SSC re-invents Hume

“…no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavors to establish”
— David Hume
— An Enquiry Concerning Human Understanding, 1748
— (I can’t find said direct quote in google books, but I agree this is the gist of the matter)

“So. Alternate hypothesis. About one million people view Reddit every day. Let’s assume 10% of those see threads like the above – which were pretty popular and which I think both made it to the front page. That’s 100,000 people. Now let’s assume that even 1/10,000 people on the Internet are annoying trolls, which is maybe the easiest assumption we’re ever going to have to make. If each of those annoying trolls posts one fake story to a thread like that for the lulz, that’s enough for ten really convincing stories per thread – which is really all there are, the other fifty or sixty are just the usual friend-of-a-friend-had-a-vague-feeling stuff.”
— Scott Alexander
— Slate Star Codex: Redditors Lie?
— (Since Moldbug retired, Scott might be the most verbose guy on the internet)

It’s all part of the same problem.  (Warning, Math):

If a drug researcher discovers a drug which has an effect at p<0.001, what are the odds it was a fake discovery?

Of course, the answer is “Not enough information”

But you can’t do a real calculation until you figure out how likely the drug really is to work.
The real decision matrix requires a comparison of how likely something really is to be true, vs how likely it is to be measured true, when false.

If drugs are effective 1/2 the time, and the test is only wrong 1/1000 of the time, then odds that the drug works are pretty good.   Start with 2000 drugs, and here’s what happens

 2000 works doesn’t work
tests true  999  1
tests false  1  999

Look, there’s 1000 cases where the drug tests true, and only one of them is a mistake.  The odds of the drug working, once it tests at p<0.001 is 99.9%

But that’s not the reality.   Far less than 1/2 substances are effective towards our goals.   If we instead suggest that only 1 in a Million drugs are effective towards a goal, then the numbers look very different.   Start with a billion drugs, and here’s what happens

 1,000,000,000 works doesn’t work
tests true  999  999,999
tests false  1  998,000,001

Look, there’s 1,000,998 cases of drug testing true, and only 1 in 1,000 of those is actually true.   Think about that.   If a drug has a prior probability of 1/1,000,000 of being effective, than a test that tells you it is effective with p<0.001 is wrong  1,001/1,002 times.  Prior probability matters.  Prior probability overwhelms the measured probability an awful lot of the time.

At the end of Scott’s piece, he asks: “If you’re like me, and you want to respond to this post with “but how do you know that person didn’t just experience a certain coincidence or weird psychological trick?”, then before you comment take a second to ask why the “they’re lying” theory is so hard to believe. And when you figure it out, tell me, because I really want to know.”

And this is where it gets interesting.   This means that to a first approximation, people’s approach to accepting evidence if they already agree, and dismissing it if they don’t already agree is the rational thing to do.    Does “XYZ study on climate change” change your opinion on climate change?   Odds are strongly no.   If you agree, you now have extra evidence, and you hold the same opinion.    If you disagree, then you dismiss the study as probably being wrong, and don’t change your opinion.    AND this is the smart thing to do. In the short term, anyhow.

In the long term, I continue to insist that the smart thing to do is hold low certainty levels. If new information comes out, update a little bit.   But that’s hard to do.    And odds are the other side is trying to get you to change your mind regardless of the truth.   But still, low certainty levels and actual updating are the best answer I’ve run into.

On the separation of powers

These United States were founded upon a complex balancing act.   Individual rights were a paramount concern at the time of the founding, but it was well understood that any concentration of authority would push against individual rights.   And so the government was set up in balance, with various power centers competing against one another.    The only part of the balance of power taught in the schools this last 35 years (what I remember) is the balance between the Legislative, Executive, and Judicial branches.   However, that wasn’t the only balance built into the foundation of the country, nor even the most important one.    The primary balance built into the founding of this country was the balance between the federal government and the states.

Without taking away from the American Revolutions of 1776, 1860, and 1933, I’d suggest that we start our discussion of the Revolution of 1789, and the enumeration of separated powers there.

In the re-revolutionary US Constitution of 1789, there were a lot of balancing powers built to prevent either the federal government or the states from achieving too much power.

  1. Secession.  The states are understood, much like the colonies, to have the unilateral right to secede from the union.  “When in the Course of human events it becomes necessary for one people to dissolve the political bands which have connected them with another and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature’s God entitle them …”.   When membership in a federation is secession-prone, the federal government may not push too harshly.    This balance was removed in the revolution of 1860.
  2. Taxation.  The Federal government is explicitly prohibited from taxing the citizens directly.  It may only tax the states, and only by headcount.  A dependency upon the states for funds is, after fear of exit, the single largest constraint on a central federal system.   This balance was removed in 1913.
  3. The Senate.   The Senate was constructed explicitly for the purpose of disallowing large populous states from pushing their Agenda unilaterally upon less populous, but still understood to be independent smaller states.
  4. The Electoral College.  Again, the choice of the president is not understood to be by the population, but rather by the states.   One or two large pushy states should not be able to centrally enforce their agendas upon the rest of the country.
  5. The Senators.  The original Senators were appointed by the states’ governments to the Senate, providing a strong voice for the states’ interests in the federal government.   This balance was removed in 1913 as well.
  6. Enumeration of Powers.  The constitution explicitly lists the powers of the federal government.     Article I, Section 8 enumerates legislative authority.   Article II, Section 2 enumerates executive authority.   Article III, Section 3 enumerates judicial authority.   As far as I’m able to tell, this limit on the enumerated powers of the federal government died in 1937, with Parrish.
  7. Original Amendments.  The 9th and 10th Amendments to the United States Constitution were both built in order to further remind the federal government that nothing except what was explicitly included in the constitution was in the scope of federal power.  Again, it seems to me that this died in 1942 with Wickard.
  8. Amendment Process.  The Constitution may be amended by a majority of the states.  The states may propose an amendment, and then the states may ratify it.

Overall, there were at least eight elements built into the fabric of the federal government for the purpose of balancing the states’ power against that of the federal government. There are still four three [ed: oops]left.

Now, you may be wondering what I think about proposals to drop the electoral college in favor of a national popular vote.   That is left as an exercise for the reader.