Voting

Question 1

Voting

Answer 1

Combine preferences to derive a social outcome

Question 2

Pairwise election

Answer 2

2 candidates

Question 3

General voting scenario

Answer 3

More than 2 candidates

Question 4

Social welfare function

Answer 4

Produces a social preference order

Question 5

Social choice function

Answer 5

Produces a single outcome

Question 6

Aggregated ranking

Answer 6

Outcome of social welfare function

Question 7

Plurality vote

Answer 7

Each candidate gets one point for each preference order which ranks them first

Question 8

Condorcet paradox

Answer 8

There are scenarios in which no matter which outcome is chosen, a majority of voters will be unhappy

Question 9

Condorcet winner

Answer 9

Candidate who always wins in pair-wise elections using plurality
Doesn’t always exist

Question 10

Condorcet criterion/Condorcet methods/Condorcet consistent

Answer 10

Voting system always chooses the condorcet winner when one exists

Question 11

Copeland method

Answer 11

Scoring based on pairwise victories - pairwise losses
Can also work when there is no condorcet winner

Question 12

Borda Count

Answer 12

add up ranking nums for each vote
not a condorcet method

Question 13

Pareto efficiency (Social welfare function)

Answer 13

Whenever every agent prefers one outcome over another, then that is shown in the aggregated ranking

Question 14

Independence of Irrelevant Alternatives (Social welfare function)

Answer 14

Whether one outcome ir ranked above another in the social outcome depends only on the relative orderings of the outcomes in the agents’ preferences

Question 15

Nondictatorship (Social welfare function)

Answer 15

There is no voter who has all of their preferences shown in the social outcome

Question 16

Arrow’s Theorem

Answer 16

For elections with more than 2 candidates, any social welfare function satisfying pareto efficiency and IIA is dictatorial

Question 17

Arrow’s Theorem result

Answer 17

Negative result - There are fundamental limits to democratic decision making

Question 18

Social welfare functions desirable properties

Answer 18

Pareto efficiency
Independence of irrelevant alternatives
Nondictatorship

Question 19

Social choice functions desirable properties

Answer 19

Weak pareto efficiency
Monotonicity
Nondictatorship

Question 20

Weak pareto efficiency (Social choice function)

Answer 20

When every agent prefers one outcome over another, the latter cannot be the outcome of the social choice function

Question 21

Monotonicity (Social choice function)

Answer 21

IIA equivalent for social choice. If the relative orderings between outcomes are maintained, the outcome of the function shouldn’t change

Question 22

Nondictatorship (Social choice function)

Answer 22

There doesn’t exist an agent where the function always selects the top choice in their preference ordering

Question 23

Muller-Satterthwaite’s Theorem

Answer 23

For elections with more than 2 candidates, any election satisfying weak pareto efficiency and monotonicity is dictatorial

Question 24

Manipulable (Social choice function)

Answer 24

Voter can gain a better outcome for themselves by unilaterally changing their preference profiles

Question 25

Gibbard-Satterthwaitte’s Theorem

Answer 25

Any social choice function with at least 3 outcomes which satisfies citizen sovereignty and is truthful (not manipulable) is dictatorial

Question 26

Citizen sovereignty

Answer 26

For every outcome, there is a preference ordering profile such that the social choice function will return that outcome

Question 27

Issues with manipulation

Answer 27

Unknowns
Other voters’ preferences
If they are also trying to manipulate the voting
Costly computation depending on the voting protocol used