A quarter of a century after the first series of Big Brother, there is still some life in reality TV. Most of it is dross, but reality TV at its best tells you something about the human condition. What The Traitors (BBC One) tells us is that people are very good at lying. We over-estimate our ability to read people, and ‘body language’ is as likely to mislead us as it is to provide a ‘tell’. It is because people are good at lying that the faithfuls spend most of their time banishing fellow faithfuls based on nothing but vibes. They are then filled with remorse before picking another target at random and doing exactly the same thing again.
The other thing The Traitors shows us is that people act in their rational self-interest and generally do it rather well. This is what the Russian social scientist Dimitry Davidoff would have been interested in when he invented the game Mafia in the 1980s. An experiment in game theory, Mafia became the inspiration for The Traitors. In The Traitors, as in life, we are so used to people behaving in their rational self-interest that it comes as a shock when they don’t.
A classic example is Mollie’s failure to banish Harry at the end of Series Two when a cool assessment would have told her that he was the only person left who could possibly be a traitor. She was 100 per cent convinced of something that she could not be 100 per cent about. Jas would have been insane to force another banishment if he had been the traitor, but Mollie voted for him anyway. Insofar as this was rational behaviour, a behavioural economist would say it was like a player rejecting a derisory cash offer in the ultimatum game, therefore ensuring that they both get nothing. Punishing people for being unfair helps the world go around and benefits us all indirectly, even if it requires the occasional sacrifice by individuals. Mollie thought Jas and Harry were both faithfuls and decided to punish Jas for making them vote again. An alternative explanation is that she let her head rule her heart and didn’t think it through.
The Traitors throws up situations in which, if you assume rational self-interest, the probability of guilt or innocence can be logically calculated until it approaches 100 per cent. You don’t need body language or eye contact. There was a nice example in the season finale yesterday. Francesca became a ‘seer’ and won the right to find out whether the contestant of her choice was a traitor or a faithful. She picked Charlotte who, as the last remaining traitor, had been on a roll, stabbing Minah in the back as soon as she looked vulnerable and recruiting young Freddie so that he could be immediately sacrificed. The plan worked like a charm, especially after Freddie gave himself away by telling an obvious lie.
Charlotte had cleared the path to victory and probably would have won if she hadn’t been selected by her best buddy Francesca, who only picked her because she was convinced that she wasn’t a traitor. This was a rational and intelligent strategy by Francesca who, I’m sure, could foresee that discovering a traitor would be a poisoned chalice.
The seer game has four possible outcomes:
1. Both the seer and the other player are faithfuls. This is the most likely outcome (60 per cent) with four faithfuls and one traitor and would surely result in the seer telling everyone that the other player is a faithful. The other player would obviously say the same.
2. The seer is a traitor and the other player is a faithful. The seer knows this already and has nothing to gain from the arrangement except avoiding being in the hot seat themselves. The seer would tell everyone that the other player is a faithful. Calling them a traitor would gain them very little and would only serve to make the other player believe that the seer was a traitor (and tell the others of their suspicion). The risk is too great and, all other things being equal, the potential upside is too small.
3. Both the seer and the other player are traitors. The best strategy would be for the seer to declare the other person a faithful. At this stage at the game, the other players will never find out that this is a lie. The seer could frame the other traitor, but it would lead to the kind of squabbling that puts them both in a bad light (see Scenario 4 below).
4. The seer is a faithful and the other player is a traitor. If the seer tells everybody that the other player is a traitor, the other player’s only survival strategy is to accuse them of lying and of being a traitor themselves. This puts them both under suspicion. To avoid this, the seer could make an agreement with the traitor to keep the secret. The traitor would readily agree to this, but it poses a problem for the seer. At some point the seer, being a faithful, will have to banish the traitor and it will look very suspicious when they vote for someone the seer said a day earlier was a confirmed faithful. The seer could try to talk their way out of it, but the others would likely err on the side of caution and kick them both out. Moreover, the traitor has a strong incentive to get the seer banished before it comes to that. Neither strategy is ideal for the seer, let alone the traitor, but telling the truth is less risky for the seer.
In fact, it should not be risky at all if the other players are thinking clearly. Scenario 4 is what happened in the final episode of the 2025 series and it is what Francesca was trying to avoid. Charlotte played such a good game that she was selected by someone who wanted to select a faithful. She then had to do some weapons grade lying, complete with tears, to have any chance of survival. Both were accusing the other of being traitors. It was she said/she said and they were both pretty convincing. Who was the traitor? You could be forgiven for thinking it was 50:50.
But it wasn’t at all. For the other players, the decision should have been a simple one. Consider Scenario 2 again. That is what Charlotte wanted the others to believe happened and yet it would make no sense for a traitor (or indeed a faithful) to falsely accuse a faithful of being a traitor, as this would only serve to convince the falsely accused player that the seer was a traitor.
If players are being rational, the seer will always tell the truth except in Scenario 3, where both the seer and the other player are traitors. In that scenario, the lie will be that the other player is a faithful. In other words, if the seer says the other player is a traitor, you have to believe them.
That, at least, is how it would go the first time the game is played. One thing about game theory is that people change their tactics the more they play. If it came to be accepted as a golden rule that the seer never falsely accuses anyone, seers might start falsely accusing people to get them out of the game.
Why would they do that? Perhaps because the format incentivises the banishment of faithfuls during the endgame. The fewer people left at the end, the bigger share of the prize pot they get. As I said last time I wrote about the show, this seems to me to be a flaw in the game that could be addressed by reducing the prize money whenever a faithful is banished. So long as the majority of players are confident they won’t be banished, they will vote to banish again (especially since not voting to banish again makes you look suspect if everyone else does). In the first series, Wilf played a blinder as a traitor and was on his way to winning before the players voted for another banishment. There was only a tiny shadow of doubt over him, but it was enough for the other players to know that if another vote took place, he would be out, but none of them really believed he was a traitor. They voted. He went. And the remaining three only agreed to stop because voting again would have given each of them a one in three chance of being kicked out themselves.
Last night, they kept firing shots until they ran out of bullets and the last two people to be banished were faithful. Leanne and Jake had a financial incentive to keep banishing and no incentive to stop, because it was fairly obvious who was in the firing line. They each ended up with twice as much money as they would have got if they had stopped when the last person whom they seriously believed was a traitor had been expelled. A rational interpretation of her role as seer showed that Francesca was a faithful, but she was booted out anyway. As the mob boss says in Casino, ‘Why take a chance?‘
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