Lecture 2 - Voting

Question 1

Features of unanimity voting

Answer 1

• leads to Pareto-improving decisions
• time-consuming if many alternatives
• vulnerable to strategic behaviour (<=> veto to get an even better outcome)

Question 2

3 Criteria for good collective decision-making mechanism

Answer 2

1) Achieves a clear-cut stable decision
2) Should be the efficient outcome
3) A reasonable balance b/n the costs and quality of decision-making

Question 3

Arrow’s Impossibility Theorem - definition

Answer 3

Impossible to devise a social choice rule that meets some fairly basic requirements. Hence, we need to weigh up the relative advantages and disadvantages of different decision rules.

Question 4

Arrow’s Impossibility Theorem - requirements (5)

Answer 4

INPUT

1) Independence of irrelevant alternatives
2) Non-dictatorship: decision not determined by the preferences of one individual
3) Pareto criterion: the collective ranking should coincide with the unanimous individual ranking (if it exists)
4) Unrestricted domain: should accommodate any possible individual ranking
5) Transitivity

Question 5

Condorcet paradox

Answer 5

Transitive preferences at the individual level do not necessarily imply transitive majority-voting outcomes.

Question 6

When do voting cycles arise?

Answer 6

When voter preferences are NOT single-peaked.

Question 7

Single-peaked preferences + Black’s conclusion

Answer 7

For each voter there is an optimum amount of the public good, utility declines with distance from it.

Black: majority rule produces an eq. outcome when prefs are single-peaked.

Question 8

Cases where preferences are NOT single-peaked

Answer 8

1) All-or-nothing prefs (eg. spending to stage an Olympics)
2) Multi-dimensional choices
3) Opt-out alternatives (eg, private education or health care)

Question 9

Condorcet winner

Answer 9

An option which would win successive majority votes if considered in pairwise votes against all others

Question 10

Agenda-setting & manipulation

Answer 10

When no Condorcet winner exists, the person deciding the sequence of pairwise votes has real power.
May lead to manipulation, with people misrepresenting their preferences.

Question 11

Log-rolling - when is it useful and what effects does it have on welfare?

Answer 11

When preference intensities are unevenly distributed, some may benefit from ‘vote-trading’. This can increase community welfare but imposes costs on non-vote-traders.

Question 12

Borda voting - procedure, which outcomes does it favour, and important result

Answer 12

Voters rank all options, they get points depending on their position in each individual ranking.

• > consensus-orientated, i.e. favours outcomes with broad support, which is not necessarily the pref of the majority
• > violates IIA requirement

Question 13

Plurality voting

Answer 13

‘First-past-the-post’, only first preference is recorded (parliamentary elections)

• > encourages tactical voting, i.e. voting for an option forecasted to be likely to win
• > can fail to select Condorcet winner.

Question 14

Approval voting

Answer 14

Ranking of as many options as voters wish, cutoff b/n ‘acceptable’ and ‘unacceptable

• > generally does better than plurality voting, but may still fail to pick a Condorcet winner
• > large strategic implications of the cutoff

Question 15

Run-off voting

Answer 15

French election mechanism

-> can fail to select a Condorcet winner

Question 16

Citizen-candidate models

Answer 16

Solving by BI, voters will choose candidates with preferences close to theirs (as winner implements her preferred policy), either sincerely or strategically (vote for one standing a chance)
-> complex outcomes, depend on cost of running, typically multiple equilibria