2.6 Elections

Election is simply a choice. To elect means “to choose or make a decision”.

An election is a formal decision-making process by which a population chooses an individual to hold public office.

2.6.1 The basic elements of an election (Retrieved from: Tannenbaum, P. (2018) Excursion in modern mathematics.)

• The candidates. The purpose of an election is to choose from a set of candidates or alternatives (at least two—otherwise it is not a real election).

Typically, the word candidate is used for people and the word alternative is used for other things (movies, football teams, pizza toppings, etc.), but it is acceptable to use the two terms interchangeably.

• The voters. These are the people who get a say in the outcome of the election. In most democratic elections the presumption is that all voters have an equal say, and we will assume this to be the case in this course.

• The ballots. A ballot is the device by means of which a voter gets to express his or her opinion of the candidates. The most common type is a paper ballot, but a voice vote, a text message, or a phone call can also serve as a “ballot”.

  There are many different forms of ballots that can be used in an election. The simplest form is the single-choice ballot. Here very little is being asked of the voter (pick the candidate or party you like best).

  At the other end of the spectrum is the preference ballot, where the voter is asked to rank all the candidates in order of preference; in this ballot, the voter has entered the candidates’ names in order of preference. An alternative version of the same preference ballot contains the names of the candidates that are already printed on the ballot and the voter simply has to mark first, second, third, etc. In elections where there are a large number of candidates, a truncated preference ballot is often used. In a truncated preference ballot the voter is asked to rank some, but not all, of the candidates.

• The outcome. The purpose of an election is to use the information provided by the ballots to produce some type of outcome. But what types of outcomes are possible? The most common is winner-only. As the name indicates, in a winner-only election all we want is to find a winner. We don’t distinguish among the nonwinners.

  There are, however, situations where we want a broader outcome than just a winner—say we want to determine a first-place, second-place, and third-place candidate from a set of many candidates (but we don’t care about fourth place, fifth place, etc.). We call this type of outcome a partial ranking. Finally, there are some situations where we want to rank all the candidates in order: first, second, third, . . . , last. We call this type of outcome a full ranking, or just a ranking for short.

• The voting method. The final piece of the puzzle is the method that we use to tabulate the ballots and produce the outcome.

A voting rule/method is a winner-selection mechanism (individual preferences aggregation method); a voting method aggregates voter personal (individual) preferences into a collective (social) choice (a collective preference ranking over alternatives).