We’ve heard it all our lives — size matters and bigger is better. But David Velleman wants you to believe that shape can matter more! 
How? Imagine two lives (depicted in the chart below). Sally starts out very happy from birth (80/100) and gets just slightly less happy each year before dying at age 75 just very slightly happy (5/100). Summing each point of happiness in each year gives Sally a grand total of 3230 happiness points for her life. Doris’s life had a very different shape. Doris was not the happiest child, starting out neither happy nor unhappy (0/100) and gradually getting slightly happier each year until her retirement, when her happiness rapidly increased, ending on a very happy year (80/100). Doris had only 1615 happiness points in her life, half of the points in Sally’s life.
Who has the better life out of Sally and Doris? Which life would you prefer to live if you had to choose one? Velleman would think that most people will prefer Doris’s life because we like the idea of a life that continuously gets better, certainly more than a life that gets continuously worse. If that’s right, the shape of a life can guide our evaluations, perhaps even more than the size (the total amount of happiness).
This seems like a problem for hedonists, who generally don’t like to do any mathematics more complicated than simple addition. Sure, they say, curves are nice, but they don’t have magic powers! Consider cashing out your bank account into coins. You could put all those coins in stacks of 100 to count them up. If you then changed the stacks to a nice upwards curve (like Doris’s average happiness per year) you don’t magically get more money — the total value of the collection of units of value didn’t increase by moving them around.
Velleman disagrees. Velleman has argued that summing the wellbeing in each moment cannot generally tell us how to evaluate the wellbeing of a longer period, such as a life.  According to Velleman, the value of a moment depends only on the immediate context whereas the value of longer periods depends on the broader context of that whole period. He argues that the huge difference between most immediate contexts and most broader contexts means that the value of a moment is not directly commensurable with the value of a life.
Here’s another way of looking at Velleman’s argument. The value of lives is often evaluated through a narrative lens because we are reflective beings with long memories that see our lives as an evolving story, not a series of unrelated moments. But we are also momentary beings that can surely evaluate our current state over and over again in the moment. According to Velleman, from the narrative self’s point of view it doesn’t make sense to add up the value of the moments. 
The best, most inspiring stories tend to involve struggle toward eventual success and a happy ending. Success against the odds (think The Mighty Ducks or nearly any sports movie) is a lot more pleasing a storyline than success given a huge head start (think Donald Trump). Given the value of momentary struggle for overall narrative wellbeing, momentary pains could actually have a positive impact on lifetime wellbeing. So, either the basic sum-the-moments view has a very creative accountant, or it must be wrong.
So, the best reason for why a life that curves up at the end is preferable to a life with objectively more happy moments but a gradual-decline shape seems to be that the more reflective big-picture versions of ourselves love a struggle-before-success story. Velleman thinks this is an appropriate way to assess lives. 
Not so fast.
The best, most inspiring stories tend to involve struggle toward eventual success and a happy ending.
There are two reasons for why we intuitively prefer Doris’s “hockey stick” life over Sally’s “trucks use low gear” life, neither of them good. First, we tend to double-count the happiness in Doris’s happiness line. We see her line go up and think ‘that would feel pretty good’, so assign it more mental value. But, that it would feel pretty good is already built into the line itself! All of the benefits of increases in happiness due to upswings later in life are already included. If we add extra happiness points while holistically judging the line, then we are double-counting.
Secondly, we intuitively prefer Doris’s “global temperature projection” life over Sally’s “box office takings of sequels” life because we can’t help but make our judgments at least partially from the position on the lines that corresponds to our own age. This is important because, from the midpoint of their lives, Doris actually accrues more happiness points than Sally. But the initial question was not about comparing the second half of the lives, it was about comparing the whole lives, so the value of Doris’s life gets artificially inflated again.
Hedonists will tell you that, once these mistakes in judgment are taken into account, Sally’s life is better than Doris’s (despite its shape) and that size is what really matters.
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 Photo by Alexandr Podvalny from Pexels.
 Velleman, J. D. (1991). Well-Being and Time. Pacific Philosophical Quarterly,72(1), 48–77.