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Final Rankings
The results have been calculated! Here are the rankings:
1: Mixed-Member Proportional Ranking: 10/11
2: Approval Instant Runoff Voting 8/11
3: Condorcet Method 6/11
4 + 5: Borda Count and Disapproval Instant Runoff 5/11
6: First Past the Post 3/11
According to this chart, Approval IRV and Mixed Member Proportional are the best systems!
Bibliography
Works Cited
C.G.P. Grey. Dir. Alternative Vote Explained, The by C.G.P. Grey. Perf. C.G.P. Grey. Prods. Video. < Http://www.youtube.com/watch?v=3Y3jE3B8HsE >
Mixed-Member Proportional Representation Explained. by C.G.P. Grey. Prod. C.G.P., Grey. Video. < Http://www.youtube.com/watch?v=QT0I-sdoSXU >
O'Shaunessey, Kathleen. Electoral Systems Problem Set. N.d. Worksheet.
An explanation of the Mixed Member Proportional system.
These videos brought to you by C.G.P. Grey (http://www.youtube.com/user/CGPGrey?feature=watch)
Mixed Member Proportional Ranking
This method, used in multi-winner elections, is a way to directly use a proportional preference list to find a set of winners that are not only local, but also proportional to the preferences. There are 2 parallel rounds of voting: Round 1, a FPTP vote, and Round 2, a preference list of political parties. The first half of the seats are decided by Round 1, and it shares the same problems with FPTP. However, Round 2’s preference list reveals the preferences of political parties, and the other half of seats are filled in according to how over- or underrepresented that political party is. This is meant to fix all problems that arise due to the Round 1 votes. These results are interpreted as a whole, so no problems arise from this. However, the representatives for the Round 2 seats are determined by a Round 2 ranking for each political party. These rankings determine the order in which the Round 2 candidates are awarded seats.
Majority Criterion: A true majority will win a majority, as a majority can still be underrepresented.
Condorcet Criterion: Generally preferred candidates always win a seat!
Pareto Criterion: Pairwise preferred candidates would also win, and be ranked higher on the runoff-repair stage.
Irrelevance of Independent Alternatives (IIA): Political parties that drop out are filled in by the runoff-repair rankings.
Monotonicity Criterion: More votes will not hurt anyone, as they increase the chance of the candidate or party winning either election.
Spoiler Effect Prevention: The elections allow preferences to be equally ranked, and can be a tool to allow smaller parties to grow.
Minority Rule Prevention: Although a minority may win, a majority will be filled in with the Round 2 seats.
Preference Proportionality: The second stage is introduced solely to fix proportions.
Gerrymandering Prevention: Gerrymandering only influences Round 1. The runoff-repair round, Round 2, is a generalized ranking!
Political Diversity: This method strongly encourages smaller political parties.
Definitive Outcome: Although this works perfectly with a multi-winner election, this method does not work if the seats can not be divided or doubled, or if there can only be 1 winner.
Ranking: Alpha
Borda Count
This method takes a ranked ballot, assigning values to each rank, then counting which candidate has the most points. Last place is 0 points, second-last 1 point, and so on, where first place has X points, where X is 1 less than the number of candidates.
Majority Criterion: Majorities would have many first place rankings, and thus would win.
Condorcet Criterion: General comparisons do not occur, causing the problem of a Condorcet candidate, or a generally preferred candidate, to lose.
Pareto Criterion: Pairwise comparisons occur, and work through the point decisions.
Irrelevance of Independent Alternatives (IIA): Dropping out can change the number of points a candidate gets, and pushes another up.
Monotonicity Criterion: All extra favorable votes increase the points a candidate gets!
Spoiler Effect Prevention: The spoiler effect still draws points away from similar candidates.
Minority Rule Prevention: A minority still can receive the largest number of points, as there may not be a majority candidate, and this method does not simulate elections until a candidate is preferred by a majority.
Preference Proportionality: This method ranks winners proportionally with multi-winner elections.
Gerrymandering Prevention: The points should carry through districts, and thus gerrymandering is prevented!
Political Diversity: This method still trends towards 2 political parties.
Definitive Outcome: Candidates can have the same number of points!
Ranking: Zeta
This video explains Disapproval IRV, also known as the French system and the Alternative Vote.
Condorcet Voting
This method is also called “instant pairwise voting,” or IPV. IPV starts off like Approval IRV, where a ranked ballot is filled out. However, afterwards, each member is compared to the others, and if one wins a majority with every one of the pairwise simulations, the member wins!
Majority Criterion: Majorities are both pairwise and generally preferred.
Condorcet Criterion: The IPV method is designed to satisfy pairwise and general preferences.
Pareto Criterion: IPV, as stated before, satisfies pairwise and general preferences.
Irrelevance of Independent Alternatives (IIA): Dropping out would retain the same values, as this wouldn’t change the opinion stated in the ranked ballot.
Monotonicity Criterion: Any voters switching to the winner would increase the preference ratio, helping the winning candidate.
Spoiler Effect Prevention: Introducing new parties still can cause another to lose! There is no runoff function in this method.
Minority Rule Prevention: A minority could not possibly be preferred by a majority!
Preference Proportionality: With this method, the pairwise comparisons may still result in a slim majority (around 51%) to win all seats in a multi-winner election. A different function is needed to fix this problem...
Gerrymandering Prevention: This method still would require districts, which are a main deciding factor of the winner.
Political Diversity: This method does not strongly encourage new political parties, and still trends towards a bipartisan system.
Definitive Outcome: This voting method may not return a winner, due to the Condorcet Paradox. Candidate A can be preferred to Candidate B, Candidate B is preferred to Candidate C, but Candidate C is preferred to Candidate A! An example occurs with 3 voters and 3 candidates: Candidates A, B, and C, with voters X, Y, and Z. X’s preferences are A, then B, then C. Y’s preferences are B, then C, then A. Z’s preferences are C, then A, then B. The Condorcet paradox occurs in this situation, as explained before!
Ranking: Epsilon
Instant Approval Runoff Voting
The Approval IRV system first starts the same as Disapproval IRV, except only the top 2 candidates, determined by pairwise comparison, advance to the second "runoff" round. The lower rankings simulate the reelection.
Majority Criterion: Yes, a majority will win all elections through this method.
Condorcet Criterion: General comparisons may not determine the top 2.
Pareto Criterion: A pairwise comparison is the method of finding the top 2.
Irrelevance of Independent Alternatives (IIA): Dropping out? Will not affect the winner at all!
Monotonicity Criterion: Drawing a candidate to prematurely drop out will cause IIA, and still retains the winner!
Spoiler Effect Prevention: The runoff portion will redirect your votes to the preferred candidate.
Minority Rule Prevention: At the end, the winner must have a majority!
Preference Proportionality: With multi-winner elections, all runoff methods allow large amounts of deviation, like plurality voting.
Gerrymandering Prevention: Yes, the districts still impact the outcome. Still susceptible to gerrymandering.
Political Diversity: Using the runoff systems encourage smaller parties to grow, a main advantage of runoff voting.
Definitive Outcome: This method always returns a winner.
Ranking: Gamma
The Problems with First Past the Post voting, explained.
Source: http://www.youtube.com/watch?v=s7tWHJfhiyo
Instant Disapproval Runoff Voting
This voting method is the exact same as plurality voting, except for one point: The loser is eliminated, and the preferences simulate another round of voting.
How it Works: http://www.ctl.ua.edu/math103/voting/methodof.htm
Majority Criterion: The first item checked is the presence of a majority.
Condorcet Criterion: With clearly preferred candidates, a candidate still may not win!
Pareto Criterion: Pairwise comparisons sometimes reveal a candidate being indicated as “better” to a majority, but losing!
Irrelevance of Independent Alternatives (IIA): This method simulates dropping out, but the wrong candidate dropping out may change the election.
Monotonicity Criterion: Linked to IIA, changes that “help” a candidate may cause another to prematurely drop out, causing that candidate to lose!
Spoiler Effect Prevention: The runoff feature effectively removes the spoiler effect from the vote! This works!
Minority Rule Prevention: There will, at least, be a majority at the final analysis stage, as the method loops until 2 candidates are left and 1 has a majority.
Preference Proportionality: The proportionality can still be thrown off by the same way FPTP can be.
Gerrymandering Prevention: Gerrymandering still can mess up elections with IRV.
Political Diversity: This method encourages smaller political parties to start up, since the spoiler effect is gone.
Definitive Outcome: This method always returns a result!
Ranking: Zeta
Voting Ranks
After each voting method summary, I grade the method. Grading the method helps rank the method along a scale from 1 to 11, according to how many criteria the method satisfies. As no methods I know of are perfect, according to Arrow's Impossibility Theorem, a 10/11 would be the best possible grade, and a 0/11 the worst.
Rank 11: Alpha Best possible method!
Rank 10: Beta
Rank 9: Gamma
Rank 8: Delta
Rank 7: Epsilon
Rank 6: Zeta
Rank 5: Eta
Rank 4: Theta Rank of FPTP
Rank 3: Iota
Rank 2: Xi Really bad method
Rank 1: Omega Worst voting method ever!!! (very rare)
First Past the Post
The most common voting system used is called First Past the Post voting, FPP, or FPTP. FPTP is a fairly simple system, which is why it is used so often: Whoever has the most votes ranking them as first place wins. However, this has many problems!
Here are the points about the FPTP system:
Majority Criterion: A majority implies a plurality.
Condorcet Criterion: Clearly preferred candidates actually lose, due to the Spoiler Effect.
Pareto Criterion: Also by the Spoiler Effect, a pairwise loser still can win.
Irrelevance of Independent Alternatives (IIA): Yet another “Spoiler Effect” related problem, the dropping out of candidates that know they will lose will affect the election through the inverse of the Spoiler Effect.
Monotonicity Criterion: Once a candidate wins, any more votes for that candidate would increase the plurality.
Spoiler Effect Prevention: As many FPFP problems are related to this, this is important. Starting with a bipartisan system, there are 2 parties: Alpha and Omega. The outcome would have been 40% to Alpha and 60% to Omega. However, a new political party joins: Xi. Many Omega voters would rather vote for the Xi candidate, and the Xi party rises to almost equal status with the main 2 political parties. However, with the exact same preferences, the vote is divided this way: 40% to Alpha, 35% to Omega, and 25% to Xi. However, Alpha wins the election, instead of Xi. This is the main problem with FPTP, strategic voting. This is voting against a candidate, instead of for a candidate. This is the case with the election above: Xi voters agree most with Omega, and would vote for Omega to prevent Alpha from winning. This is where the spoiler effect comes in: Both Omega and Xi voters lost, as Alpha won the election. However, without Xi joining, Alpha would have lost! It also may be possible that the Alpha party supported Xi, as every vote for Xi is a vote away from Alpha’s main enemy, Omega.
Minority Rule Prevention: In a 30-party system, 5% may be enough to win a plurality!
Preference Proportionality: Slim pluralities can result in candidates spread out, and winning all localized elections.
Gerrymandering Prevention: This is highly susceptible to gerrymandering, as visible by some countries with FPTP voting systems, like the United States.
Political Diversity: Through this system, a study shows that FPTP elections tend towards bipartisan systems.
Definitive Outcome: This system always returns a winner.
As this particular voting system shows, a simple, seemingly logical system isn't always the best!
Ranking: Theta
Criteria
To effectively judge different voting methods, I need to know what to judge them on. The criteria I will be using are:
Majority Criterion: If a majority prefers a candidate, the candidate should win.
Condorcet Criterion: If a candidate is clearly preferred, then that candidate should win.
Pareto Criterion: If a candidate beats all other candidates when comparing one-on-one, the candidate should win.
Irrelevance of Independent Alternatives (IIA): If all other candidates except for a winner and one other candidate drop out, the result should stay the same.
Monotonocity Criterion: It is impossible for the winning candidate to lose if the conditions improve for that candidate.
Spoiler Effect Prevention: See explanation on the Spoiler Effect
Minority Rule Prevention: If a majority dislikes a candidate the candidate should not win.
Preference Proportionality: In multi-winner elections, the winners should be roughly proportional to the preferences of the voters.
Gerrymandering Prevention: Changing the voting districts will not change the outcome of the election. See explanation on gerrymandering.
Political Diversity: The system should allow smaller political parties to thrive, while not allowing the first 2 favored parties to be the only political parties left standing.
Definitive Outcome: The voting system in a single-winner election should not result in an indecisive election or a tie.
No one voting system will satisfy all of these criteria, but some voting systems work better than others at satisfying these criteria.
Introduction
Many voting methods exist, for the purposes of coming to a consensus of choices by a great amount of people. The various methods all work in different ways, and have their own advantages and disadvantages. This project exists to review each method, explaining the method in use, and will use a combination of text, videos, and images to explain each method, and review the advantages and disadvantages of each.