Unit 2 Flashcards
What does public choice theory study?
The aggregation of individual preferences
What is the goal of voting theory?
To make the greatest number of people happy whilst allowing all to vote honestly
What does a voting method do?
It contains rules for valid voting and how votes are aggregated to yield a final result
What is a Condorcet voting method?
It is an election method that elects the candidate that would win a majority of the vote in all of the head-to-head elections against each of the other candidates, whenever there is such a candidate. A candidate with this property is called the Condorcet winner.
Explain the steps in the Condorcet voting algorithm?
1) Rank all candidates (elements) in order of preference, 1 best through to n, worst
2) Pairwise comparison between each candidate; the winner is determined by winning the majority of the pairwise competitions (1 v 1 contests)
How do we deal with an incomplete preference list in the CVA?
Ranked candidates assumed to be better than unranked ones
What type of method is a CVA?
Majoritarian
Note about CVA:
The Condorcet voting algorithm is a majoritarian method which specifies that the winner of the election is the candidate(s) that beats or ties with every other candidate in a pair-wise comparison.
How can we generalise these pairwise competitions? Why is this rarely done in reality?
Model elections with a digraph
BUT this is too slow for any real life applications
check I know what a digraph is!
See
Example 2.1 on doing a CVA
2 problems with using Condorcet voting?
1) Is too slow with any significant number of voters/candidates
2) Doesn’t always generate a winner; can observe a Condorcet cycle
What is a Condorcet cycle? What does it lead to? Define this?
Situation when cyclic voting preferences lead to inability to determine a winner
Causes the Condorcet paradox = situation in which collective preferences are cyclic
Why does the Condorcet paradox occur?
It occurs when there are conflicting majorities made up of different groups of individuals
eg. 1) ABC, 2) BCA, 3) CAB
If a majority rule such as the CVA leads to no solution, what has happened? What does this mean for voters?
The rule has generated socially intransitive preferences!
Therefore, voters may not have an incentive to truthfully reveal their preferences!
EV point regarding the Condorcet paradox?
Quite unlikely with small no. of Vs and Cs: eg) 3 voters, 3 candidates (with strong pref. orderings) -> 12/216 chance of cyclic preferences
But the larger the no. candidates and voters, less more likely it becomes!!!
Explain a hypothetical political application of the Condorcet voting method?
3 MPs must divide ‘m’ budget between their 3 districts, with an objective of maximising the funds for their home district (see notes for rest of example, check I understand it!)
Why may someone change their vote in CV method?(2)
1) To win
2) To avoid their worst outcome!!!
A CV method is very slow to find a winner in a large set, what can be done about this?
It can be modified to increase its speed and therefore usefulness: eg. Debian voting system/Condorcet-fuse algorithm
What is Arrows impossibility theorem?
NO method of aggregating individual preferences will produce coherent results if 4 minimal conditions are met: universal domain, unanimity, independence and non-dictatorship (can I explain all these?)
What did May’s theorem show?
It proved that the only satisfaction of Arrows conditions is Simple Majority Voting (ie. Majoritarian) (note: must have odd no. voters and indecision is not allowed!)
How can we obtain coherent results whilst abiding to AIT?
Placing restrictions on universality
What are single-peaked preferences?
The restriction that every individual is assumed to have one most preferred alternative; this is a restriction on the domain!
Draw diagram showing SPPs vs non SPPs
see notes
Give a political example of SPPs?
eg. interest rates set by CB