in order to win. Hence, V 2.x.

So you need to order not by percentage closeness by number of votes closest. But that then might put DC and WY into play.
Solution:
Chop out the tails of safe Dems and safe Republicans learned from looking at totality of the simulations which gets rid of DC, HI, CA, UT, WY, etc. Then it doesn't matter about cutting out landslides.

Then order the left over middle by closeness of number of votes needed to flip.

Then flip until the winner is no longer a winner.

Two tables/maps one for each candidate.

Finally, separate out wheat from chaffe.

written as usual in haste without proofreading.

信次 said...

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平平 said...

^^ nice blog!! ^@^

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平平 said...

^^ nice blog!! thanks a lot! ^^

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酒店上班請找艾葳 said...

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