In another edition of how misunderstanding statistics can lead to misleading political predictions, let’s talk about base rates, predictive power and presidential re-election. In psychiatry, there is a fun logical problem in which students are asked to generate an instrument that will accurately classify people with and without schizophrenia in a sample of the population. Students draw up elaborate series of questions and diagnostic procedures and sometimes do as well as being right 95% of the time. But those approaches are all inferior to a different diagnostic system, which classifies all people as non-schizophrenic without bothering to ask them anything. Because only 1% of people have schizophrenia, such a system is correct an impressive 99% of the time. When you are trying to predict something with a very low base rate, most of the time you make a positive prediction (e.g., this person has schizophrenia) you will be wrong, and most of the observations you make about the group for which you make a negative prediction (e.g., this person doesn’t have schizophrenia) will be true but have trivial predictive power because they are true of almost everyone.

Now consider a far more rare condition than schizophrenia: Being elected President of the United States. Only 43 of the hundreds of millions of people who have been U.S. citizens have been President, and an even more infinitesimal fraction of the U.S. population has been re-elected President. This incredibly low base rate opens the field for many predictions that seem on their face to show great historical understanding and political acumen but are in fact of dubious value.

For example, do you remember that George H.W. Bush was not going to get elected because no sitting Vice-President had been elected President since Martin Van Buren? At that point, 39 people in U.S. history had been elected President, of whom 3 were sitting Vice-Presidents. This success rate compares very favorably to the chance of the average American, or the average politician or even the average politician seeking the Presidency. It would have been more reasonable to say that as a sitting Vice-President George H.W. Bush was unusually well-positioned to be elected President.

The G.H.W. Bush prediction also illustrates another tactic of faux-sage prognosticators, namely shaping the frame of reference to make the statistic more extreme. The U.S. had elected and re-elected former Vice-President Richard Nixon in living memory, so the ominous G.H.W. Bush statistic was artfully limited to “sitting” vice-presidents. And the time frame was chopped off at Martin Van Buren to misrepresent the full picture of U.S. electoral behavior; two other sitting Vice-Presidents had been elected before MVB. It’s a bit like saying Rick Perry cannot win because for the first 223 years of our history no Governor of Texas ever became President.

Fast-forward to President Obama, whom you may have heard cannot win in 2012 because no President has been re-elected with high unemployment. After it was pointed out that FDR and Ronald Reagan were both re-elected with high unemployment, the shocking historico-statistical proof of Obama’s political demise was re-framed to “No President since World War II other than Ronald Reagan has been re-elected with high unemployment”. But so what? Only 5 people have been twice elected President since World War II, and an infinite number of things is true of all the people who haven’t.

No one who wasn’t from California, Texas or Arkansas has been re-elected President since World War II (Doom for Obama!). No one whose last name starts with an O has been re-elected President since World War II (Double doom!). No one who was African-American has been re-elected (Triple Doom! Hey wait a minute, how did he get elected the first time…he was African-American then wasn’t he?). At least President Obama can take comfort in the fact that every single left-handed President who ran for re-election since World War II has won, as long as you don’t count George H.W. Bush.

[Cross-posted at The Reality-Based Community]

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Keith Humphreys

Keith Humphreys is a Professor of Psychiatry at Stanford University and served as Senior Policy Advisor in the White House Office of National Drug Control Policy in the Obama Administration. @KeithNHumphreys