I Was Not Almost Wrong But I Was Almost Right: Close-Call Counterfactuals and Bias

54 Kaj_Sotala 08 March 2012 05:39AM

Abstract: "Close-call counterfactuals", claims of what could have almost happened but didn't, can be used to either defend a belief or to attack it. People have a tendency to reject counterfactuals as improbable when those counterfactuals threaten a belief (the "I was not almost wrong" defense), but to embrace counterfactuals that support a belief (the "I was almost right" defense). This behavior is the strongest in people who score high on a test for need for closure and simplicity. Exploring counterfactual worlds can be used to reduce overconfidence, but it can also lead to logically incoherent answers, especially in people who score low on a test for need for closure and simplicity.

”I was not almost wrong”

Dr. Zany, the Nefarious Scientist, has a theory which he intends to use to achieve his goal of world domination. ”As you know, I have long been a student of human nature”, he tells his assistant, AS-01. (Dr. Zany has always wanted to have an intelligent robot as his assistant. Unfortunately, for some reason all the robots he has built have only been interested in eradicating the color blue from the universe. And blue is his favorite color. So for now, he has resorted to just hiring a human assistant and referring to her with a robot-like name.)

”During my studies, I have discovered the following. Whenever my archnemesis, Captain Anvil, shows up at a scene, the media will very quickly show up to make a report about it, and they prefer to send the report live. While this is going on, the whole city – including the police forces! - will be captivated by the report about Captain Anvil, and neglect to pay attention to anything else. This happened once, and a bank was robbed on the other side of the city while nobody was paying any attention. Thus, I know how to commit the perfect crime – I simply need to create a diversion that attracts Captain Anvil, and then nobody will notice me. History tells us that this is the inevitable outcome of Captain Anvil showing up!”

But to Dr. Zany's annoyance, AS-01 is always doubting him. Dr. Zany has often considered turning her into a brain-in-a-vat as punishment, but she makes the best tuna sandwiches Dr. Zany has ever tasted. He's forced to tolerate her impundence, or he'll lose that culinary pleasure.

”But Dr. Zany”, AS-01 says. ”Suppose that some TV reporter had happened to be on her way to where Captain Anvil was, and on her route she saw the bank robbery. Then part of the media attention would have been diverted, and the police would have heard about the robbery. That might happen to you, too!”

Dr. Zany's favorite belief is now being threatened. It might not be inevitable that Captain Anvil showing up will actually let criminals elsewhere act unhindered! AS-01 has presented a plausible-sounding counterfactual, ”if a TV reporter had seen the robbery, then the city's attention had been diverted to the other crime scene”. Although the historical record does not show that Dr. Zany's theory would have been wrong, the counterfactual suggests that he might be almost wrong.

There are now three tactics that Dr. Zany can use to defend his belief (warrantedly or not):

1. Challenge the mutability of the antecedent. Since AS-01's counterfactual is of the form ”if A, then B”, Dr. Zany could question the plausibility of A.

”Baloney!” exclaims Dr. Zany. ”No TV reporter could ever have wandered past, let alone seen the robbery!”

That seems a little hard to believe, however.

2. Challenge the causal principles linking the antecedent to the consequent. Dr. Zany is not logically required to accept the ”then” in ”if A, then B”. There are always unstated background assumptions that he can question.

”Humbug!” shouts Dr. Zany. ”Yes, a reporter could have seen the robbery and alerted the media, but given the choice of covering such a minor incident and continuing to report on Captain Anvil, they would not have cared about the bank robbery!”

3. Concede the counterfactual, but insist that it does not matter for the overall theory.

”Inconceivable!” yelps Dr. Zany. ”Even if the city's attention would have been diverted to the robbery, the robbers would have escaped by then! So Captain Anvil's presence would have allowed them to succeed regardless!”


Empirical work suggests that it's not only Dr. Zany who wants to stick to his beliefs. Let us for a moment turn our attention away from supervillains, and look at professional historians and analysts of world politics. In order to make sense of something as complicated as world history, experts resort to various simplifying strategies. For instance, one explanatory schema is called neorealist balancing. Neorealist balancing claims that ”when one state threatens to become too powerful, other states coalesce against it, thereby preserving the balance of power”. Among other things, it implies that Hitler's failure was predetermined by a fundemental law of world politics.

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Precommitting to paying Omega.

5 topynate 20 March 2009 04:33AM

Related to: Counterfactual Mugging, The Least Convenient Possible World

MBlume said:

What would you do in situation X?" and "What would you like to pre-commit to doing, should you ever encounter situation X?" should, to a rational agent, be one and the same question.

Applied to Vladimir Nesov's counterfactual mugging, the reasoning is then:

Precommitting to paying $100 to Omega has expected utility of $4950.p(Omega appears). Not precommitting has strictly less utility; therefore I should precommit to paying. Therefore I should, in fact, pay $100 in the event (Omega appears, coin is tails).

To combat the argument that it is more likely that one is insane than that Omega has appeared, Eliezer said:

So imagine yourself in the most inconvenient possible world where Omega is a known feature of the environment and has long been seen to follow through on promises of this type; it does not particularly occur to you or anyone that believing this fact makes you insane.

My first reaction was that it is simply not rational to give $100 away when nothing can possibly happen in consequence. I still believe that, with a small modification: I believe, with moderately high probability, that it will not be instrumentally rational for my future self to do so. Read on for the explanation.

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