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Features of unanimity voting

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


3 Criteria for good collective decision-making mechanism

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


Arrow's Impossibility Theorem - definition

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.


Arrow's Impossibility Theorem - requirements (5)

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


Condorcet paradox

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


When do voting cycles arise?

When voter preferences are NOT single-peaked.


Single-peaked preferences + Black's conclusion

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.


Cases where preferences are NOT single-peaked

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)


Condorcet winner

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


Agenda-setting & manipulation

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.


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

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


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

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


Plurality voting

'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.


Approval voting

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


Run-off voting

French election mechanism
-> can fail to select a Condorcet winner


Citizen-candidate models

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