Voting systems
Plurality voting Plurality voting refers to elections in which more than one candidate is to be chosen There are multiple reasons One reason: so that everyone gets a chance to have their view represented Second reason: so that the right combination of candidates gets chosen
Plurality voting system Plurality voting is used in 43 of the 191 countries in the United Nations for either local or national elections. In single winner plurality voting, each voter is allowed to vote for only one candidate, and the winner of the election is whichever candidate represents a plurality of voters, that is, whoever received the largest number of votes. it is however very contentious to draw district boundary lines in this system Plurality voting is based on minimal information
Example: class president election (compare to Bush, Gore, Nader) Suppose: Each class has a president, who sits on a school council. Further assume that, in this imaginary school, male and female students disagree on many issues; students prefer to vote for candidates of their gender. Three candidates: Tofu, Milo and Leila. Each class member gets a ballot, with these three names on it. Each voter must put an "X" by one of the names on their ballot. Votes for Tofu, for Milo, and for Leila placed in separate piles.
Candidate Tofu Milo Leila # votes 11 16 13
Milo Wins with only 40% of the vote Electors only vote once
Plurality voting Suppose that candidates are ranked (1-3). Then Milo might be the favorite of fewer than half the voters. In some systems a runoff election among the top placing voters is called for.
Candidate Tofu Milo Leila # 1 votes # 2 votes # 3 votes 11 22 7 16 6 18 13 12 15
advantages/disadvantages OMOV Constituency Tactical voting Party effects (block voting) Wasted votes (< majority) Manipulation
Multiple step voting Runoffs Diminish tactical voting Majority rule (if enough steps) Voter burnout
Single transferable vote: a Here s an example: compromise The student council wants to organize a rock concert A list of 5 bands is considered as candidates but the council can only afford 3 bands. There are twenty council members who list their preferences
Only first two preferences shown # council members xxxx xx xxxx xxxx xxxx x x 1 st preference Car Seat Headrest Radiator Hospital Grimes Grimes Courtney Barnett Palehound 2 nd preference Car Seat Headrest Courtney Barnett Palehound
Setting the quota Droop quota (votes/(seats+1))+1 =20/4+1=6
Finding the winners Any candidate who has reached or exceeded the required quota is declared elected If not enough candidates have been elected, the count continues. If a candidate has more votes than the quota, then their surplus is transferred proportionally with rounding to remaining candidates according to the next preference on each voter's ballot. If no one meets the quota, the candidate with the fewest votes is eliminated and their votes are transferred. Repeat from first step until the seats are filled
Round 1 Grimes meet the quota. Grimes is chosen
Round 2 Grimes excess transferred to Courtney Barnett and Palehound based on second choices. No quota. Radiator Hospital eliminated
Round 3 Radiator Hospital votes transferred to second choice. Car Seat Headrest reaches quota; no extra votes
No remaining candidate meets quota. Palehound eliminated Round 4
Candidate CSH Radiator Hospital Grimes Courtney Barnett Palehound Round 1 xxxx xx xxxx xxxx xxxx x x Grimes meets quota; elected Round 2 xxxx xx xxxx xx xxxxx xxx Grimes excess transferred to Courtney and Palehound based on second choices. No quota. RH eliminated Round 3 xxxx xx xxxx xx xxxxx xxx RH votes transferred to second choice. CSH reaches quota; no extra votes Round 4 xxxx xx xxxx xx xxxxx xxx No remaining candidate meets quota. Palehound eliminated
Call for nominations I m going to conduct a popularity poll I need six (6) nominations for Favorite Bands of Math 210 Prior winners of TV show contests not allowed The Pride not allowed. Someone else in the class has to have heard of the band Your homework: figure out the top 3 bands based on the STV method
M210 Nominees in 2012 1) Queen 2)Lonely Island Group 3) Red Hot Chile Peppers 4) Rise Against 5) Day to Remember 6) Wu-Tang Clan
M210 Nominees in 2016 1) Metric 2) At the Drive In 3) Queen 4) 30 seconds to Mars 5) Beatles 6) Gorillaz
Clicker: turn clicker on number mode and enter the bands in your order of perference, e.g., 1) Group 1 2) Group 2 3) Group 3 4) Group 4 5) Group 5 6) Group 6 143625
Clicker: turn clicker on number mode and enter your top two bands in your order of perference, e.g., 36 1) Queen 2)Lonely Island Group 3) Red Hot Chile Peppers 4) Rise Against 5) Day to Remember 6) Wu-Tang Clan
Voter table 1 st choice 2 nd choice Queen Lonely Island RHCP Rise Against Day to Remember Wu-Tang Clan Queen 2 13 2 1 Lonely Island 4 3 2 RHCP 8 2 1 2 1 3 Rise Against Day to Remember Wu-Tang Clan 1 6 1 1 3 1 1 4 3 Total 13 6 30 6 3 7
Group work Use the single transferable vote method to choose the top three bands of MATH 210G Write date and names of each of your group members You will be given 10-15 minutes for this.
Recap Mathematics: seeks optimal solution Voting: optimally represent public opinion No voting system is perfect Outcome often depends on system employed
Lattice models for opinion Renormalization in physics Ising/Potts model applet: renormalization grou