Sharing an Olympic gold medal can be about maximizing utility

On 1 August 2021, an incredible event took place at the Tokyo Olympics—Mutaz Essa Barshim of Qatar and Gianmarco Tamberi of Italy shared the gold medal for men’s high jump. Both Barshim and Tamberi had cleared 2.37 metres and were unable to clear the 2.39-metres bar even after three attempts. When the Olympic official came to discuss the modalities of the sudden-death jump to determine the winner, Barshim asked if they could share the medal. The official replied that this was a possibility, and the rest is history.

In a world under siege by a virus that constantly threatens life and keeps loved ones and people apart from each other, this story of two champion athletes choosing to share the honours went viral. It became one of the major stories of the Tokyo Olympics and probably the top feel-good story of the 2021 Games.

It is not that medals have not been jointly awarded in previous Olympic Games. Over 2,600 medals have been given to athletes in Olympics, but there have been only 120 instances of medal sharing since the modern Summer Olympics began in Athens back in 1896. The gold medal itself has only been shared 31 times, a majority of them in sports where the winners were determined either by judges (like gymnastics) or by two athletes performing equally well and officials deciding to declare them both as joint winners. This, however, is the first instance where rival athletes from different countries asked about the possibility themselves, and then chose to share the medal.

Although we found this story heartwarming, as economists, we can also explain this result as the outcome of rational behaviour in one’s self- interest. To understand this, we need to first account for how economists view risk.

In everyday parlance, risk means exposure to a chance of loss, and a risky venture is something that involves the possibility of a loss. Economists, however, measure an individual’s satisfaction from their consumption or actions through an abstract ‘point system’ called the utility function, and risk refers to the curvature of this utility function that captures the uncertainty associated with different outcomes. Economists assume that individuals fall into three categories: risk loving, risk neutral and risk averse. In terms of curvature, risk neutrality implies linearity, risk aversion implies a concave utility function (like a bowl facing down) and risk loving means a convex utility function (bowl facing up).

What these curves imply is something simple: a risk-averse individual derives greater satisfaction from a guaranteed or ‘certain’ outcome, than a combination of uncertain outcomes that on average offers a higher pay-off by taking probabilities into account. A risk-lover prefers exactly the opposite. A risk-neutral person is equally happy with a guaranteed outcome and a combination of uncertain outcomes that on average offers the same pay-off. Thus, a risk-neutral person derives the same amount of utility or satisfaction from a rupee worth of gains and losses. For a risk-averse person, the utility from losing a rupee is worth more than the rupee, while the same is true for a risk-lover for gaining a rupee.

Not surprisingly, most of us are risk-averse, which explains, among other things, why a chunk of our savings is held in bank deposits or government bonds that offer a much lower average return than stocks over the long term. These are also the people who are willing to pay an insurance premium to protect their life and limb. Risk- lovers on the other hand are the ones who haunt casinos and are willing to take the chances life throws at them.

Now consider the interaction between Barshim and Tamberi. If they participated in a jump-off, only one of them would win a gold medal and the other would face the chance of losing that medal. However, if they were both risk averse, then the only rational and selfish choice was to share the medal because it makes winning the gold medal a certainty.

But there is a little more to this tale of medal sharing. Even though Barshim suggested the idea of sharing, why did Tamberi accept it? It turns out that both Tamberi and Barshim are good friends on and off the track, and this provides yet another reason that made medal-sharing possible. In contrast to standard neoclassical economics, behavioural economics argues that people may have inter-dependent utilities. These are usually described using an umbrella term called ‘other- regarding preferences’.

One example may be inequality aversion—when people care about equality, they will share things with others. The opposite is true of folks who only care about doing better than their neighbours, such as those who like keeping up with the Joneses.

Consider another very simple interdependent utility function: imagine that your happiness depends not only on your happiness but also on that of your child or fiancé. In other words, your utility is a sum of own utility and a proportion of your loved one’s utility. Then it is easy to see why the two friends might want to share an Olympic gold medal.

Economics is often cast as ‘the dismal science’ and economists are blamed for developing models that suggest we exhibit selfish rational behaviour. Our goal here has been to show that such behaviour can lead to sharing and produce some of our most heartwarming stories.

Chandan K. Jha & Sudipta Sarangi are, respectively, an associate professor of finance at Le Moyne College, and professor of economics at Virginia Tech and author of ‘The Economics of Small Things’