How the winner or winners are determined

A method is needed for determining the winner, or winners, once all the votes are cast.  Individual votes express each individual voter’s view, but all of these need to be aggregated to determine the choice of the group.  There are a number of different ideas about how to determine the aggregated choice of the group.  There are differences based on concepts of how to define the aggregate choice and also differences in the mathematical formulae that deliver on these concepts.

Ideas about the winner and the formula used differ depending on whether one, or more than one, person is being elected.  Parliamentary elections can be a series of elections, each for one person – in each electorate, or it can be a single election for all members.  Some councils also elect a number of people to each ward, rather than one per ward.

The choice of how to determine the winner can have an impact on the overall election result.  Most books that describe electoral systems include an example showing how the same set of ballot papers will deliver three different winners, depending upon which system is used.  There is not agreement amongst those who study elections on which is the best system.  Kenneth Arrow has shown that it is impossible for one voting system to meet all five basic criteria that he proposed are needed to fairly choose (using maths) between three or more preferences.  So the decision of which voting system to use cannot be purely objective because choices have to be made about which criteria to favour.  However, there is wide agreement that plurality is less desirable than the other alternatives.   Each organisation or country has to make a choice on what electoral system to use.

Electing one person or option

There are four different ideas of how to define the winner.  It may be the one:

• with the most votes – plurality or simple majority; First Past the Post
• who (or which) is acceptable to at least half of the voters – absolute majority; runoff, second ballot or alternative vote
• who is accepted by most of the voters and disliked by few – Borda count
• who can beat every other option in a pair-wise contest – Condorcet.

Simple majority

A common method of deciding which one candidate or option wins is that it has the most votes.  This is a plurality winner, sometimes called a simple majority.  In elections this is called First Past the Post.  This is the method used in New Zealand for electorate MPs.  It is also used for elections in most of the Westminster democracies such as the USA, Canada, the UK, and India.  This method is liked because it is easy, but the main problem that is raised is that it can happen that the plurality winner may not get half of the votes, which means that more people voted for something else than voted for the winner. 

Absolute majority

When the winner has to have the backing of at least half of the voters this is an absolute majority.  This system is used for the Australian parliament, for presidential elections in France and Timor-Leste, and for mayoral elections in some parts of New Zealand.  People like this system because it ensures that more people like than dislike the winner.  One of the problems raised is that while for some people the winner is their favourite, for others it will be their second, third or later choice.  The most that can be said for sure is that over half of the voters preferred the winner.

There are two ways of finding who has an absolute majority.  The method used in France and Timor-Leste is to hold two rounds of voting. Each voter marks one candidate.  If a candidate has half of the votes, they win – this is unusual.  If no-one wins on the first round, a second vote is held between the two candidates with the highest votes in the first round, and the one who gets the most votes wins.  This system is called the runoff or double ballot.

Under the other method, voters mark their preference order for candidates or options (1, 2, 3, etc).  All first preferences are counted and if a candidate has more than half of the votes, they are elected.  If this is not the case, the candidate with the fewest votes is eliminated.  Each ballot paper that gave this eliminated candidate a first preference is then redistributed as a vote for the candidate who was given second preference.  These new votes are added to the existing votes and if any candidate now has more than half of the votes, they are elected.  If no-one has won, the candidate who now has the fewest votes is eliminated and their ballot papers are redistributed to the next preferred candidate, as above.  This process continues until one candidate has half of the votes.  This system is called the alternative vote.

Broadest acceptable

There are two other important concepts about defining a winner, although neither is used for national elections.  Both the Borda count and the Condorcet winner seek to find the candidate who is acceptable to a broad range of voters.  So, rather than identifying the option that is strongly liked by a large group (plurality), these methods seek the option that is acceptable to as many as possible.

In a Borda count voters rank all of the candidates in order.  For each candidate the number of 1st, 2nd, etc, preferences given is recorded. Each preference is then given a value: the lowest preference receives 0, the next highest 1, and so on until the 1st preference receives a value that is one less than the total number of candidates (if there are five candidates the 1st preference gets a value of 4, if there are 19 candidates the 1st preference gets a value of 18).  The total value of preferences received is then calculated for each candidate and the one with the highest score wins.  The winner may not have the highest number of first preferences but will not have many last preferences.  People like the Borda count because it is easy to vote, the winner has wide approval and the idea is intuitive.  Those who dislike the system say that the count is time consuming if there are a lot of voters, and it is very easy to be strategic and alter the result.

A Condorcet winner is the option that can beat all other options in a series of pair-wise votes.  To conduct a Condorcet vote, voters can mark their preference orders, which are then tabulated as in the first stage of the Borda count.  Then a calculation is done for each pair of candidates to see who, or which, is preferred by the larger number.  The winner is the one that wins the most pairings.  Those who like Condorcet think the idea is intuitive – in fact, many academics who study elections think that one test of an election system is that it will find the Condorcet winner.  A Borda count usually produces the Condorcet winner, while plurality often has the Condorcet loser as the winner.  The main problem with the Condorcet method is that there may not be a winner because preferences may be circular.  In practical terms, one of the primary demands of an election system is that it finds a winner.

Electing more than one person

In many countries the electoral system provides for voters in an area to elect more than one representative.  In New Zealand, many councils have wards with several councillors.  As discussed in the section on electorates, some countries use the whole country as one electorate whilst many others divide into regions or cities.  Electing a number of people from one area is based on the idea that there is a diversity of views in any given area so it is necessary to elect more than one person in order to represent the range of views.  The issue, then, is how to determine who these people will be.

Again, there are a number of ideas and also a range of mathematical formulae which can be used to put the ideas into practice:

• the proportion of seats for each party is close to the proportion of votes the party won – proportional representation, list PR (proportional representation), MMP
• each sizeable group of voters elects one of the candidates – Single Transferable Vote
• the candidates with the most votes win – plurality, block vote.

The three groups of systems used for electing multiple candidates differ in ways other than the definition of a winner.  In particular, the proportional representation with party list systems need to have political parties contesting the election.  These systems also work better when electing a large number as they make it easier to reach proportionality.

Proportional representation

The most common method to elect a number of people to a parliament is using proportional representation with party lists.  Each party nominates a list of candidates and voters choose one of the parties.  A formula is then used to ensure that each party wins about the same proportion of seats as they won votes.  It is not possible to produce exact proportionality as that would entail having a half or a third of an MP. So the formula determines what to do with the fractions remaining at the end of the process.  Again, there is no perfect formula as each gives a slight advantage to one kind of party (eg, large, medium or small).  The main formulae used are Saint Lague (used for MMP in New Zealand), Hare, Droop, D’Hondt, and ‘largest remainder’.

In some systems there is a threshold that a party has to cross before it is included in the allocation of seats.  For instance, a party may need to get a certain percentage of all votes cast, often between 3% and 5%. Another variation is whether or not voters have any choice between candidates on the list.  In a closed list the party determines the rank order of candidates, while in an open list voters can indicate their preferred candidate and this may alter the order that was determined by the party.  People who like this list system see it as giving a fair result and recognising the central role of political parties in modern democracies.  People who do not like the system are critical of giving political parties prominence and concerned at the lack of direct local representation.

Mixed Member Proportional

Mixed Member Proportional (MMP) as used in New Zealand is a form of proportional representation with party lists.  The party vote treats the whole country as one electorate and uses the Saint Lague formula to allocate all 120 seats proportionally between the parties.  In this regard it is no different from proportional representation with party lists.  The difference is in how it is determined who will occupy the seats allocated to the party in the parliament.  In MMP some of the seats are filled by the MPs who win a plurality contest in each electorate.  The rest of the seats are filled with people from the party list.  People who like the system like the mix of the best aspects of proportional representation with party lists and local representation from electorates.  Those who dislike the system do not like the central role of parties and think that the two types of MP have different roles and workloads.

Single Transferable Vote

When choosing a number of options or holding an election where there are no political parties, another method is needed.  The Single Transferable Vote (STV) uses the preferences of voters to ensure that the range of views in the electorate is represented amongst the elected people.   The results are often proportional but it is not the primary aim of STV to be proportional.

Counting votes for STV is similar to that for alternative vote (above).  The main idea is that the winners have to get just enough votes, but no more to ensure that no one else could get more votes than them.  Once it is known how many valid votes have been cast, a calculation is made to determine what quota is needed in order for a candidate to be elected.  The calculation is the number of votes/(number of seats + 1), plus 1.  So if there are three places to fill the quota is one-quarter of votes plus one, and if there are 14 seats to fill the quota is one-fifteenth of votes plus one.  The first step is to count the first preferences received by each candidate.  If any candidate has reached the quota they are elected.  If there are positions still to be filled, the candidate with the fewest votes is eliminated and those ballot papers reallocated to the voters’ next preferred candidate.  So far the process is identical to the alternative vote, but with a different quota.  The key difference is that when a candidate is elected their surplus votes are also reallocated.  So if a candidate has 100 votes more than the quota, these votes continue to be part of the count.  As it is not fair to randomly select 100 ballot papers, all of the winning candidate’s papers are reallocated but each is given a value of less than one so that the total to be reallocated equals the surplus – in this case 100.  People who like STV like the fact that it does not need parties and that most votes are used in determining the winners.  People who do not like the system do not like the use of some people’s first preferences alongside other people’s later preferences.

Block vote

Many countries that use FPP to elect one person extend the same system when they want to elect multiple people from an electorate.  So, if electing three people, each voter can mark three candidates.  All votes cast for each candidate are counted and the three candidates with the most votes win.  This system is often called the block vote and is basically an extension of plurality.  The pros and cons are the same as for plurality.  A close variation is where each voter has one vote and again the three candidates with the most votes win.  This system is the Single Non-Transferable Vote.