prior probability

This classic is from the July 5, 1993 issue of The New Yorker.

Answers are below the fold:

Or just clickbait?

“Half of the pandemic’s unemployment money may have been stolen.” That is the title of this recent report by Felix Salmon for Axios, but the only evidence in support of this increduble claim is a statement by Blake Hall, the CEO of ID.me, who says that “America has lost more than $400 billion to fraudulent claims” and that “as much as 50% of all unemployment monies might have been stolen.” I would not be surprised if unemployment fraud were rampant, but this is pretty weak evidence.

You cannot make this shit up! I found the following message waiting for me in surprise (see screenshot below) when I recently re-activated my Facebook page in order to get into my Expedia account:

So, Facebook’s algorithms are censoring legal history papers now? My paper “Domestic Constitutional Violence,” available here via SSRN and which I presented in 2018 at a special symposium at the University of Arkansas at Little Rock, surveys a series of laws enacted by Congress, beginning with the Militia Acts of the mid 1790s, authorizing the president to use military force inside the United States. Suffice it to say I not only closed my Facebook account for good; I went ahead and deleted it!

One week ago, Tyler Cowen, the prolific co-author of the popular “Marginal Revolution” blog, published this odd post on “The IRS tax data leak.” Instead of engaging the merits of these damning allegations — the fact that many of the most wealthiest Americans are self-righteous hypocrites who game the tax system in order to avoid paying their fair share of federal taxes — Cowen decided to dwell on the “ethics” of the data leak. Among other things, Cowen concluded that “ProPublica acted unethically, and in fact nothing fundamentally new or interesting or surprising was learned from their act as accessory.”

Let us assume for the sake of argument that Cowen is right, that ProPublica somehow acted unethically by publishing private tax data and that nothing new was learned from these sordid revelations. (Put aside the fact that Cowen, like most commentators calling for greater ethics, never bothers to share with his readers what theory of ethics was in play here. Virtue ethics? Duty Ethics? Consequentialism?) Even so, Cowen is committing a version of the genetic fallacy. Instead of questioning the ethics of our perverse tax system itself, Cowen chooses to focus on the illegal provenance of ProPublica’s data. Sorry, but no dice …

On the contrary, a strong case can be made that ProPublica’s exposé, by revealing how little U.S. billionaires pay in taxes and by exposing their rank hypocrisy, was highly ethical–under whatever theory of ethics you prefer. After all, what ProPublica did was to reveal the truth, and how can transparency and truth ever be inconsistent with ethics? Furthermore, although I already knew that companies like Amazon pay little in taxes, I did not know, contra Cowen, that Jeff Bezos–the richest man in the world–pays little in taxes. Also, thanks to the N.Y. Times, I knew Donald Trump paid only $750.00 in federal income taxes in 2016; I did not know that Elon Musk paid $0 in 2018! So, don’t lecture me about “ethics”!

On this day (June 14) in 1959, the Disneyland Monorail System, the first daily operating monorail system in the Western Hemisphere, opened to the public in Anaheim, California. Via Wikipedia, here are some facts and figures about Disneyland’s original monorail system:

• Grand opening: June 14, 1959
• Designer: WED Enterprises
• Three trains: Mark VII Red, Mark VII Blue, and Mark VII Orange
• Max train cars on beam: 3
• Track length: 2.5 miles (4 kilometers)
• Ride duration: 10 minutes, 30 seconds
• Coupon required (originally): “E”
• Ride system: Each train was propelled by six DC electric motors mounted in articulated powered trucks shared between cars, not just the lead car.
• 1959 construction costs of the entire system averaged over $1 million per mile (>$620,000/kilometer)
• Oversized ceremonial scissors failed to cut the ribbon during the televised opening ceremony, so Walt simply tore it

Alternative Title: Review of Robert Sanger, “Gettier in a Court of Law” (Concluding Post)

Alternative Title #2: The Irrelevance of Gettier Problems (with Apologies to Linda Zagzebski)

I want to conclude my review of Sanger’s Gettier paper with the following observation: Truth is not some binary value — i.e. a belief is not either true or false — but rather truth comes in degrees. In a word, truth is often probabilistic.

This unorthodox idea is often referred to as “degrees of belief” or “credences” and is associated with Bayesian epistemology a/k/a “subjective probability”–a topic that I have explored in some of my previous posts; see, for example, here and here. (This approach to truth can be traced back to Frank Ramsey and Bruno de Finetti; more recently, one of the leading contemporary exponents of this approach was Richard Jeffrey; see here.) Stated simply, a credence or degree of belief formally represents the strength with which we believe the truth of various propositions. Stated simply, the higher one’s degree of belief for a particular proposition, the higher one’s confidence in the truth of that proposition. In other words, beliefs may vary in degrees of strength or weakness–beliefs may come in shades of grey–or put another way, beliefs are not binary, are not all or nothing. Instead, my belief in a given conspiracy theory, for example, may range anywhere from 0 to 1.

Before proceeding, I now want to pose two further questions about the idea of degrees of belief. One is definitional. To the point: what is the difference between a plain and simple “belief” and a Bayesian “degree of belief”? In particular, is there some threshold or cut-off point (say, .9 or .95 or .99) above which a degree of belief acts like a full-fledged belief? The other question is logistical in nature. Specifically, when we are engaged in human reasoning, are our degrees of belief “infinitely precise real numbers”–e.g., exact numerical values ranging from 0 to 1–or “something less precise”–e.g., high, medium, and low? In other words, can a degree of belief really be expressed in precise numerical terms, and if so, how? (This second question is especially delicate because, if it turns out that, for whatever reason, we cannot assign a precise numerical value to a degree of belief, how can we transpose the axioms of probability into the Bayesian “subjective probability” framework? See also the entry for “Imprecise Probabilities” in The Stanford Encyclopedia of Philosophy.)

Putting aside these subsidiary questions (for now), the main question is, What do “degrees of belief” have to do with the things we have been talking about in our previous posts in this series, such as Gettier problems and photographic evidence, such as the picture of the sheep-dog in Sanger’s case of the negligent shepherd or the Zapruder film of the JFK assassination? In brief, two key conclusions or points flow from the idea of subjective probability or degrees of belief. One is that Gettier problems are often an irrelevant sideshow. Why? Because we cannot always determine whether a belief is true or false, except in the simplest or most trivial cases–like the number of coins in someone’s pocket (Gettier’s example) or the presence of a sheep in a field (Sanger’s example). In difficult cases, like whether Lee Harvey Oswald acted alone, or acted at all, in JFK’s murder, our beliefs are probabilistic.

The second conclusion is this: even if Errol Morris is correct to conclude the “photographs [and film clips] are neither true nor false” or “have no truth-value,” my Bayesian reply is, “So what?” Truth is often probabilistic anyways, not a binary or all-or-nothing value. Whether the photograph or film clip weakens or even falsifies our beliefs–shows that our beliefs might be or are, in fact, false, as in Sanger’s sheep-dog example–or whether such evidence supports our pre-existing beliefs, either through confirmation bias or because our beliefs are indeed likely to be true, the main point is that a photograph or a film clip can change, either up or down, our degrees of belief.

I am interrupting my series on Sanger’s Gettier paper to share this New Yorker cartoon. Benjamin Franklin, among others, is reported to have said, “… in this world nothing can be said to be certain, except death and taxes.” Shall we now add “emails” to this list of unavoidable horribles?