5: Some fundamentals about Democratic Decision-making

Question 1

Arrow’s theorem

Answer 1

under no circumstances is there a group preference ordering that could sensibly be called the public interest

Arrow’s theorem is not telling us things always go wrong but there is no guarantee that things go well

in a specific framework, it is impossible to find a social welfare function which simultaneously satisfies all conditions: universal domain, independence of irrelative alternatives, non-dictatorship, transitivity and unanimity

institutional trilemma between stable outcomes, universal admissibility and non-dictatorship

shows that even when individuals are rational, a group might not be

Question 2

conditions of Arrow’s theorem: universal domain

Answer 2

aggregation rule has to satisfy normative criteria for all possible collections of alternatives and rational individual preferences

voting must account for all individual preferences

all choices are equal - violated with unbalanced choices

Question 3

conditions of Arrow’s theorem: independence of irrelevant alternatives

Answer 3

kind of basic coherence/consistency

one should not be able to manipulate social preference by introducing new alternatives

e.g. IIA is violated if an election’s winning candidate would have won if the losing candidate was taken out

Question 4

conditions of Arrow’s theorem: non-dictatorship

Answer 4

wishes of multiple voters should be taken into consideration

Question 5

conditions of Arrow’s theorem: unanimity

Answer 5

if every individual in society prefers X to Y, then social preference should be X to Y

basic standard of aggregation rule to represent views of individuals in society

Question 6

conditions of Arrow’s theorem: transitivity

Answer 6

if X is preferred to Y, and Y is preferred to Z, then X is preferred to Z

Question 7

4 functions of elections

Answer 7

1. aggregate and represent voters’ conflicting preferences - use vote as a means to come to a decision
2. aggregate dispersed information about the correct political decisions
   - different pieces of information as to how to effectively put into place policy changes to achieve a particular goal
3. address an adverse selection problem by allowing the citizens to select the most competent individuals for public office
4. provide a mechanism to control moral hazard, by holding elected officials accountable to the citizens

Question 8

Borda count aggregation

Answer 8

give each preference a number of points

e.g. max number of points for the alternative you like the most, that -1 for the next best alternative, etc.

Question 9

median voter theorem

Answer 9

50% of the population below that voter and 50% of the population above them

in some ways, can be the ‘deciding’ vote in an election