An arbitrary number you see first shapes your judgment on completely unrelated questions. In one study, people who saw higher phone number digits estimated more African countries than those who saw lower digits, even though the numbers had nothing to do with each other.
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I think the idea of anchoring is so simple that people think it's not going to be effective, but study after study shows just how easily our perceptions can be changed with a quick anchoring. Let me give you an example. There was a study where they asked participants to say, "What are the last 2 numbers in your phone number?" And then they asked, "How many countries are in the continent of Africa?" Two totally unrelated questions. If your phone number numbers were high numbers, you guessed considerably higher when guessing how many countries there were. If you had a low phone number, like, you know, 05 or 12 or something, you guessed a low number on the countries of Africa. Totally unrelated, but just giving you that anchor of a low number drastically changes what you think on a totally unrelated question. Fascinating.