Consider there are three groups of people in Congress: Liberals, Moderates, and Conservatives. It does not matter the size of the groups - just that none of the groups is large enough for a majority - so it requires two groups to vote a certain way for something to pass. Therefore we can treat this like three people and voting where majority rules (another example of this is you with two friends trying to decide on what to do tonight). The Congress needs to vote on the passage of a piece of legislation in regards to nationalized health insurance. Each group has well established preferences which are known to all groups: Liberals: Complete > Partial > None Moderates: Partial > None > Complete Conservatives: None > Complete > Partial Essentially the liberals want to pass their nationalized health insurance, if that fails – they at least want some nationalization rather than a completely private health insurance. The moderates realize that either extreme is terrible and are looking for a compromise. While the conservatives want health insurance to stay privatized – but would rather go whole-hog than some sort of messed up halfway approach that will end up with the worst of both worlds in their opinion. Since no one group has the majority – then the voting cannot be done by a simple majority over the 3 options. Therefore, the voting will be done by pairwise voting. There are three different voting options:

Option 1: Complete vs. Partial then winner vs. None

Option 2: Complete vs. None then winner vs. Partial

Option 3: Partial vs. None then winner vs. Complete

One group will have the right to set the agenda (aka – which order you are voting in) – all

groups will then vote in whichever way will maximize their overall utility. (Important: utility of a

group is ONLY based on how high in the preference ranking the ultimate outcome is.)

Consider that the liberals control Congress and are able to set the agenda. How should they set

the agenda to achieve their preferred result?

Question 3: Geek Russian roulette

Consider the game of geek Russian roulette. The rules are: two players stand across from each

other and the first person calls out a word that starts with one of the first 3 letters of the alphabet

(for example: Ash, Bash, or Crash). The second player after hearing the first word calls out

another word that is up to 3 letters further along in the alphabet (so if player 1 called out

Crash...then player 2 could call out Dash, Eyelash, or Flash). When able, a player will call out

Zap – the 26th and last letter of the alphabet. When “Zap” is called out the other player usually

(with flair if they are a good sport) falls down...the player that calls out “Zap” collects the money

on the table and has won the game. Do you want to be the first or second player – what is the winning strategy?

Question 4: Jar Game

Consider the following game:

Players: 2

- We designate player #1 to be the one that starts with the jar.

Actions:

- Each round at the same time both players deposit between 1 to 4 pennies into the jar.

- Then both players are able to count the pennies in the jar.

- If there are 21 or more pennies, the person with the jar is the winner.

- If there are 20 or less pennies, the jar is passed to the other person and another round

begins. Do you want to be the first or second player? What is the winning strategy?

Answer rating: 100% (QA)

Question 3 Geek Russian Roulette In geek Russian roulette the winning strategy depends on whether you prioritize minimizing risk or maximizing reward ... View the full answer