LECTURE 5 Flashcards
Direct democracy
voters directly cast ballots in favour or opposition of particular projects.
2 forms of direct democracy
- Referendum
2. Voter initiative
How do referendum and voter initiative differ?
Referendum = already passes state legislation.
Voter initiative = vote to then be proposed as legislation.
Indirect democracy =
voters elect representatives who then make decisions about public projects.
Another name for indirect democracy
representative democracy
Majority voting is a method to…
aggregate individual voters into a social decision.
What’s a majority?
50% + 1 of the total votes.
3 conditions on preferences for majority voting to lead to a consistent aggregation.
- Dominance.
- Transitivity.
- Independence of irrelevant alternatives
What does dominance mean?
If all individuals choose X over Y, SWF should rank X > Y
What does transitivity mean?
If the SWF ranks X>Y and Y>Z, then it must rank X>Z
What does Independence of irrelevant alternatives (IIA) mean?
If SWF ranks X > Y, then another alternative Z is introduced, this should not affect pairwise ranking X > Y regardless of how Z relates to them.
Method to determine majority winner if there are 3 alternatives and 3 individuals with rankings over them?
PAIRWISE comparisons for each alternative
A vs B: which wins majority from 3 voter’s ranks?
A vs C
B vs C
Which ever wins in all pairwise comparisons = majority voting winner.
What is cycling and what does it violate?
Cycling = when majority voting does not deliver a consistent aggregation of preferences. Transitivity is violated and there is no clear winner.
CONDORCET PARADOX =
Individual transitivity –> social intransitivity
ARROW’S IMPOSSIBILITY THEOREM
There is NO social decision rule that converts individual preferences into a consistent aggregation decision without either restricting preferences or imposing a dictatorship.
INPUT arrows impossibility theorem
I = IIA N = Non-dictatorship P = Pareto efficiency/dominance U = Unrestricted domain T = Transitivity
What’s the issue if IIA is not satisfied?
Government could add irrelevant alternatives and affect the outcome of voting.
What is non dictatorship? What can it solve?
One person’s preferences should not determine the social outcome alone. Can solve intransitivity, but unfair.
What’s Pareto efficiency/dominance?
If all individuals rank X > Y, the SWF should rank X > Y.
What’s unrestricted domain?
SWF must account for any possible individual ranking - must choose a winner for any group of people with any set of preferences.
ARROW’S IMPOSSIBILITY THEOREM relating to INPUT
When there are >2 options, NO collective decision making process can satisfy all INPUT conditions.
2 common solutions to arrows impossibility.
- Single peaked preferences
2. Place different weights on different individuals depending on intensity of preferences.
Why do we also use pairwise comparisons for majority voting?
To reduce problem from choosing among many options to choosing among 2 at a time.
CONDORCET WINNER =
the option that defeats all others in pairwise comparisons by majority voting.
The existence of a Condorcet winner requires…
Single peaked preference.
What are the axis for graph of single peaked preferences?
Y axis = utility / rank / score
X axis = alternative e.g. low, middle, high school spending.
Single peaked means…
Constantly increasing
Constantly decreasing
OR go up, reach a peak, then down.