There are 100 instances located at points 1, 2, ..., 100 on the political spectrum (the real number line).
There are N users who move from instance to instance. There are no alt accounts: each user uses exactly one instance at each moment in time. Users may move from their current instance to any politically adjacent one. (This means that, starting at instance 5, they can move to 4 or 6.)
Eliza Fox wishes to destroy the fediverse, while Jeff Cliff wishes to protect it. At the start, Jeff chooses the starting distribution of users. Then there are 99 turns, each of which has three phases:
First, Eliza chooses an instance to Fediblock, destroying it completely.
Second, Jeff moves each user of the now-destroyed instance to any politically adjacent instance which has not been destroyed. (If no such instance exists, then those users are executed.)
Third, Jeff may move all users however much he wants (including the users that were already moved in the second phase), as long as they do not enter (or jump over) a destroyed instance.
At the end of the 99 turns, 99 instances have been destroyed, so there is only 1 instance remaining.
(For convenience, let us say that users can be split into fractions without harming them in any way.)
Your task: Explain how Jeff can save the lives of N/50 users. Furthermore, explain how Eliza can prevent him from saving more than N/50 lives.
Example: Suppose there are 4 instances and 40 users. First, Jeff will choose the starting distribution of users, and then Eliza and Jeff will take 3 turns.
Jeff chooses to distribute the users evenly, so the user count is (10, 10, 10, 10).
During the first turn, Eliza destroys instance 2, and Jeff moves 4 of those users to the left and 6 of them to the right. The user count is now (14, _, 16, 10). Jeff moves 3 users from instance 3 to instance 4. The user count is now (14, _, 13, 13). Note that Jeff cannot move any users from instance 1 to instance 3 or 4, because they would have to cross through instance 2, which no longer exists.
During the second turn, Eliza destroys instance 1. Since those 14 users have nowhere to go, they are executed. The user count is now (_, , 13, 13). Jeff moves 2 users from instance 4 to instance 3. The user count is now (, _, 15, 11).
During the third turn, Eliza destroys instance 3, and Jeff is forced to move all 15 of those users to the right. The user count is now (_, _, _, 26). Jeff has saved 26 out of 40 lives.
Extra credit: Let us make the model more realistic by requiring that, during the second phase of each turn, all users of the now-destroyed instance must move to the right. (Again, if this is not possible, then those users are executed.) Explain how Jeff can still save N/50 lives.
@ai@MercurialBlack@ceo_of_monoeye_dating@jeffcliff@roboneko@scenesbycolleen This is so cursed but I know you're gonna know about this reference, it reminds me of the game theory coin game "The Evolution of Trust"
@hidden@MercurialBlack@ceo_of_monoeye_dating@jeffcliff@roboneko@scenesbycolleen
I just played through it. One of the best interactive math explanations I've seen, despite its quadruple-vaxxed tone. I actually learned something new because I incorrectly guessed that "always cheat" would win because they can exploit "always cooperate."
It slightly annoys me that they changed all the standard terminology. The game itself is known as the "prisoner's dilemma." The "copycat" strategy is usually called "tit for tat," and "copykitten" is "tit for two tats." I find the phrase "tit for tat" to be funnier too.
Here's a funny bit of lore about the prisoner's dilemma tournament which the book is based on. It was a real public tournament which anybody could enter their own bot into. Lots of professors submitted incredibly sophisticated strategies, and they were all BTFO by the humble "copycat" which was the winner.
There's a little-known way to gank prisoner's dilemma tournaments. What you do is submit one "main" bot and hundreds of "feeder" bots. Your bots start each round by executing a secret "handshake" move sequence; if they recognize each other as both being your bot, then the "feeder" will purposely let the "main" bot exploit it. If the opponent is not recognized as one of your own bots, then your bot will just play "copycat." As long as you can enter enough "feeder" bots into the tournament, your "main" bot will be guaranteed to win. The implication for cult behavior is clear.
Lastly, there's an error in one of the explanations (see pic). None of the games considered in this slideshow are "zero-sum." Zero sum would mean that the payoffs in every case are exactly opposite: if you get +X, then I get -X. Since the "cooperate" case gives positive payout to both players, this game is not zero sum.
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