Question

Question 2: Agenda Setting

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 1

Question 2.

Liberal : complete > partial > none.

Moderates : partial > none > complete

Conservatives : none > complete > partial

Let's see how each option will play out but note that liberals control the Congress and are able to set the agenda. And the liberal wants complete health insurance since it is the most preferred choice for liberals.

Option 1. Complete vs partial then winner vs none.

In this option first the choice has to be made between complete and partial and then the winner will put up against none. So in the choice between complete and partial, complete will be selected since liberals and conservatives prefer complete over partial while only moderate prefers partial over complete. And then in the choice between complete and none, none will be selected since moderates and conservatives prefer none over complete while only liberals prefer complete over none.

So option 1 will not lead to the preferred choice of liberals so they shouldn't choose this option.

Option 2.

In option 2 the first decision has to be made between complete and none and then the winner of the first will be put up against partial.

Let's see whether this will lead to the ideal choice of liberals or not.

So in the choice between complete and none, none will win since moderates and conservatives prefer none over complete while only liberals prefer complete over none. So the choice of completel health care insurance will be rejected in immediately in this option.

So liberals shouldn't choose option 2 also.

Option 3.

We have seen that option 1 and option 2 aren't ideal options for liberals so we know this option has to be the answer but let's verify it.

In option one the first decision has to be made between partial and none and then the winner will be put up against the complete.

So in the first choice between partial and none, partial will win since moderates and liberals prefer partial over none and only conservatives prefer none over partial. And then the second choice will be made between partial and complete and in the choice between partial and complete, complete will win since liberals and conservatives prefer complete over partial while only moderates prefer partial over complete. And choice complete will adopted under option 3.

So liberals will choose option 3.