Exam 2 - Voting Systems

Borda Count

Each rank given a number of points - most points wins

Sequential Pairwise Voting

Head to head based on random pairs of candidates

does satisfy cwc

Black’s System

1. If there is a Condorcet winner they win

2. if there is no cw use Borda count

Instant runoff

1. remove candidates with the fewest first place votes i.e those who come in last via plurality

2. Repeat Step one with a new election with the remaining candidates, moving up candidates who were below those eliminated

Plurality

Most votes wins

Majority Rule

Whoever gets over half the votes wins - is monotone, anonymous and neutral

Dictatorship

Not all voters treated equally - not anonymous

Imposed Rule

not all candidates treated equally - not neutral

Approval voting

A voter can vote for as many candidates as they want and whoever gets the most votes wins

Minority Rule

getting votes is bad - not monotone

Majority Criterium

A voting system satisfy MC if whenever someone gets the majority of first place votes they win the election.

Arrow’s Condtions

1. Universality

2. IIA

3. Monotone

4. Citizen Sovreignty

5. Non-Dictatorship

Universality

voters can rank candidates in any order they want

non-dictatorship

Doesn’t want a dictatorship

citizen sovereignty

any societal preference order can happen

monotone

getting more votes cant cause a candidate to go from winning to losing - a candidate should be liked to win

neutral

A voting system is neutral if whenever everyone swaps who they vote for, the outcome should swap - fair to candidates

anonymous

A voting system is anonymous if whenever 2 voters swap ballots the outcome doesn’t change - fair for voters-each vote counts the same

IIA

A voting system satisfies IIA if whenever no one changes their relative rank between A and B then society does not change the relative rank of A and B.

Condorcet winner criterian

A voting system satisfies cwc if whenever there is a Condorcet winner then that person wins the election

Condorcet winner

A candidate that beats all other candidate head to head

May’s theorem

In an election with 2 candidates and an odd number of voters, majority rule is the only voting system that is anonymous, neutral and monotone and can’t end in a tie.

Societal Preference order

Candidates ranked based off of societies approval

Arrows Theorem

No voting system satisfies Arrows Theorem

(Individual) Preference Order

A persons rank based on approval

Quota system

A voting system where there is a quota “q” - a number that may depend on the number of voters and any candidate that gets at least “q” votes is declared a winner.