Sunday, October 22, 2006

Survivor-nomics

If you're not a fan of Survivor, you can probably just skip this one.

We here in the Economics Department at West Virginia University are fans of Survivor. Big fans. Building voting coalitions is a crucial aspect to the game-- you certainly see the Groseclose supermajority come into play more often than not. Over the seasons, end-game strategies have migrated themselves to the beginning of the game.

In the last two seasons, CBS introduced the idea of an exile island-- at certain junctions in the game, players can be sent to this island for a couple of days. On the downside, there is no shelter on the island, you have to fend for yourself with regards to nourishment, and you are removed from the social doings of your tribe. There does exist, however, a hidden immunity idol on the island-- if you find it, you (or anyone you choose to give it to) basically have a get-out-of-being-voted-off-the-island free card. If you receive enough votes to be voted off the island, you present the idol, your votes become null, and the remaining votes then eliminate the next highest vote-getter from the game.

Here's the question: Do you reveal to anyone, or everyone, that you ever have the hidden immunity idol, and at what point do you do so?

I'm of the opinion that there does not exist any situation by which it would be strictly beneficial to withhold the information from the rest of the players that you have the coveted immunity idol. The only time that the immunity idol would become a factor is when your tribe wants to vote you out. (Let's assume for the time being that you are not considering giving it to someone else.) Should you choose not to tell your tribemates and they want you gone, they will vote accordingly, you will present the idol, and a surprised member of the tribe will be sent home. At this point, they know that the idol can't be played at any point in the game henceforth, and can move forward with confidence in pursuing your exit from the game.

Now let's consider that the tribe wants you out and you do choose to tell them that you have the idol. Knowing the voting rules, the majority faction looking to eliminate you from the game now knows that it is going to have to take one for the team this round in order to remove the immunity idol from the game, and then vote you out during the next meeting. Now, with payment redistribution from the winners to the "sacrificial lamb," an agreement could be reached to value the sacrifice. Survivor, however, expressly prohibits this-- so who would volunteer to be placed in the situation of being picked off for the good of those remaining in the game?

Of course, here's the kicker-- once the "sacrificial lamb" effect is strong enough to deter the voting, it only gets stronger in the next round, in the sense that each person would have a higher probability of becoming that "sacrificial lamb." It's not like the idol is good for only one round-- it is good every round as long as you don't have to use it. It would seem to me that once you could incorporate this effect, you could stroll well into the depths of the game without having to worry a large amount over coalition building. Any coalition looking to vote you off would necessarily have to lose one of its members before doing so.

Alternatively, the majority faction (and necessarily a supermajority greater than 2/3) could arrange a voting strategy such that two members of a minority faction receive enough votes to be voted off. In my example, it is known who has the immunity idol, and thus the other member could simply be targeted. However, if the immunity idol were suspected to be held by a minority faction, a spread voting strategy against the minority grouping could achieve the desired effects. And this is actually what happened in last week's episode-- or was attempted , anyway. Combined with the fact that the organizer of this voting theory was not in the entire tribe's best graces, the opportunities for shirking with this strategy are just too great. With trust being anything but a certainty on the island, I don't think it's a stretch to say that a two-pronged voting strategy, as such, will never likely be achieved in the game.

Anyway-- the lesson is: Let everyone know you have the hidden immunity idol, and ride the "sacrificial lamb" wave to the Final 3!

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