Happiness Equation Reveals Key to Cheery Life
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A little delight goes a long way toward making people happy, according to a newly-developed equation for happiness.

By studying how people respond to recent events in their lives, researchers have developed a mathematical formula that can predict people's happiness based on their moment-to-moment mood swings.

So what's the solution to happiness? It's all about managing your expectations.

The equation shows that people are happiest when things go better than expected, such as when study participants outperform their own expectations on a decision-making task, according to research published yesterday (Aug. 4) in the journal Proceedings of the National Academy of Sciences. [5 Wacky Ways to Quantify Happiness]

Looking forward to a lunch date with friends, finding a prime parking spot at work, having a typically cranky toddler tack an extra hour onto his or her nap … when life exceeds your expectations, it makes you happy, researchers report. On the flip side, if that lunch is poorly cooked, your work inbox is full of hectoring emails or your child wets the bed, the disappointment can quickly sour a good mood.

However, in the real world, the study results don't mean the scientists recommend people go through life with lowered expectations.

"Emotions aren't something we should be afraid of," said lead study author Robb Rutledge, a neuroscientist at University College London in the United Kingdom. "Happiness and sadness are part of being human. Happiness depends not on how well things are going, but whether they are going better or worse than expected. That means that happiness may be useful for telling us whether to change what we're doing. If we're more unhappy than usual, maybe sometimes that means we should try something different. If we're happy, maybe that means we're doing the right things," Rutledge told Live Science in an email interview.

For example, if an activity, such as checking your work email in the morning, triggers a bad mood for a long time afterward. Rutledge advises spacing out these unpleasant parts of the day so your mood never drops too low. "Also, try to end the day on something that might be good, so that you don't go home in a bad mood," he said.

Rutledge and his co-authors initially developed their mathematical formula by studying 26 people who were asked to make decisions that led to fixed or risky financial wins and losses. The study participants played the money game in an fMRI (functional magnetic resonance imaging) machine that tracked their brain activity. After every few decisions, they were asked to report their level of happiness.

Happiness correlated with activity in two brain areas — the ventral striatum and the insula. Both areas are linked with feelings of well-being, and the ventral striatum helps produce dopamine, a brain chemical that transmits signals between cells and is linked with pleasure and cravings.

The happiness equation.
The happiness equation.
Credit: Robb Rutledge, UCL

From the results, the researchers developed their happiness equation, which included variables such as: a forgetting factor, in which more-recent events are more influential than those earlier in life; a term that weights events by how much influence they'll have on happiness; the average reward for a gamble if chosen; and the reward received minus the expectation. [Find Out Where the Happiest (and Saddest) People Live]

The researchers then crowdsourced the next step. The equation was tested on 18,420 people who played a smartphone game called "The Great Brain Experiment." (This risk-reward game research is still ongoing, and the app can be downloaded online.) The app also asked people to take risks to gain rewards, this time playing for points instead of money. The results showed a consistent relationship between rewards, expectations and happiness, the researchers found.

Happiness depended more on a participant's recent rewards and expectations than on the overall wealth he or she accumulated in the game, the results showed. For instance, a sense of happiness comes from the gap between what one expects and one what achieves. A positive gap promotes happiness, while a negative gap makes for bad feelings.

"Our subjects make choices between safe and risky options, and they often take risks hoping to get a better outcome," Rutledge said. "If they get the better outcome, that definitely brings them happiness, but their happiness does go down if they lose. Much as in real-life situations, the greatest happiness tends to be after several things have gone well. The greatest unhappiness tends to be after several things go badly. These extremes are more likely when people take a lot of risks."

Eventually, by using the equation to analyze the differences in how people react to events such as wins and losses in the brain game, the research might lead to a better understanding of mood disorders, the researchers said. The team is now testing people with depression to see if the equation can predict those individuals' happiness, Rutledge said.

Email Becky Oskin or follow her @beckyoskin. Follow us @livescience, Facebook & Google+. Original article on Live Science.