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JoshuaZ comments on A sense of logic - Less Wrong
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Car insurance ads that advertise how much people save by switching to _ Company. If people weren't going to save money, there's no way they would be switching to the company. They probably also wouldn't go through the hassle of switching if the savings were unclear or trivial. Therefore, knowing that the people who looked into it and then switched are completely, totally useless and misleading for the typical viewer who has not looked into it; and if they had looked into it, then they'd already have information rendering that statistic useless.
Though I suppose this vexes me only because it's so obviously stupid once you hear it dozens of times.
It does make sense as an argument that you should look into it not as an argument itself to switch.
Good point, but I disagree on a detail: just knowing that there's some threshold of savings that some people have achieved when switching to X Brand Insurance tells us that at least one person passed that threshold... but it doesn't tell us how likely we are to pass that threshold.
For that I think you'd need something like "10% of the people who got a quote from X Brand insurance later switched, saving on average Y dollars!" Except, no insurance company would run that ad, because 10% is an unimpressive "sounding" number even though in this context it would actually be really high.