Strange Comparisons

Today I am going to discuss something I find confusing, not because it is confusing but because so many people don't seem to understand it. To see what I'm referring to, look at this tweet:

If you follow the climate debate, you've likely heard this claim before. Part of the global warming debate is figuring out how much influence humans are having on the planet's temperatures. This tweet shows a "mainstream" position, that humans are causing all of it and more. You can find this argument posted in many locations. For one example, you can look here to see an argument humans might be causing as much as 160% of global warming.

I'm not going to delve into that today. People are so polarized on climate issues it seems most people will agree with you if you're on their "side" and disagree with you if you're not. I want to avoid that trap. I want to avoid it because what's wrong with that argument has nothing to do with climate or how it might change. It's entirely about logic and forthrightness.

Put simply, it is nonsensical and misleading to say humans have caused 110% of global warming just as it would be nonsensical and misleading to say Black people caused 894% of Hillary Clinton winning the popular vote in the recent United States presidential election.

You might be wondering what a presidential election has to do with how much humans contribute to global warming, but before I explain, I should point out all results in this post are based on provisional vote counts and estimations. Official, final numbers are not available yet. That said, the unofficial estimates I have say the results are:

Donald Trump		61,500,332
Hillary Clinton		62,842,333

This gives Clinton a 1,342,001 lead in the popular vote. Due to how American presidential elections work, Clinton lost despite that lead, but it is still a sizable lead. People are spending quite a bit of time looking at why she got it despite losing the election. In today's post, I'll try to help those people by showing the contribution to that lead from African Americans was 1040%.

(I hope those people will remember Trump has condemned the American Electoral College in the past for not reflecting the popular vote, going so far as to call it "a disaster for democracy" and calling for a "revolution" when he thought Barack Obama lost the popular vote but won the 2012 election anyway.)

That number may seem a bit difficult to believe. In fact, it might even seem nonsensical. It's fairly straightforward math though. Approximately 16 million black people voted. Of them, approximately 12 million voted for Hillary Clinton and ~1,200,000 voted for Trump.

That means ~13,400,000 more black people voted for Clinton than Trump. If we remember Clinton's lead was estimated as only ~1,342,001, we can do some simple math and find out:

12,000,000/1,342,001 = ~8.94 = ~894%

Simple math, right? African Americans contributed 1040% to Hillary Clinton winning the presidential elections. This is the same reason we can say humans cause 110% of global warming. I'm not going to use exact numbers, but the idea is:

1.1C/1C = 1.1 = 110%

Where we've seen 1 degree Celsius of warming but would expect to have seen 1.1 degree Celsius of warming (again, not the real numbers). The math works out the same whether we use the planet's warming (with warming and cooling influences) or the outcome of a presidential vote (with Clinton and Trump votes).

Do either of these results make sense? I would argue no. They are mathematically valid. If you present them with the necessary caveats and additional information, they may even be useful. They are nonsensical and misleading if you present them on their own though. To understand why, consider the influence Asian voters had on Clinton winning the popular vote.

Approximately 5.25 million Asians voted in the presidential election. Of them, approximately 3.4 million voted for Clinton. Approximately 1.5 million voted for Trump. That means ~1.9 more Asians voted for Clinton than Trump. Do some simple math:

1,900,000/1,342,001 = 1.42 = 142%

And bam! Asians contributed 142% to Clinton winning the popular vote.

What if instead of looking at ethnicity, we looked at religion? Approximately 4 million Jews voted. Of them, ~~2,800,000 voted for Clinton while ~950,000 voted for Trump. That's a difference of ~1,850,000. The math says:

1,850,000/1,342,001 = 1.38 = 138%

Jewish people contributed 138% to Clinton winning the popular vote! They can't hold a candle to the atheists though. For atheists, the math shows:

8,400,000/1,342,001 = 6.26 = 626%

Atheists contributed 626% to Clinton winning the popular vote! With numbers like these, how could Clinton possibly have lost?!

Because this "math" is nonsensical and misleading. Maybe you can properly break down all the demographics of voters in the presidential election, add up all the percentages you get via this "math" and come up with a total of 100%. Maybe you could add in a bunch of large negative percentages for white people, Protestants and other groups that favored Trump over Clinton. Maybe doing so would ultimately tally up to the right answer, that in total, the number of votes cast for each candidate caused 100% of the difference in the votes each candidate received.

I hope you could. Mathematically, that should work. Nobody will do it though. It's a ridiculous amount of work to come up with numbers that have no meaning.

What if it turns out the current estimates of votes are wrong and Clinton only wins by 1,000,000 votes? Every percentage calculated above would go up. It's the same if we redid out estimates of global warming and found there has actually only been .8 (instead of 1) degrees Celsius because natural cooling influences had had more impact than we had thought. Our math would become:

1.1C/.8C = 1.375 = 137.5%

Note, The actual human influence on the planet's temperature in this calculation is the same as before. Humans still had an influence of 1.1 degrees of warming. The only difference is what influence non-human factors had. This math shows the percent contribution of humans to global warming can increase even if we keep the actual human contribution to global warming constant.

Mathematically, that is valid. It's just how percentages work. If there's a period of time in which humans exert an influence of .3C of warming but there is only .15C of warming due to natural influences like volcanic eruptions, the percent contribution from humans is:

.3C/.15C = 2 = 200%

Humans contributing 200% to global warming sounds dramatic. It's nonsense though. If nature had a cooling influence in this scenario in stead of a warming influence (with the magnitude kept the same), we would find:

.3C/.45C = .67 = 67%

This is the "math" used to show humans have contributed 110% to global warming. It's nonsense. Absent information about how much total warming (or how many total votes were cast), these percentages tell us nothing. Saying humans have contributed 110% to global warming is utterly meaningless on its own.

There is even a parallel to how the Blacks, Jews and whatnot vote. Consider this figure from the 2007 Intergovernmental Panel on Climate Change Report:

Take note of how there are a number of different factors displayed as contributing to the "Radiative Forcing." That forcing is (in simple terms) what causes the planet's temperature to change. In the presidential election, it is like the difference between the number of votes Clinton and Trump received. What percent contribution do you think each of those factors has on global warming?

I'm not going to do the math. There are more detailed (and more up-to-date) sources we could use if we wanted to do the math, but there's no point. Just eyeballing that chart is enough to see anthropogenic carbon dioxide is causing ~105% and methane ~30%.

If we broke down all the possible influences on the planet's temperature, both natural and anthropogenic, we might find the absolute values add up to 2000%. Maybe it'd be more. I don't know. What I do know is without real numbers, any percentage we might give is meaningless.

Are the numbers used to claim humans are responsible for 110% of global warming correct? I don't think so. I think there are a number of issues with them. That doesn't matter for any of this though. Whether this math says human s contribute 110% to global warming or Jews contributed 138% to Clinton winning the popular vote, it is meaningless.

What matters is how much warming there has been over any given period of time and how much of a warming (or cooling) influence humans have had. If the planet has warmed by 1 degree that is what people should say. If humans have contributed 1.1C of warming influences, say that too.

Only after having done so should anyone say humans have contributed 110% to global warming. It's okay to use that number as shorthand once you've made it clear what it means. If you don't provide that information and the appropriate caveats, a person could easily say:

Yup, I agree. Humans have caused 110% of global warming. I don't care though. After all, the planet has only warmed a hundredth of a degree. What do I care if humans have caused 0.011C of warming?

They'd be wrong, but they wouldn't be any more wrong than the people who grossly over-simplify complex problems to give tidy results like, "Humans have caused 110% of global warming."


  1. I don't dispute your argument but are you sure ".3C/.15C = 3" ? Must be this new maths I heard about.

  2. There is an even bigger problem: the whole forcing accounting thing only counts man-made forcings. I'm sorry if I'm repeating myself as I made a very similar comment on a thread about paleo sensitivity, but the thing is nobody knows what are the natural forcings, except for volcanoes and solar radiation. Since these other influences or forcings cannot be quantified, in practise they are ignored.

    Most obviously we don't know what the clouds would be doing (or would have done) in the absence of human influence. Hell, we barely know what they *are* doing in the real world, under our influence. Apart from the clouds you have the oceans' currents, cosmic rays, changes in surface albedo which might lead to changes to changes in water vapor, ozone and what not... now, most of these things may change very slowly, but if you're trying to 'attribute' a change of 1ºC over a century, you cannot simply dismiss them.

    To say that 'attribution is a nearly solved problem' is ludicrous on its face.

  3. Chris Morris, thanks for catching that. I had originally used different numbers, but I decided they were more extreme than I wanted so I changed them at the last minute. Apparently I rushed the changes and messed up the math. I'll get that fixed.

    Alberto Zaragoza Comendador, I do think the stated certainty in regard to various forcings (and even just our knowledge of what forcings exist) is exaggerated. I'd criticize this sort of "math" even if I didn't feel that way though. This is something we should all be able to agree on whatever we think about global warming.

    For instance, this sort of "math" let's us say something like, "Carbon dioxide causes more than 75% of global warming."* The reasons is if you take the forcing caused by CO2 and divide it by the total forcing, you'll come up with a number greater than 75%. Yet, if we actually look at the budget, CO2's contribution to anthropogenic forcings is listed as well under 75%. Clearly, that "math" is misleading.

    *Like with the post, I am treating radiative forcing as the sole cause of warming. I get feedbacks do exist, but they only amplify the effects of changes in radiative forcing. As such, I think this is reasonable.

  4. (I hope those people will remember Trump has condemned the American Electoral College in the past for not reflecting the popular vote, going so far as to call it "a disaster for democracy" and calling for a "revolution" when he thought Barack Obama lost the popular vote but won the 2012 election anyway.)

    Of course. The loser almost always wants to change the rules. But the Electoral College was a rather ingenious compromise that brought some balance to the power differences between small and big states. It also put a buffer between the populace and the election of the president that was meant to counter the effects of manipulation of the passions of the citizenry by a demagogue. With this election and it's aftermath we can see how passions are so easily inflamed.

  5. Gary, I'm personally opposed to the Electoral College system, but that's mostly for unusual reasons. For instance, I think the idea of "faithless electors" (members of the Electoral College who vote contrary to the vote of their state) is creepy. In theory, you could bribe, blackmail or threaten enough members of the Electoral College to swing an election. I don't think it'll ever happen. I don't think faithless electors will ever cause the "wrong" candidate to win. I just think the idea they could is messed up.

    There are other reasons I dislike the Electoral College (including mathematical ones), but I don't think people would be very interested in them.* The thing I do think people should find interesting is how opposed Donald Trump was to the Electoral College system in the past, both when he thought it would give Obama the win over Romney (because Trump was dumb enough to believe Romney had won the popular vote when he hadn't), and when it looked like it might give Clinton the win.

    I think it's pretty interesting for the President Elect to basically go, "The Electoral College system sucks! It's undemocratic! It's a rigged system! It's a fraud! It... gave me the win? Oh, uh... the Electoral College system rules! It's genius!"

    *If people would like to hear them, I'd enjoy discussing it. While I think the original compromise to balance state powers was wise, I think there were a lot of problems even then. Some are obvious, like poor people, women and slaves not getting to vote. Others are less obvious. One of the issues I find most intriguing (and worrying) is how using Electoral College is impacted by the decision to stop creating new seats in the House of Representatives. It even involves some fun math... if you're a nerd like me.

  6. Brandon, a restricted franchise (limiting who is qualified to vote) is a separate issue from the EC. Another is the cap on the number of electors. Both deserve some contemplation and debate -- but only for solving deficiencies and not making them weaker. I'm on the side of making it harder for government to change how it's organized. It's much too powerful a tool for those who want to use it to their advantage. Inertia when it benefits the personal autonomy of the citizenry is good.

  7. I know it's not relevant to your point, but lots of these numbers are off.

    13.4 M /1.342 M can't be over 10, for example.

    Not sure where you are getting Trump at 600K blacks out of 16 M, which is <4%. Exit polls say 8%, and I suspect it's higher given Hillary's share.

    I like the 110% number. It means that without humans, we would be having the global cooling they predicted.

  8. MikeN, I'm not sure I'd say a lot of the numbers are off. So far, people have pointed out two. The one you pointed out was even sort-of corrected in the post. Note, the post says:

    13,400,000/1,342,001 = ~10.4 = ~999%

    I had gone back and checked the numbers, and I realized I had forgotten to subtract off the 600,000 votes Trump got. I redid the math, and I got 9.99 million. I corrected the final result in the post, but I forgot to update the intermediary number as well. I've fixed that now.

    That said, I think Trump might have gotten 8% while I used the 4% the "other" candidates got. I'll have to check. I normally put more effort into the math I post but given the results are completely irrelevant, I'll admit I was lazy.

  9. Gary, the Electoral College isn't as divorced from franchisement as you suggest. Democracy wasn't as big a focus in the country's earlier days. Back then, people's votes didn't matter that much. The Electoral College was one example of why. Another example is the Senate. The Senate wasn't intended to be elected by the people. Senators were elected by state legislatures for over 100 years. The idea there, like with the Electoral College, was people shouldn't have much direct influence on the national government.

    The Electoral College was created partially to (try to) balance power between the states, but it was also created in order to further restrict who had influence over the national government and how much influence they would have. Remember, the Constitution doesn't even say people get to vote for their representatives in the Electoral College. It was up to each individual state to decide how their electors would be chosen.

    The Electoral College system made it so states could completely deprive their citizens of any direct say in the presidential (and vice-presidential) election. When the "winner-take-all" approach of giving all electoral votes to whoever won a state was first adopted by several states, architects of the Electoral College system protested in part because that approach disenfranchised people. (Removing the independence of the electors and forcing them to pre-pledge votes was a bigger issue to them.)

    Ultimately, the Electoral College system has involved the disenfranchisement a great deal of people throughout the nation's history. Some it disenfranchised directly, others it did so indirectly (e.g. by being part of a system which prohibited women from voting). On top of that, the Electoral College system we have today is practically nothing like what the plans for it were when the compromise to (try to) balance state powers was struck.

    Speaking of which, this is one case where the Constitution being a "living document" doesn't seem to bother anybody. While plenty of people complain about the Electoral College, I've never heard anyone say they want the Electoral College to exist but only in the form the Founding Fathers intended. I suspect many "conservatives" would hate the idea of electors actually being independent voters who could make up their own minds even though that's exactly what electors were supposed to do.

  10. Alright, I checked the polling data I had used for these numbers, and it turns out I did swap the Trump and "other" voters for the Black vote. I've updated the post to correct the results. It has nothing to do with any conclusion of the post, but I do regret being lazy enough to allow such errors to slip into the post. Thanks to the commenters who caught them for me.

    For what it's worth, I checked the rest of the numbers and calculations in this post. They all seem correct. I think you guys have caught all my errors. If not, feel free to point any more you find out.

  11. Brandon, I agree with much of what you state about the EC. The crucial point, though, is that the states get to decide how their representation works. This provides for the "living document" element without destroying the original intent. Maybe not perfectly, but a workable compromise of competing interests. Ultimately, each state's solution to the question of how to deliver its EC votes will be controlled at some level by its citizens and their sense of balance and fairness. It may take time to adjust to what they consider the appropriate level, but unbalanced systems tend toward an equilibrium.

  12. If anything, the system would lead to more imbalance. Amending the electoral college would require states to agree to deliver electoral college votes to candidates not selected by their residents. On the other hand, if there are large votes for a candidate in a small number of states, then it means the remaining states could pass an amendment against that.

  13. Gary, I don't think how states deliver their EC votes could ever be handled fairly in the current system. As it stands, a state's importance in the election process is determined by how many EC votes it can give to a candidate. Splitting votes across multiple candidates reduces the value of campaigning in that state. A reason states go for the "all or nothing" approach is it gives them more leverage. (There are a couple caveats here which I don't want to spend time on today given the holiday.)

    That said, I wouldn't even want that change to happen. If you care (a lot) about the Founding Fathers' original intent, then you should reject the idea of states assigning votes at all. The point of this system was to elect a group of people who would have would have discussions and debates then each cast their vote as they wished. Electors were meant to be free to make their own decisions. I've never seen anyone call for a return to that.

    Interestingly, part of the reason for this system's design was it wouldn't work in many cases. People who designed this system expected there to be too much disagreement for electors to reach a majority in many elections. The idea was when there'd be a tough election, the electors wouldn't reach an agreement and Congress would take over.

    If you go by the ideas that went into designing the Electoral College system, it's turned out to be a massive failure. It hasn't worked out at all like it was supposed to. Maybe that's for the better. I don't know. What I do know is what we have was neither planned nor designed. It's the result of a rather bizarre evolution.

    I guess given that, asking it to evolve a bit more wouldn't be unreasonable.

  14. MikeN, if I were going make just one change to the Electoral College system, I would probably say to make it where each state was divided up into districts which would each have their own vote.

    That was actually part of the plan when the system designed. It didn't take off (at least in part) because states felt they could get more influence and power by using a "winner take all" approach. That's unfortunate because it means states with widely disparate demographics can wind up with a sizable portion of their population having no say.

    Take, for instance, Illinois. Before I go any further, I want to point out Illinoi's 20 EC votes are for a population of approximately 13 million, or ~650,000 people per EC vote. That's far worse than a number of states, such as Wisconsin with a ratio of ~200,000 per EC vote. Just something I thought was interesting.

    Anyway, Illinois has been pretty much in the bag for any democratic candidate for quite a while because Chicago has ~3 million people in it. It dominates the state's results for every national election. It also has a very different culture than most of the rest of the state. The result is much of the area of the state has no voice in national votes. That's true for a number of states.

    If I were making a single change, it'd be to make a similar compromise at the state level as was made at the national level. The two votes given by Senate seats would be voted on by the population as a whole. The remaining votes would be determined by votes in a number of districts equal to the number of seats that state has in the House of Representatives.

    I'm not saying that'd be the best approach (it wouldn't be), but I do think it'd be a reasonable change.

  15. Your problems continue. You haven't even finished correcting your original errors, and then you post that the populations of ILL and WISC are
    about 13 million for 20 EV and 2 million for 10 EV, which doesn't seem at all likely.

  16. MikeN, it's a bit cheeky to say someone "hasn't even finished correcting [their] original errors" when you won't identify the supposed errors so they can be corrected. Regardless, nobody said anything about Wisconsin having 10 electoral votes. There is an error in that comment, but you do nothing to help identify it.

    It's incredibly easy to figure out what the error was. The ratio I referred to is determined largely by how large the population of a state is (due to Senate seats granting electoral votes regardless of population). Wisconsin's population is relatively large. That means it could not have a ratio like I described. Checking a list of the population of states would make it easy to see a state more likely to fit my description is Wyoming. Indeed, one can easily find charts showing the ratio I refer to for each state:

    That I mixed up two states starting with 'w' is a mistake, but I struggle to care about accuracy when people are going, "You won't fix these errors I refuse to identify for you!" I don't like making mistakes, but the amount of time or effort I care to put into anything does change with how obnoxious people are being.

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