Week 9 Flashcards
Define stability
The tendency of the decision-making process to eventually reach a settled conclusion, and not to keep jumping around between alternatives.
What is the social choice theory?
Determining the preferences of an individual is just a matter of accepting that an individual’s judgement cannot be open to dispute.
What is a Collective level? When does the Condorcet paradox arise?
There is a cycle in preference and no final decision is possible.
The Condorcet paradox arises when there are cyclical preferences.
What is the Condorcet paradox?
Intransitivity of group preferences can arise even when individual preferences are transitive.
Define independence of irrelevant alternatives.
Adding new options should not effect the initial ranking of the old options, so the collective ranking over the old options should be unchanged.
suppose a group prefers A over C, adding B as an option should not change the relative preference between A and C.
Define non-Dictatorship
The collective preference should not be determined by the preference of one individual.
Define Pareto criterion.
If everybody agrees on the ranking of all the possible options, so should the group; the collective ranking should coincide with the common individual ranking.
Define unrestricted domain.
The collective choice method should accommodate any possible individual ranking system.
Define transitivity.
If the group prefers A to B and B to C, then the group cannot prefer C to A
Define Arrow’s impossibility theorem
When choosing among more than two options, there exists no collective decision-making process that satisfies the conditions I, N, P, U, T
- Independence of irrelevant alternatives
- Non-dictatorship
- Pareto criterion
- Unrestricted domain
- Transitivity
what is may’s theorem?
May’s theorem says that when choosing among two options, there is only one collective decision-making process satisfying the four conditions below:
- Anonymity
- Neutrality
- Decisiveness
- Positive responsiveness
–> Majority rule
What is the Condorcet method?
Complete each round of majority votes:
- Each option against all other options
–> The option that defeats all others in pairwise majority
voting is called a Condorcet winner.
simple example
Assume there are three vote options [a,b,c]
1) start by voting a against b
2) winner of the first vote is opposed to c
3) winner of the second vote is the chosen option
Does the median voter theorem depend on honesty?
- No, voters have an incentive to misrepresent their
preferences. - Misrepresenting preferences to the left does not change the median and the final outcome.
- The median gets her most-preferred outcome and thus cannot benefit from misrepresenting her preferences.
Does the median voter theorem depend on efficiency?
The efficient choice will only be made if this is the most preferred alternative for the median voter. No reason why this should be the case.
The median voter theorem will not, in general, produce an efficient choice.
What is multidimensional voting?
- Extend the vote to the location of the bus stop and the time at which the bus is to arrive.
- Even though preferences are single-peaked, the social ordering is intransitive and the median voter theorem fails - it does not extend beyond the one-dimensional choice problems
if voting was carried out on each dimension separately, it can generate, for some preferences, inefficient voting outcomes.
What are the alternatives to majority rule?
1)Plurality voting
2) Approval voting
3) Borda Voting
Explain Plurality voting.
Voters give 1 point to their first choice and zero points to all other options.
Explain approval voting
Voters can give 1 point to more than one option , in fact to as many or as few options as they want to.
Explain Borda voting
Voters give the highest possible score to their first choice, and then progressively lower scores to worse choices.
What is the Borda voting procedure? What are its properties?
- Suppose there are n options
- Each possible choice gets some points:
- first choice gets n points
- Second choice gets n - 1 points
- Xth choice gets n - X points
- Last choice gets 1 point
Pick a winner by adding up scores, the option with the highest score wins.
- Very simple procedure almost always picks a winner
What is the Plurality voting procedure?
- only the first choice of each voter matters and is given one
point. - Choices other than the first do not count at all.
- Add up the scores, then the option with the highest score is the plurality winner
What is the approval voting procedure?
- Voters may vote for as many options as they like
- Winning option is the one that gathers the most votes
- Rules out strategic voting
What is the runoff voting procedure? what are its drawbacks?
- Only first-place votes are counted.
- If there is no majority, a second runoff election involving
only the two strongest candidates is held
Two drawbacks:
- it may fail to select the Condorcet winner
- It can violate positive responsiveness.
What are the drawbacks of the various alternative voting schemes?
- Borda rule: irrelevant alternatives influence outcome.
- Approval voting: fails to select the Condorcet winner
- Runoff voting: fails to select the Condorcet winner and can
violate positive responsiveness - Plurality voting: fails to select the Condorcet winner.
