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• The amazing Drew Foster is at it again with a puzzle to decide who gets the Iron Throne via logic:

- Tyrion

- Dany

- Sansa

- Cersei

- John Snow

Apparently, no one is nominating the Night King.

Our potential rulers have three rules to guide their decision of who to vote for:

1) The five know each other’s voting preferences. (See the 2nd pic.)

2) They cannot commit to vote against their own preferences in the future,

3) If indifferent between possible nominees, everyone would prefer to nominate the ultimate winner.

If Tyrion makes the first nomination to be voted on by the group, who will he nominate and who will win?

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So I thought about how best to approach this problem.

Obviously you first need to read it in its entirety: my Cliff’s Notes version above leaves out some necessary details to know in order to solve this.

One thing thing that came to mind is to focus on the most preferred nominees:

Dany is the preferred second choice with 2 votes.

Sansa is the preferred indifferent choice with everyone, excluding Sansa, choosing her third.

So if no winner is chosen during the first four rounds, John should vote for Dany since she will get three votes and consequently his nominee will win.

• I'm terrible at math! I wonder if @JazliAziz would want to join in the fun?

• This isn't math. There are no numbers 🤣

I love logic puzzles by the way.

• So if no winner is chosen during the first four rounds, John should vote for Dany since she will get three votes and consequently his nominee will win.

1) The five know each other’s voting preferences.

Tyrion: T>D>S>J>C

Dany: D>T>S>C>J

Sansa: S>C>J>T>D

Cersei: C>J>S>D>T

John: J>D>S>T>C

2) They cannot commit to vote against their own preferences in the future,

3) If indifferent between possible nominees, everyone would prefer to nominate the ultimate winner.

**********

Everyone knows John would nominate Dany.

Sansa and Cersei hate Dany. They therefore want to prevent John from nominating her.

Tyrion does not want Cersei to be nominated. He also knows that

if a Cersei votes “no” on a nominee in one round, she cannot then vote “yes” for them in a later round.

Why?

Because of rule #2 above, Cersei cannot commit to vote against her own preferences in the future,

So Tyrion needs to force Cersei to vote no in an earlier round.

• Okay, time to try to solve this!

I am going to walk through my thinking for this (most likely) first attempt.

A quick rehash of the three rules to live by if you hope to sit on the Iron Throne:

1) The five know each other’s voting preferences.

Tyrion: T>D>S>J>C

Dany: D>T>S>C>J

Sansa: S>C>J>T>D

Cersei: C>J>S>D>T

Jon: J>D>S>T>C

2) They cannot commit to vote against their own preferences in the future,

3) If indifferent between possible nominees, everyone would prefer to nominate the ultimate winner.

**********

Tyrion gets to nominate first. In games, such as chess, this is referred to as the “first-move advantage” [1]. In marketing, a similar concept is called the “first-mover advantage” [2]. Oftentimes, there is an advantage to going first since it causes the other players to react in predictable ways.

**********

I apparently lied about John Snow’s nomination. Re-reading the rules, “if Cersei’s nomination doesn’t pass with three votes, Jon will get to appoint the new ruler (with no voting necessary).”

**********

Let’s see what happens if Tyrion goes contrary to expected and nominates Cersei, his mortal enemy.

In the voting, Cersei will receive “no” votes from Tyrion, Dany and Jon. As a result, none of these three can vote “yes” for Cersei in later rounds (rule #2). Cersei will therefore be unable to win the Iron Throne now because she can’t get three “yes” votes.

**********

Dany now votes. Her initial preferences are

Dany: D>T>S>C>J

Dany cannot vote “yes” for Cersei, since voted “no” in round one, and she won’t vote for Jon Snow.

Dany knows that Cersei, Jon and Sansa do not prefer Tyrion. Tyrion also knew this and that he therefore would not win in round one if he nominated himself.

Dany should therefore nominate herself:

Dany is Tyrion’s top choice because in the last three rounds the nominators (Sansa and Cersei) won’t be nominating Tyrion.

However, if she nominates herself there’s no guarantee that Jon will vote for her.

***********

• Victoria, I am in such edge of my seats excitement for tonight’s battle that I do not want to read any “suggested spoilers”. 😉

However, it will be interesting to me to read the Vox article after tonight to see how the military experts’ strategy matches up with the Night King’s. I think I may even chime in on this during @JazliAziz ‘s (hopefully) Episode 3 discussion. 😎

Finally, a bit of a topic drift but still interesting I think. There is a great book on famous military failures and an anatomy of what went wrong. Perhaps some further reading for those intrigued by your article share.