Arthur C. Brooks cites a 2001 Oxford study showing extroverts report higher happiness because they naturally think about the future, set goals, and tell others their plans. Happy introverts do the same things intentionally. The habit of committing to future rewards, not personality type, drives wellbeing.
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Extroverts are great about thinking about future rewards, which is one of the sources of their happiness. There's a 2001 study from Oxford University that broke a sample of survey respondents into 4 groups: happy extroverts, unhappy extroverts, happy introverts, and unhappy introverts. They're interested in what drove the happy introverts into higher wellbeing. What were they doing differently than the unhappy introverts? And they found that they were doing something that extroverts do naturally. Which is that a sense of optimism, a sense of life purpose, a sense of direction, a sense of goals, a sense of progress. Now, extroverts do this naturally. They think about the future and they dream about the future naturally. They love to talk to people about their future. They talk about their dreams. They talk about life's purpose. They talk about it all the time. We tend to act according to the commitments that we've articulated to others. And the result of it is that when extroverts, when they express their thoughts and hopes and dreams to others over the course of their extroversion and sociability, their gregariousness, they tend to live according to these dreams. They tend to follow these goals. They tend to take that trajectory, and that's one of the secrets to their great happiness.