There are many things about which we don’t know much, but that ignorance doesn’t stop us having an opinion
An indoor swimming pool. The smell of chlorine in the air is palpable, and the kids are coughing. You’re not the only person to notice, and another parent asks what you think an acceptable concentration of chlorine in the air should be. You take a wild guess: “4ppm?” The other person seems to be in the know: “It’s 2ppm now,” she says. “Oh, then it should be less,” you state.
There doesn’t seem to be anything amiss with this conversation. You are not a chemist or a health and safety expert, so you had no real idea. You nevertheless gave an opinion based on your superficial knowledge about concentration levels of noxious gases, offering a vaguely plausible number. If you had had to estimate how much chlorine there actually was in the air, you’d probably have suggested something like double your guess at the acceptable level.
Equivalent or perhaps not so equivalent
Now picture a very similar conversation about a different subject: taxes. You ask a friend, if the total personal income tax revenue is 100%, what proportion of that would be acceptable for the top 1% earners to pay. “20%”, she says. Asked how much she thinks they actually contribute, she ventures a guess that it’s something like 5%. You have of course looked up the correct figure, and reveal to her that it is close to 40%, and then ask again, what proportion of total income tax revenue would be acceptable to be paid by the 1% highest earners. “Oh, a lot more than 40%,” she answers.
These two dialogues are formally entirely the same. The first data point is an estimate of an acceptable value for a given variable (chlorine concentration — “4ppm”; proportion of income tax paid by the 1% highest earners — “20%”). The second data point is an estimate of the actual value (implied in the pool conversation at 8ppm, and 5% in the tax discussion). Next is the revelation of the actual value (2ppm and 40%).
Crucially, these values turn out to be ‘better’ than the acceptable value as initially estimated: 2ppm is lower than 4ppm, and 40% is higher than 20%. Yet at that point, the reaction is not to say, “Great!”, but to reject the original estimate for the acceptable value, and demand a more extreme one even than the actual value ( even less chlorine, even more tax).
The uninformed opinion about what would be an appropriate value would be was adjusted once the real value — more extreme than the initial estimate — was revealed. That may seem strange, but there is, in principle, nothing unusual about updating one’s estimate about an unknown variable when more information emerges.
Imagine, for example, that you are visiting a friend in a part of the country you don’t know well. You are walking through a street with some sizeable houses. As you pass a particularly impressive mansion, your friend says that it recently sold, and asks you to guess at what price. “£700,000”, you venture. He then tells you that an average house in this street is valued at £1 million. It is then perfectly sensible to update your original estimate to, say, £1.5 million, because you have learned something about the price distribution that you did not know before — your opinion will be more informed.
But is that also true for the discussion about the tax? Here are two other equivalent conversations. Two colleagues are discussing a court case. Alex has just described the crimes that the perpetrator committed and asks Chris what sentence he should get as a punishment. Chris ponders for a moment, and suggests, “12 years”. Alex then says that he was sentenced to 15 years, upon which Chris says, “In that case, it should have been 20 years.” Some time later, we find Alex and Chris at the watercooler again and Chris, who went out for a meal with her team the night before, asks Alex what proportion she should have covered of the total bill. “I’d say a third would be adequate”, says Alex. “I actually paid half of the bill”, Chris says. “Oh, I think you really should have paid two-thirds”, Alex concludes.
Two kinds of ignorance
There is something odd about these conversations. In the anecdotes at the chlorine-rich pool and the expensive street, there was an objective, but unknown norm (the safe concentration, and the average price). When that became known, it was perfectly logical to update the estimate accordingly. You knew that the chlorine concentration was too high, so whatever the current level was, the safe limit would have been lower. You knew the large house was larger than average, so learning the average price allowed you to update your guess.
But when it concerns prison sentences or the proportion of the bill for a meal that a team leader should pay, there is no such objective norm to be determined. There is only a personal, subjective opinion — and that seems to be rather a movable feast: one gets the impression that it is never enough.
Is that the case for the discussion on taxation too? Not necessarily. Someone might be of the opinion that the current tax revenue is insufficient to properly fund all the public services they think are essential, and that the people who earn the most should contribute more. If they believe that the tax revenue should be 20% higher, that the 1% top earners should provide that extra revenue, and that they currently contribute 5% to the total, then their guess that they should contribute 20% is about right (5+20/120 = 21%). If they are then told the actual contribution is 40%, it should be increased by a quarter to 50% to meet their desired 20% revenue increase (40+20/120=50%).
Few people think that way, though, and it is more likely that the thinking is more in line with the “never enough” viewpoint of the slippery subjective norm. And that is indicative of a different, and altogether more pernicious kind of ignorance. It is perfectly acceptable to have an uninformed opinion, and update it when you obtain more information (as in the pool and the house anecdote).
But someone who maintains the view that it ought to be ever “more (or less) than whatever it is now” not only signals they will never be satisfied, but also exhibits an ignorance of the trade-offs that is not rectified with new information. For whether it concerns prison sentences, taxation or even the boss’s contribution to a dinner with the team, the unlimited escalation of the key variable will have other consequences. Wilfully ignoring these might be allow for some pompous posturing, but intelligent reasoning it is not. There are always trade-offs.
So, if you have to be ignorant, make sure it’s ignorance of the right kind.
(This article was inspired by a Twitter thread started by Shane Frederick, a Decision Scientist at Yale University’s School of Management, and several others, including Daniel Read, Oleg Urminsky, David Hagmann and Alex Imas. The conversation about taxes paraphrases real ones in this clip.)
Originally published at http://koenfucius.wordpress.com on April 30, 2021.
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