If you haven’t yet watched Love Island, a British reality TV show, you haven’t missed out. Its premise is simple: a few dozen very attractive, heterosexual twenty-somethings spend seven weeks in a villa in Mallorca without much more than a bathing suit and a raging libido. Once a week they get to decide whom they want to “couple up with”. Anyone who remains single at the end of a “recoupling” gets “dumped from the island.” Occasionally, new members arrive at the Love Island villa or the members of the house vote on whom to dump.
The objective is to avoid being single throughout the series and the public’s favourite couple gets £50,000.
And, yes, there are cameras everywhere and the viewers can hear every word, squeal, and grunt made by the contestants.
Lesson 1: look for stability in two-sided matching markets
In 1962, David Gale and Lloyd Shapley wrote a beautiful mathematics paper on the “stability of marriage”. They imagined a group of men and women who are interested in marrying each other. They showed that no matter what preferences men have over women and no matter what preferences women have over men, there always exists a “stable matching”. This means that there is no man and woman who would want to leave their current partners for each other. Supply equals demand, if you like. In real life, this theory already helps to match medical residents to hospitals and children to schools in a way that avoids any complaints about unfairness.
For Love Island, existence of stable matchings means that we would not expect the same group of attractive men and women to recouple constantly but to find their best partner and stick with them.
But what happens when a new woman arrives at the villa? Now all the women instantly lose their bargaining power (this phenomenon is also known Aumann’s “glove game”). The supply of women outstrips the demand by the outnumbered men. Matching theory suggests that this will result in men leaving their current partners for women they prefer.
That’s exactly what happened when Tyne-Lexy, Gabby and Mike came to a villa and skewed the gender balance in the second week: there were a lot of tears and drama.
To entertain the public, the producers ensured that new men and women would regularly arrive at the house disrupting the delicate balance of the matching market. But towards the end of the show there are four happily matched couples awaiting the final vote. The “stability of marriage” prevails even on Love Island.
Lesson 2: game theory predicts love
Halfway through the current Love Island series, the men were unexpectedly moved to another mansion called Casa Amor. There they were then joined by a set of new female contestants, while their unsuspecting partners back in the Love Island villa were treated to the company of new set of handsome men. Neither group knew what was happening in the other villa.
After a couple of days of cuddling and snogging, the men in Casa Amor were told they could either bring a new partner back to the Love Island villa or return to the villa to their old partner. But if a man decided to return to his old partner, who herself decided to recouple, he would be immediately dumped from the island.
How would a game theorist think about their difficult decisions? For a couple in love, this is a simple coordination game: there is a good outcome (a “Pareto-dominant Nash equilibrium”) in which both contestants decide to stay loyal and a pretty awkward outcome (a “Pareto-inferior Nash equilibrium”) in which both sides decide to recouple (it’s also worth knowing the “whole game”: Kem and Amber cleverly recoupled in order to get back together in the villa.). Olivia and Chris as well as Gabby and Marcel both stayed loyal and lasted until the end of the series.
But what if a contestant was keen to get rid of their partner? Then they faced a prisoners’ dilemma: both contestants are too tempted to recouple, so staying loyal makes no sense. Camilla and Jonny both decided to recouple and they ended up with new partners by the end of the series. But poor Dom was dumped from the island because he stayed loyal to Montana who decided to recouple with new arrival Alex (they were together until the bitter end).
Lesson 3: first-past-the-post is a terrible voting system for elections with many candidates
Shortly before the end of the series, the islanders were given a secret vote to dump one couple from the island. The couples with the most votes were put at the mercy of a public vote. But instead of simply telling the producers their preferences honestly, the couples spent a lot of time strategising about which couple to vote off. This is not surprising. In a first-past-the-post system like the one on Love Island or, say, in the UK general elections, your expectations about whom others are voting for really matter for your choice. As a result, many voters misreport their true preferences and vote strategically. A system that reduces this agony (but also viewers’ entertainment) is instant-runoff voting in which you can rank all the candidates and all your preferences are taken into account.
So, here’s some consolation, Alex and Montana. You were not the least popular couple on the island. You were simply victims of a shoddy voting system.