The ultimate rulers of our democracy are not a President and senators and congressmen and government officials, but the voters...

Former US President Franklin D Roosevelt

The USA uses a few different methods to choose their elected officials. Although the most common and important form of voting is the plurality method (see below), there are several other methods sometimes used for various other elections where plurality isn't acceptable. This entry attempts to examine voting methods and practices.

Plurality

Three against one! We win.

Plurality is by far the most commonly used system of voting, used almost universally for many types of voting and elections. It has been used for thousands of years, almost certainly predating written history. Most countries use the plurality system to elect public officials, and most people use it in day to day life. Some people use it as a default system of voting, because it is democratic and gives everyone an equal say in voting. The plurality system simply that says that the choice with the most votes wins.

The major problem with this system is that in elections with more than two choices, there can be (and there often is) a winner without a majority. At first, this may seem like a fairly obvious flaw that is simply a fact of life. But another flaw makes this one more serious. The preference of the candidates you didn't vote for makes no difference in the Plurality system. In theory, a majority of voters could absolutely hate a candidate, but he could still win in a plurality election. This occurs most often when a majority of voters with similar ideas are split between two candidate with similar ideas.

Mathematicians collect data and draw what are called Preference Diagrams, which illustrate what percentage of people prefer which order of candidates - for instance if 34% of people voting preferred Candidate B, then A, then C, a Preference Diagram might look like:

However, as stated above, a situation could occur where there are three candidates and most voters did not like the candidate elected. For instance, 34% could vote for Candidate B, and another 21% could vote for Candidate A, both of them hating another candidate... let's call him 'Candidate C'. However, supporters of Candidate C would win the race with 45% of the votes, while 55% of the people hated the winner.

Of course, this is not particularly common, and it's impossible to accurately determine if it has happened, but this could have happened in several major elections. Take for instance the 1912 Presidential Race between Theodore Roosevelt, William Taft and Woodrow Wilson¹. In it, Wilson received about 45% of the vote, Roosevelt received about 30% of the vote and Taft received about 25% of the vote. As far as political historians can tell, voters for Wilson generally preferred Roosevelt over Taft. Roosevelt voters supported Taft over Wilson and Taft voters supported Roosevelt instead of Wilson. Wilson won the Presidency.

This means that Wilson (the winner) was generally ranked last by voters for Roosevelt and Taft, who made up a majority, demonstrating the flaw in the plurality system.

This is a rare occurrence however, and is rare enough that most election organizers held feel content to ignore the flaw, as it is unlikely to happen, especially in the United States, where there are usually two political parties - the Democrats and the Republicans, winning most elected positions.

Even though the plurality method has its flaws, it is generally a good system. It has several benefits. It is a generally easy to understand, simple system that is clear and obvious to most voters. It is also usually cheaper to administer than the alternative voting methods that can require multiple elections. It also does give everyone a democratic, fair say in the election of their public officials. This is likely to stay the voting method for most elections in the future.

Instant Runoff

The Runoff method is an alternative method to plurality that is based around the system of plurality. The main idea is to have a normal election, similar to any election one would normally expect, with one exception - if no candidate wins a majority of the vote, a second election is held with the top two vote getters from the first election. With only two candidates, it is impossible for one of them not to get a majority of the vote. This method gets rid of the flaw in the plurality system because it guarantees a majority.

The results of runoff elections can be much different from the results of a plurality election, because the people who originally voted for the eliminated candidate will instead vote for one of the other candidates, often changing the vote margins significantly. In areas that observe the Runoff Election Method, knowing which candidate supporters of the eliminated candidates will vote for is important. So knowing the preferences of voters is especially how one can predict the runoff election.

In the same 1912 Presidential Race from above between Wilson, Roosevelt and Taft, Political Historians have determined a number of interesting things. If a Runoff Election was held, Roosevelt and Wilson would have been in the second election. It is also important to note that most voters for Taft preferred Roosevelt over Wilson. With their 25%, the Taft voters probably would have voted for Roosevelt, securing him the Presidency, if a Runoff had been held.

As with most voting systems, there is a variation to this system. The most important variation of the Runoff method is the Sequential Runoff. In it, if no candidate receives a majority, the candidate who receives the fewest amount of votes is eliminated and another election is held with the remaining candidates. If that election again produces no candidate having a majority, the one receiving the fewest votes is eliminated again. Then another election occurs, and so on, until one candidate receives a majority. This can be a very complicated, long system to find a winner (and as demonstrated by the Olympics, who use this method to find a host for the games, it generally is). The Sequential Runoff system also has all of the same problems of a runoff election, including the Paradox where a candidate who would win would lose by getting more votes. In fact, in a three candidate election, the Sequential Runoff and Runoff systems are identical.

As with every system, the runoff method has its share of problems. For one thing, the supporters of candidates that don't participate in the second election (the 'runned-off' candidates) have little say in their choice of an elected official (and, because there has to be significant support in a third party, there would be a number of supporters for the runned-off candidate). Financing the elections are also twice as expensive. Some contend that the runoff system gives only two candidates an election and doesn't really allow minor candidates to participate in elections.

This method is becoming more popular, but it is not yet widely used.

Runoff Paradox

One interesting thing about the runoff system is that in a certain situation, giving a vote to one candidate could actually cause him to lose, while voting for another one will let the first candidate win. Consider the following election, as illustrated in preference diagrams²-

Now, in this case, the winner of the plurality election would be Candidate C, although C did not get a majority. However, if a runoff election was held after this one, Candidates D and A would be eliminated for having the fewest votes. Assuming that all voters followed the above pattern and voters for C and B didn't change their vote, after the choices D and A were off the ballot, they would vote for the candidate they preferred next, which would be C. Therefore, C would win that runoff election with 36% more of the vote.

But consider if instead of voting for Candidate A, the 12% of voters in the last diagram decided to vote for Candidate C (in the first election) instead. The preference diagrams would change to:

A runoff election would still be held, but Candidate A would be eliminated, and would not be in the runoff, because Candidate B would suddenly have more votes than A. However, the winner of the runoff election would not be C (assuming that all voters follow the preferences in the diagram and opinions don't change between elections) because eliminating A would give B a extra 24% of the vote. Therefore, in this situation, giving Candidate C 12% more of the vote would have led it to lose.

This is of course a theoretical situation that hardly ever happens, but there is always the strange possibility that in a runoff, adding more votes to a candidate could make it lose.

Points

Many people think that a system of points is the best solution to the election flaw in the plurality system. However, it is rarely used in politics and not often used in many other types of voting, being relatively complicated.

A point system generally consists of a ballot in which you rank the order you prefer the candidates. Then, usually each candidate is given a certain number of votes based on what you ranked them as. Most often, the candidate you ranked first is given the amount of points that there are candidates in the race. The one you ranked second would usually be one less point than the amount of candidates. For instance, if there was a four candidate race, the one you ranked first would be given four points, the one you ranked second given three points, etc. Of course there are many variations on this - too many to list here.

The best part of the Point System is that it would be difficult for a candidate to win an election with a generally low ranking among voters. In fact, it is almost impossible for voters to elect a candidate that is disliked by the majority. Since the Point System doesn't rely on plurality or majority, it can create some unexpected answers, often dramatically different from winners of plurality. In fact, a candidate who got last place in a plurality election could win in a Point system election.

The major flaw in the point system is that the results can be manipulated fairly easily (see below).

Electoral College

This system is used in the United States to determine the its President. It is not used anywhere else, but it is still an important method, because it is the system used in this very important election. The method was first introduced in the 1700s, when the Founding Fathers of America reached a compromise on the issue of States' Rights³ that led to the Electoral College. There are other historical reasons as well, but few have modern applications.

In the Electoral College system, each state is given a certain number of Electoral Votes calculated by the number of Senators and Representatives each state (and the District of Columbia⁴) has⁵. Each state has a plurality election with the people in its borders, and if a state's plurality election is won by a certain candidate, that candidate 'wins' those votes and that state.

This method has produced a number of results that are controversial at best. No less than three clear⁶ times in history, including in 2000, the Electoral College came up with a different decision from the popular, plurality vote. Each time, this has resulted in protest and annoyance from supporters of the candidate who lost.

Of course, no method is not without its benefits. Many people believe that the College helps keep sparsely populated areas an important part of the country, and if the College didn't exist, a candidate might campaign only in cities and populated states, or make policies that benefit city folk to get their votes.

Approval

A relatively new method called Approval voting was proposed by American mathematicians in the 1970s. It is a simple method that allows voters to vote on their ballot normally in a multi-candidate election, except that they can vote for any number of candidates they want, often indicating if they approve of a candidate with a simple 'Yes' or 'No'. The winner is the one with the most votes. Of course, it encounters some of the same flaws as other systems. Insincere or strategic voting, which occurs in Point Systems can be done in Approval Voting.

It is a relatively good choice for a voting method for a number of other reasons as well. It would reduce negative campaigning or 'smear campaigns', because candidates would be more likely to try to please another candidate's supporters, to get their approval. A candidate might respect other candidates, so that they would get the approval of voters who support the candidate that others are imitating. Saying bad things about one candidate could alienate his supporters. Approval Voting is also a relatively simple system, where Point System ballots and runoff elections might discourage voter turnout with confusing ballots and systems.

Of course, no system is perfect, Approval Voting included. The system has a serious flaw that allows people to contribute to a candidate's election that wasn't their true favourite. Consider the following situation in Preference Diagrams:

Candidate 1 (not to be confused with Candidate A) would win the Plurality Election, and Candidate 2 would win the Runoff election. However, assuming that voters for each group approved of their first and second choices, Candidate 1 would get 75% of the vote, and win. The flaw in this election is that Candidate 1 won, even though 60% of voters preferred Candidate 2 over Candidate 1.

Many people believe that Approval Voting is the future of Elections. It is one of the fastest growing voting methods.

Other Methods

A system that requires a unanimous vote is sometimes used, often when inducting a member into a club or society. These are usually used in private groups though, and never used for elections. This is sometimes referred to as the 'black ball' method, because in some private groups, members would secretly place a ball or marble down. All white balls meant that the membership was accepted. One black ball might mean that a membership was rejected.

A French mathematician named Marquis de Condorcet proposed a voting method in the 1700s that is now called the Condorcet method. This method requires the elected public official to have been able to beat each other candidate head to head. Each voter would have to vote multiple times for one candidate 'over' another candidate on their ballot. Unfortunately, this method doesn't always bring a winner in the race, in fact it is more common for no candidate to win at all using the Condercet method.

The Condorcet method is another form of Pairwise voting. Pairwise Voting is a system in which voters choose between two candidates a number of times on their ballot. The difference with this and the Condorcet method is that it doesn't require the candidate to beat every other candidate - only win the most votes.

Sometimes there are elections where there are more than one positions to be elected into. Usually, there are individual elections for each seat, but in elections for positions like a School Board, where there are identical positions, one election is sometimes held for multiple seats. This often ends up misrepresenting the voters as being all part of one group, while a minority has no say in their elected officials. One answer to this problem is Cumulative Voting, in which the voter is given as many votes as there are positions to be filled, and can give them in any combination to the candidates. For instance, an election with four positions to be filled gives voters four votes, and they could vote for one candidate four times.

This nicely solves the problem of misrepresentation of a minority group. If there are three positions to be filled, voters in a minority group might all vote for a candidate of their group with all three of their votes. It is likely then, (given that the minority is not too small) that a minority can be represented.

Sample Ballots

Here are some sample ballots for each system of voting using the candidates from the 1992 Presidential Election in the United States:

• Plurality Voting and First Runoff Election - Vote for one candidate you prefer most.

  ___	Ross Perot
  ___	George Bush
  ___	Bill Clinton

• Second Runoff Election - Vote for one candidate you prefer most.

  ___	George Bush
  ___	Bill Clinton

• Condorcet and Pairwise Method - Rank the following candidates in the order of which you prefer them - Bill Clinton and George Bush.

  1. ___________
  2. ___________

  Rank the following candidates in the order of which you prefer them - Bill Clinton and Ross Perot.

  1. ___________
  2. ___________

  Rank the following candidates in the order of which you prefer them - George Bush and Ross Perot.

  1. ___________
  2. ___________

• Approval Voting - Do you approve of the following candidates? Mark yes for any number of candidates if you do and no if you don't.

  Yes/No	Ross Perot
  Yes/No	George Bush
  Yes/No	Bill Clinton

• Cumulative Voting - Give three votes in any combination to these three candidates.

  ___	___	___	Ross Perot
  ___	___	___	George Bush
  ___	___	___	Bill Clinton

Manipulating Elections

Manipulating elections and voting is a fact of life. Every election can be manipulated in some way, most of the time by doing illegal things that make the election type irrelevant. Manipulating elections is different from 'fixing' them, because manipulating is generally legal.

Buying Elections

I just received the following wire from my generous Daddy - 'Dear Jack, Don't buy a single vote more than is necessary. I'll be damned if I'm going to pay for a landslide.'
John F Kennedy

Buying elections can be accomplished in all forms of voting, but some ways are more subtle than others. You could stand on a corner and offer a hundred dollars to anyone who votes for your candidate. You could bribe election counters to massage the results. But this doesn't really have to do with the type of election held.

In runoff and preference elections, one candidate being in an election can easily change the results. One might be able to bribe a candidate trailing in the polls to drop out if it might benefit their campaign.

Insincere and Strategic Voting

My scheme is intended only for honest men.
Jean Charles de Borda - who proposed Point Systems in France in the 1700s.

Insincere and strategic voting is the biggest problem with systems based around preference. People might lie about what their preference is in order to get their first choice elected. For instance, if you support Candidate A, but also like Candidate B, your ideas are supposed to be reflected in your vote. In the point system you would rank A first and B second and you would approve of them both in Approval Voting. But suppose that Candidates A and B are running closely in the polls, and you want your vote to help Candidate A win. You might rank Candidate B last (or not approve of him in Approval Voting) so that your vote doesn't help Candidate B.

If one candidate thinks he'll lose an Approval Voting method, possibly because of the Approval method flaw (see above) he might ask his supporters to vote only for him. This is certainly legal and possible.

Another type of insincere voting that can occur in any system involves voting or ranking a person you don't like first. Consider the following situation. Candidate A, who you support is unlikely to win because of low support, but you dislike the candidate who is leading, Candidate B immensely. Another person, Candidate C is close in the polls with A. You don't want B to win, so you might vote for C instead of your true favourite, A, because C has a chance of winning.