Loss aversion and utility in Formula 1
If you didn't see the Italian Grand Prix on Sunday and you're still planning to watch it, look away now. But really. It's been three days.
So for those who didn't see it and are not planning to watch it, think about this question.
Should the order in which drivers are placed affect the aggregate happiness of all fans? (Assume for now that all drivers and teams have the same number of fans.)
Surely not, right? No matter whether Rubens Barrichello wins or Robert Kubica does, people will be - on average - equally happy. There's a certain utility gained from your driver coming first, a lower amount for coming second, third, and so on. The total utility gained by all fans is the sum of U(first) + U(second) ... + U(20th), and the only difference is the distribution of happiness between people.
On Sunday, Lewis Hamilton was running in third place and ready to get on the podium. He entered the last lap a couple of seconds behind Jenson Button and trying to catch him, but without much chance. Suddenly he pushed a bit too hard, bounced off a kerb and crashed his car. Oops.
Hamilton fans must have been absolutely gutted. The rest of us may have felt a momentary glee, but mainly sympathy. Ferrari and Kimi Raikkonen fans such as myself were happy to see Kimi promoted into third place, but how much difference did it really make to us?
My hypothesis is that the Hamilton fans' loss of utility far outweighs the gain for the rest of us. While they naturally keep a stiff upper lip - at least on the evidence of the one watching it in the pub with me - they're absolutely eaten up inside.
And yet. If total utility comes additively and directly from your driver's position at the end of the race, it surely must be equivalent in any scenario. Kimi fans should inherit all the happiness the Lewis fans would have had; Sutil fans just as happy at his fourth place as Kimi fans would have been; and so on down the line, right back to Lewis who gets all the undoubted joy that would have accrued to Timo Glock's 12th position (because the drivers placed 13th and above were a full lap behind, Lewis gets placed above them).
But surely Timo's (many) fans do not care that much that he came 11th instead of 12th. Even Kimi's podium position doesn't seem that interesting - after all, he won the previous race. The frustration of Lewis's fans must be much stronger than the pleasure from everyone else's; because the endowment effect of his long tenure in 3rd place triggers a powerful loss aversion when he loses it.
So if we wanted to design the ideal sport to make people as happy as possible, what would it be? There's a common perception that a competitive game where the lead swings back and forth all the time is the most exciting kind of sport. But that just exposes fans to continual pain every time their team or player is overtaken. What we really need is a bit of stability.
Indeed, to maximise total utility, whoever first gets into the lead should stay there for the duration of the contest. Same for the driver who gets into second place, and for that matter every other position. You could even argue that the positions should be determined before the race even starts, so that people have - let's say - a day to get used to the position and build up a strong attachment to their driver's ultimate finishing result. A result which will not be threatened by any potential overtaking or mechanical unreliability.
Regular viewers of Formula 1 will of course recognise this precise state of affairs from the Monaco Grand Prix. Not to mention Valencia, Hungary and nearly every other racetrack in the modern sport. Overtaking has been almost eliminated by the design and regulation of racing cars since the 1990s.
Now we have all been led to believe that this is an unintentional consequence of technological development. But it's a funny thing...I'm starting to see that there's more logic than we ever suspected behind those aerodynamic regulations.
Bernie Ecclestone is surely not just a deviously clever businessman, but one of the best sports economists out there. He keeps us happy by sparing us pain and loss. In my catatonic state, I must go out now and buy some of whatever that sponsor is selling...