Was Prim's selection rigged?

As we all know, Prim was originally selected to be the District 12 Female Tribute for the 74th annual Hunger Games.

However, here's the problem:

1. Prim only had one entry into the Games.
2. There were at least a few thousand more people that could have been picked.

It's a statistical improbability that Primrose would have been picked, therefore (slightly) implying that her entry into the game was rigged due to some factor (Possibly Katniss' troublemaking by sneaking into the forest?).

So, was Prim's entry rigged, or was it just terrible luck? If the entry was rigged, why?

• And it's also impossible to win the lottery with just one ticket, right? – Scimonster Mar 2 '15 at 20:37
• If you roll two six-sided dice the highest probability for the combined sum is 7 (at 17%) and the lowest are 2 and 12 (at 2.7%). Are you saying a 2 and 12 are a statistical improbability because they are the least likely? – Jack B Nimble Mar 2 '15 at 21:00
• Zaphod: That's impossible. Trillian: No, just very improbable. – phantom42 Mar 2 '15 at 21:09
• @JackBNimble - Never Tell Me The Odds! – DVK-on-Ahch-To Mar 2 '15 at 21:39

Any given lottery ticket has an equal chance of being selected as all the other lottery tickets. The fact that one person holds more tickets increases their chances, but the fact is that everyone who holds even a single ticket has a chance of getting picked. I mean, that's kind of the foundational point of lotteries - that everybody has a chance.

At the time Prim's ticket was selected, there is nothing to suggest that Katniss' extralegal activities would lead anyone to act against the family. The local law enforcement representatives partook in the black market and abused their position to get favors, and there is no evidence of conflict.

Acting against Prim to impact Katniss is a subtle, vicious attack. While Katniss made enemies of that sort, it was only after she went to Capitol that she did so.

All in all:

1. Statistical theory supports Prim's "winning" entry as legitimate
2. Nothing in the books suggests anything to the contrary

So I think the odds were just not in Prim's favor.

• I'm sure there's some mechanism where you can name your name in multiple times for more food rations? If anything I believe there was more chance Katniss would be chosen – Liath Mar 2 '15 at 21:14
• Yes, Katniss had a higher chance of being chosen, because she did sign up for more tickets in return for food. However, because any single ticket is equally likely to be selected compared to any other single ticket, her higher chances do not negate Prim's chance... – gowenfawr Mar 2 '15 at 21:25
• @Liath It's the Tessera. – phantom42 Mar 2 '15 at 21:44
• Katniss does speculate somewhere about Prim's selection being rigged (while she's thinking of different members of the same family often being selected, a la Cashmere and Gloss). Unfortunately I haven't got the books to hand, so I can't back this up with an exact quote! – Rand al'Thor Mar 4 '15 at 23:37
• @randal'thor I remember her speculating that about the 75th Hunger Games (or later) in retaliation for her actions in the 74th. That being said I don't have the book on me either. – kaine Mar 6 '15 at 21:03

No; it was a tragic misfortune!

In-universe
Here's all we have about 'the odds' from Katniss' account of the reaping:

There must have been a mistake. This can't be happening. Prim was one slip of paper in thousands! Her chances of being chosen so remote that I'd not even bothered to worry about her. Hadn't I done everything? Taken the tesserae, refused to let her do the same? One slip. One slip in thousands. The odds had been entirely in her favor. But it hadn't mattered.
-The Hunger Games - Book One: The Hunger Games, Part One - "The Tributes", Chapter Two. [emphasis mine]

The Everdeens were a regular family with no reason to stand out against the capital, therefore there was no reason why Prim would have been 'singled-out'.

Out-of-universe
Katniss lives for her family. Ever since her father, Mr. Everdeen, passed away, she has been forced to be the primary caregiver to her sister, Prim, and her mother, Mrs. Everdeen.

Prim being reaped as the Tribute for The 74th Annual Hunger Games makes Katniss feel like she has failed in protecting her and everything she has worked for to be all for naught. This triggers her anti-Capital hate to flourish.

Up until that point she was just another girl, who hated the "system" and just had a general contempt for her and her family's plight. But once Prim's name got pulled out, she went full protective.

This was the spark which ignited the fire inside her against The Capitol; but there is no evidence that this was a purposeful act against Katniss or her family.

• Katniss does speculate somewhere about Prim's selection being rigged (while she's thinking of different members of the same family often being selected, a la Cashmere and Gloss). Unfortunately I haven't got the books to hand, so I can't back this up with an exact quote! – Rand al'Thor Mar 4 '15 at 23:37

I'll preface my answer with another question: What motivation would the Capital have to rig a Reaping to include Primrose Everdeen? I could come up with only two plausible scenarios where they would have such motivation:

1. (as previously mentioned) An indirect punishment towards Katniss for her relatively minor troublemaking.
2. "Casting" Prim into an archetypal "role" within the reality show, much the same as reality TV producers presently do.

Reasons that eliminate #1, the "punishment for Katniss" theory:

• Punishments for "local" transgressions are frequently and quickly dealt with on a local level by Peacekeepers (floggings, executions, etc.). At the time of the first Reaping, Katniss had done nothing so extraordinary as to warrant an out-of-the-ordinary punishment.
• Condemning Prim to death isn't going to be a deterrent to Katniss's behavior. Prim is one of the very few things Katniss truly loves in this world (and if the Capital was aware of her "crimes", they'd likely be aware of this as well). Removing one of the few things she cares about isn't going to stop her semi-rebellious behavior. With one less thing to live for, she may be more inspired to do such actions.
• If they were aware of Katniss ducking through the fence, they'd likely also be aware of her black market sales, including selling to Peacekeepers. The Peacekeepers appear to be fairly consistent until they are replaced in the 2nd book. If the Capital was willing to put up with military/police figures conducting black market transactions with a citizen, it's a pretty safe assumption that those individuals would have been punished at the same time.

Reasons that eliminate #2, the "casting" theory:

• To cast someone into a role, the Capital would need fairly deep knowledge of a person's personality, likely from someone who interacted with the District population on a day-to-day basis, and this person just doesn't seem to exist. Effie doesn't appear to have any advanced knowledge of any of the Tributes. By letter of the law, I'm assuming the Peacekeepers are advised not to get too friendly with the locals. Although the District 12 Peacekeepers seem to go beyond this, they wouldn't be reporting their knowledge of individuals to the Capital, as they would be violating their presumed orders. The only other person to have regular contact with the Capital would be Haymitch, and it's highly unlikely that he would be assisting the Capital given his history and future actions. That and the fact he stays hammered most of the time. And while they have a lot of cameras, to truly judge someone for a character role, that would take a ton of cameras.

I have a theory, it isn't that the Capitol rigged the Reaping; but that the Rebellion did. Think about it; when Catching Fire ends we are told that Plutarch had been planning this rebellion, developing spies, etc., for a while. The end of Catching Fire is only about a year after the Reaping for the 74th Games, the preliminary work for the rebellion had to be underway at this point. The only way to introduce her to Panem is to get her in the Games and hope she wins. And the way it was done, it's perfect that Prim is picked. If, let's say they wanted Katniss to be the "Mockingjay", this is how to enter her in the Games, as a volunteer for her sister. She gets immediate sympathy from the Districts. And lastly, her resume, for lack of a better word, is ideal. Trained hunter, attractive, sad backstory, a rebellious attitude (pouches, trades at Hob, a loner except for Gale). If you wanted to start a revolution, she is perfect choice. And Plutarch isn't avove fixing a Reaping (See the Quell rules).

• Welcome to the Science Fiction & Fantasy StackExchange! Do you have evidence from the books that Plutarch, or anyone from District 13, would have extensive knowledge on the citizens of district 12? – DBPriGuy Dec 24 '16 at 6:26

I've never watched or read The Hunger Games, but I have studied statistics. I performed a Bayesian analysis to determine what beliefs about the situation are mathematically consistent. I was surprised to find that it seems very plausible that the selection process was in fact rigged. However, this depends heavily on the assumptions one makes about the situation. Here is my full analysis:

Let S denote the event "Prim is selected" and R denote the event "the selection process is rigged to select Prim."

We know that Prim was in fact selected and we want to know whether the selection was rigged. We can't know for certain, so instead we'll ask, "how likely is it that the selection process was rigged if Prim was selected?" This corresponds to the symbol `P(R | S)`, pronounced "probability of R given S."

Now, we use a formula called Bayes' theorem to express this probability in terms of other variables:

``````P(R | S) = P(S | R) * P(R) / P(S)
``````

The formula expands further using the Law of Total Probability:

``````P(R | S) = P(S | R) * P(R) / (P(S|R) * P(R) + P(S | -R) * P(-R))
``````

The symbols `-S` and `-R` stand for the events in which `S` and `R` respectively do not happen.

Let us assume that if the selection is rigged, Prim has a 100% chance of being selected. This corresponds to the statement `P(S | R) = 1`. Additionally, let us assume that if the selection is fair, then Prim has a 1 in 5,000 chance of being selected. This corresponds to the statement `P(S | -R) = 1/5000 = 0.0002`. Let's simplify:

``````P(R | S) = 1 * P(R) / (1 * P(R) + 0.0002 * P(-R))
``````

`P(-R)` can be substituted with `1-P(R)`, leaving us with only one variable on the right side: `P(R)`.

``````P(R | S) = P(R) / (P(R) + 0.0002 * (1-P(R))
``````

We can simplify a bit further:

``````P(R | S) = P(R) / (0.9998 * P(R) + 0.0002)
``````

Now, we need to address exactly what this `P(R)` refers to. It is what is called a prior probability. What it means is a little complicated to explain, but the simplest way to think of it is what we believe about an event before we collect any data on it. In this case, `P(R)` is what our our estimate of probability that the selection is rigged to select Prim would be, if we didn't actually know the outcome.

In other words, imagine you get to the page where they're announcing the tributes, and you stop reading just before you see Prim's name. You stop and think to yourself, for no particular reason, "hmm, I wonder if the selection was rigged for Prim to become tribute. I would say that there's an X% chance of that. Let's keep reading and find out." X is our prior for `R`.

Obviously, there is no one correct answer for this value. Indeed, finding a suitable prior is one of the challenging aspects of Bayesian statistics. Like I said at the beginning, I can't define an authoritative answer for the value of `P(R | S)`, much less state with certainty whether `R` happened or not. What I can do is show how different values of `P(R)` affect our confidence that `R` happened. By plugging in difference values of `P(R)` into the equation above, we can see exactly how our backgrounds beliefs regarding the selection process affect our conclusions once we know the outcome.

For example, let's say that right before seeing Prim's name in the tribute selection scene, we believe that there is a 1 in 10 chance that the selection process was rigged to select Prim, i.e., `P(R) = 0.1`. Plugging this into our equation yields:

``````P(R | S) = 0.1 / (0.9998 * 0.1 + 0.0002)
P(R | S) = 0.9982
``````

...wow. Even with just a 10% chance of the selection process being rigged, the extremely low likelihood of Prim being selected by random chance leads us to conclude that the selection was, in fact, almost certainly rigged.

Dropping down to a 1 in 100 prior for `R`, the probability of the selection being rigged is still over 98%. Here's a table showing how our choice of prior affects the posterior (our updated belief, `P(R | S)`):

``````P(R)    | P(R | S)
--------+-------
0.1     | 0.9982
0.01    | 0.9805
0.001   | 0.8335
0.0001  | 0.3336
0.00001 | 0.0476
``````

At around 1 in 10,000, it seems fair to call it "unlikely" that the selection process was rigged. At 1 in 100,000, it's not believable.

So, in conclusion: should you believe that the selection was rigged to select Prim? It depends on how probable you think that is to be the case, if you disregard the fact that Prim was selected as evidence. If you believe that the prior probability is higher than 1 in 1,000, then you should also believe that the selection was, in fact, rigged.

In catching fire chapter 4 I believe, it is suggested that the reaping is in fact rigged. That the children of victors are often chosen to add excitement to the games even though they do not have their names added extra times for food as others do. And that this would certainly happen if Katniss and Peeta were made to produce offspring. It's improbable that both Primrose and Rue would be chosen by chance on their first eligible year for the games, as they were both 12 and only had their names written once in the selection bowl. This is especially true of Rue because she was from District 11 where there were so many other people of reaping age available.

I think the Reaping’s almost definitely rigged. The Capitol probably wanted to eliminate Katniss because she illegally hunted and got away with it, and the Capitol knew the Peacekeepers wouldn’t, like, whip her, because they bought her meat regularly.

They wouldn’t Reap Katniss, because maybe, just maybe, somebody would volunteer for her, like, maybe, Madge. They have the security cameras everywhere, (Snow even said that), so they can watch Katniss and see how much she loved Prim. They knew she’d volunteer for her. Also, how could two 12-year-olds, Prim and Rue, both with their names in once each, be chosen? Two in one year? If you think about it, they could’ve put either Prim’s name in the girls’ Reaping ball multiple times, or threatened Effie to say Prim’s name no matter what. Katniss even said she thought the reapings were rigged.

• This would be improved with sources added and the text formatted/spell-checked. – Möoz May 17 '19 at 1:32
• Mmk............ – Liv May 25 '19 at 14:39