Social Economics Exam 1

Pareto efficiency

An outcome is Pareto efficient if it is not

possible to make one person better off without hurting

someone else.

Adverse selection

When a buyer would be better off with a

randomly chosen item than with the items that are actually

selected by their owners for sale

Moral hazard

When the actions of your trading partner are

worse for you than the actions that would have been chosen if

you hadn’t traded.

Rawls’ maxmin principle

society should maximize the welfare of

the worst-off person

Pareto dominant

B>A if everyone likes B at least as much as A,

and at least one person strictly prefers B.

potential Pareto improvement

The winners could potentially pay back the losses that others have to take on.

Marshall’s approach

add up how

much each person would pay to move from A to B (may be

negative). If the sum is positive, then B is better

Plurality Voting

Pick the alternative(s) with the greatest number of

first-place rankings.

Condorcet’s Method

Pick the Condorcet winner (i.e., the alternative that beats

any other alternative in a head-to-head vote), if there is one.

Borda count

Give an alternative 0 points for each voter who ranks it last,

1 point for each voter who ranks it second-to-last, 2 points

for etc. Pick the alternative(s) with the most points.

Hare (instant runoff) system

First delete the alternative(s) with the fewest first-place

votes. Repeat. The last alternative deleted wins.

Sequential pairwise voting with a fixed agenda

Put the alternatives in a given order. Hold a head-to-head

vote between the first two, then the winner against the

third, and so on

Dictatorship

Choose the favorite alternative of a given voter (the

dictator)

Non-manipulability

a SCP is manipulable if there is any list of

rankings such that some voter can get an outcome that she prefers

by reporting a ranking different from her true ranking.

Theorem (The “What Problems Do You Want?” Theorem)

No SCP satisfies AAW, Pareto, Condorcet, Monotonicity, and IIA.

Theorem (Gibbard-Satterthwaite Theorem)

The only SCP that 1) always has a unique winner, 2) satisfies the

Pareto Condition, and 3) is non-manipulable is dictatorship.

Always a Winner

every list of rankings produces at least one winner (ideally a unique winner).

Pareto Condition

if everyone ranks x ahead of y , then y is not a winner.

Condorcet Condition

if for any alternative y , over half the voters rank x ahead of y , then x is the only winner.

Monotonicity Condition

if x is a winner, and someone moves x up one spot in her ranking, then x is still a winner.

IIA

if x is a winner and y is not, then for any other list of rankings where no voters change whether they rank x ahead of y , y is still not a winner

Dictatorship

Always a Winner? YES

Pareto? YES If everyone ranks a ahead of b, then b cannot be

the dictator’s favorite.

Condorcet? ✘ The dictator’s favorite may not be the

Condorcet winner.

Monotonicity? YES Think about why.

IIA? YES Think about why.

Iterating

Step 1: Run the SCP. Rank the winner(s) first, and remove

them from the list of alternatives.

Step 2: Run the SCP on the remaining alternatives. Rank the

winner(s) second, and remove them.

Repeat until all alternatives are ranked.

The Pareto Condition for SWFs

If everyone has the same ranking, then the SWF chooses that ranking.

The Monotonicity Condition for SWFs

If the SWF ranks x ahead of y , and someone who ranked y ahead of x switches x and

y in their ranking, then the SWF still ranks x ahead of y .

The Independence of Irrelevant Alternatives (IIA) Condition for SWFs

If no voters change whether they rank x ahead of y,

then neither does the SWF

single peaked

If 1) each voter has a favorite outcome, and 2) moving away from that favorite in either direction means a lower ranking. The ranking does not necessarily decrease at the same rate when we move to the right as when we move to the left.

The Shapley Value

each pays the average of his MC across all possible ways of ordering people. (how frequently does adding him to a group make the difference between winning and losing?)

The “Pack and Crack” strategy

Start with the first district. Fill it with almost equal proportions of voters, but with a tiny edge for your party.

Repeat until you run out of voters from one side or the other. Then fill the rest of the districts with the remaining voters

Divide & Choose

Procedure: 1 person (the Divider) splits the objects into 2 piles, each of which he values at 50% of the total. (Assume that it divides evenly.)

Then the other person (the Chooser) picks her favorite pile, and the Divider gets the

other pile.

Moving Knife procedure

the Divider starts with 2 piles, eachof which he values at 50%. Then he gradually rearranges them, maintaining his 50% value for each pile, until he reaches a split where the Chooser also values each pile equally.

Envy-free

No one values someone else’s allocation more than his/her own.

Equitable

Everyone gets the same fraction of the total value (according to their own tastes)

Condorcet

= Fails Always-a-Winner

Dictatorship

= Fails Condorcet 

Hare System

= Fails Condorcet, IIA, Monotonicity

Plurality

= Fails Condorcet, IIA

Borda Count

= Fails IIA, Condorcet