The paper begins with a conceptualization of an electoral system. This is followed by a discussion of different categories and types of electoral systems. An attempt is then made to demonstrate the importance of an electoral system and why it is necessary to spell out a country's electoral system in the constitution.

This chapter establishes the importance of the electoral system as the central political institution in representative democracy. It discusses the dimensions of electoral systems, such as district magnitude, ballot structure, and the extent of voter choice for individual candidates, levels of seat allocation, thresholds, and apportionment. It identifies the most important questions to ask about the origins and effects of electoral systems. Electoral systems consist of sets of rules that govern all aspects of the voting process: when elections occur, who is allowed to vote, who can stand as a candidate, how ballots are marked and cast, how the ballots are counted (electoral method), limits on campaign spending, and other factors that can affect the outcome. Political electoral systems are defined by constitutions and electoral laws, are typically conducted by election commissions, and can use multiple types of elections for different offices.

2. Overview:
At the most basic level, electoral systems translate the votes cast in a general election into seats won by parties and candidates (Reynolds et al. 2005) in the legislature at the national and, where relevant, the sub‐national level as well.
The key elements of an electoral system include:
·the electoral formula (plurality/majority, proportional, mixed, or other)
·the ballot structure (i.e. whether the voter votes for a candidate or a party and whether the voter makes a single choice or expresses a series of preferences)
·the district magnitude (the number of representatives to the legislature that a particular district elects

Electoral systems are important for several reasons. Firstly, there is a perception that they have an impact on the degree of coherence/fragmentation of the party system, and hence on government effectiveness. Electoral systems may also help to ease or exacerbate conflict. In addition, they help shape public policy outcomes and the behavior and incentive structures of political actors. Whether politicians depend directly on voters or on their parties for the furthering of their careers on the basis of the formula that elects them to office is an important factor in determining whom they feel most accountable to, what use they might make of public resources to build linkages with their constituencies, and even what kinds of incentives there may be for corruption and electoral malpractice. Understanding these different dynamics is essential from a governance perspective because it helps provide insights into the institutional frameworks within which political actors operate and the interests that drive them.

3. History:
3.1 Early democracy:
Voting has been used as a feature of democracy since the 6th century BC, when democracy was introduced by the Athenian democracy. However, in Athenian democracy, voting was seen as the least democratic among methods used for selecting public officials, and was little used, because elections were believed to inherently favor the wealthy and well-known over average citizens. Viewed as more democratic were assemblies open to all citizens, and selection by lot (known as sortation), as well as rotation of office. One of the earliest recorded elections in Athens was a plurality vote that it was undesirable to win; in the process called ostracism, voters chose the citizen they most wanted to exile for ten years. Most elections in the early history of democracy were held using plurality voting or some variant, but as an exception, the state of Venice in the 13th century adopted approval voting to elect their Great Council[1].

The Venetians' method for electing the Doge was a particularly convoluted process, consisting of five rounds of drawing lots (sortation) and five rounds of approval voting. By drawing lots, a body of 30 electors was chosen which was further reduced to nine electors by drawing lots again. An electoral college of nine members elected 40 people by approval voting; those 40 were reduced to form a second electoral college of 12 members by drawing lots again. The second electoral college elected 25 people by approval voting, which were reduced to form a third electoral college of nine members by drawing lots. The third Electoral College elected 45 people, which were reduced to form a fourth electoral college of 11 by drawing lots. They in turn elected a final electoral body of 41 members, who ultimately elected the Doge. lifespan of over 500 years, from 1268 to 1797[2].

3.2 Development of new systems:
Jean-Charles de Borda proposed the Borda count in 1770 as a method for electing members to the French Academy of Sciences. His method was opposed by the Marquis de Condorcet, who proposed instead the method of pairwise comparison that he had devised. Implementations of this method are known as Condorcet methods. He also wrote about the Condorcet paradox, which he called the intransitivity of majority preferences. However, recent research has shown that the philosopher Ramon Llull devised both the Borda count and a pairwise method that satisfied the Condorcet criterion in the 13th century. The manuscripts in which he described these methods had been lost to history until they were rediscovered in 2001[3].

Later in the 18th century, apportionment methods came to prominence due to the United States Constitution, which mandated that seats in the United States House of Representatives had to be allocated among the states proportionally to their population, but did not specify how to do so[4]. A variety of methods were proposed by statesmen such as Alexander Hamilton, Thomas Jefferson, and Daniel Webster. Some of the apportionment methods devised in the United States were in a sense rediscovered in Europe in the 19th century, as seat allocation methods for the newly proposed method of party-list proportional representation. The single transferable vote (STV) method was devised by Carl Andræ in Denmark in 1855 and in the United Kingdom by Thomas Hare in 1857. Belgium the first to implement it for its 1900 general elections. Since then, proportional and semi-proportional methods have come to be used in almost all democratic countries, with most exceptions being former British colonies[5].

4. Comparative Electoral Systems Research:
A comprehensive review of the literature on electoral systems establishes the progress made in the field in recent years. This area of political science research can now be regarded as a mature field. Questions concerning the relationships between electoral systems, proportionality, and the number of political parties in a party system (often summed up in terms of Duverge's Law, or variants thereof) can now be regarded as largely settled. Important questions for future research include the intraparty dimension of electoral systems, and the origins of electoral systems.

5. Types of electoral systems:
5.1. Plurality systems:
Plurality voting is a system in which the candidate(s) with the highest amount of vote wins, with no requirement to get a majority of votes. In cases where there is a single position to be filled, it is known as first-past-the-post; this is the second most common electoral system for national legislatures, with 58 countries using it to elect their parliaments[6], the vast majority of which are current or former British or American colonies or territories. It is also the second most common system used for presidential elections, being used in 19 countries.

5.2 Majoritarian systems:
Majoritarian voting is a system in which candidates have to receive a majority of the votes to be elected, although in some cases only a plurality is required in the last round of counting if no candidate can achieve a majority. There are two main forms of majoritarian systems, one using a single round of ranked voting and the other using two or more rounds. Both are primarily used for single-member constituencies. Majoritarian voting can take place in a single round using instant-runoff voting (IRV), whereby voters rank candidates in order of preference; this system is used for parliamentary elections in Australia and Papua New Guinea. If no candidate receives a majority of the vote in the first round, the second preferences of the lowest-ranked candidate are then added to the totals. This is repeated until a candidate achieves over 50% of the number of valid votes. If not all voters use all their preference votes, then the count may continue until two candidates remain, at which point the winner is the one with the most votes. A modified form of IRV is the contingent vote where voters do not rank all candidates, but have a limited number of preference votes[7].

5.3. Proportional systems:
Proportional representation is the most widely used electoral system for national legislatures, with the parliaments of over eighty countries elected by various forms of the system.

Party-list proportional representation is the single most common electoral system and is used by 80 countries, and involves voters voting for a list of candidates proposed by a party. In closed list systems voters do not have any influence over the candidates put forward by the party, but in open list systems voters are able to both vote for the party list and influence the order in which candidates will be assigned seats. In some countries, notably Israel and the Netherlands, elections are carried out using 'pure' proportional representation, with the votes tallied on a national level before assigning seats to parties. However, in most cases several multi-member constituencies are used rather than a single nationwide constituency, giving an element of geographical representation. However, this can result in the distribution of seats not reflecting the national vote totals. As a result, some countries have leveling seats to award to parties whose seat totals are lower than their proportion of the national vote[8].

5.4. Mixed systems:
In several countries, mixed systems are used to elect the legislature. These include parallel voting and mixed-member proportional representation. In parallel voting systems, which are used in 20 countries[9], there are two methods by which members of a legislature are elected; part of the membership is elected by a plurality or majority vote in single-member constituencies and the other part by proportional representation. The result of the constituency vote has no effect on the outcome of the proportional vote[10].

Mixed-member proportional representation, in use in eight countries, also sees the membership of the legislature elected by constituency and proportional methods, but the results of the proportional vote are adjusted to balance the seats won in the constituency vote in order to ensure that parties have a number of seats proportional to their vote share[11]. This may result in overhang seats, where parties win more seats in the constituency system than they would be entitled to based on their vote share. Variations of this include the Additional Member System and Alternative Vote Plus, in which voters rank candidates, and the other from multi-member constituencies elected on a proportional party list basis. A form of mixed-member proportional representation, Scorporo, was used in Italy from 1993 until 2006.

5.5. Additional features:
Some electoral systems feature a majority bonus system to either ensure one party or coalition gains a majority in the legislature, or to give the party receiving the most votes a clear advantage in terms of the number of seats. In Greece the party receiving the most votes is given an additional 50 seats[12], San Marino has a modified two-round system, which sees a second round of voting featuring the top two parties or coalitions if there is no majority in the first round. The winner of the second round is guaranteed 35 seats in the 60-seat Grand and General Council.

5.6. Primary elections:
Primary elections are a feature of some electoral systems, either as a formal part of the electoral system or informally by choice of individual political parties as a method of selecting candidates, as is the case in Italy. Primary elections limit the risk of vote splitting by ensuring a single party candidate. In Argentina they are a formal part of the electoral system and take place two months before the main elections; any party receiving less than 1.5% of the vote is not permitted to contest the main elections. In the United States, there are both partisan and non-partisan primary elections.

5.7. Indirect elections:
Some elections feature an indirect electoral system, whereby there is either no popular vote, or the popular vote is only one stage of the election; in these systems the final vote is usually taken by an electoral college. In several countries, such as Mauritius or Trinidad and Tobago, the post of President is elected by the legislature. In others like India, the vote is taken by an electoral college consisting of the national legislature and state legislatures. In the United States, the president is indirectly elected using a two-stage process; a popular vote in each state elects members to the Electoral College that in turn elects the President. This can result in a situation where a candidate who receives the most votes nationwide does not win the Electoral College vote, as most recently happened in 2000 and 2016.

6. Rules and regulations:
Electoral rules place limits on suffrage and candidacy. Most countries’ electorates are characterized by universal suffrage, but there are differences on the age at which people are allowed to vote, with the youngest being 16 and the oldest 21 (although voters must be 25 to vote in Senate elections in Italy). People may be disenfranchised for a range of reasons, such as being a serving prisoner, being declared bankrupt, having committed certain crimes or being a serving member of the armed forces. Similar limits are placed on candidacy (also known as passive suffrage), and in many cases the age limit for candidates is higher than the voting age. A total of 21 countries have compulsory voting, although in some there is an upper age limit on enforcement of the law. In systems that use constituencies, apportionment or districting defines the area covered by each constituency. Where constituency boundaries are drawn has a strong influence on the likely outcome of elections in the constituency due to the geographic distribution of voters. Political parties may seek to gain an advantage during redistricting by ensuring their voter base has a majority in as many constituencies as possible, a process known as gerrymandering. Historically rotten and pocket boroughs, constituencies with unusually small populations, were used by wealthy families to gain parliamentary representation.

7. The Importance of Electoral Systems:
Political institutions shape the rules of the game under which democracy is practiced, and it is often argued that the easiest political institution to manipulate, for good or for bad, is the electoral system. In translating the votes cast in a general election into seats in the legislature, the choice of electoral system can effectively determine who is elected and which party gains power. While many aspects of a country’s political framework are often specified in the constitution and can thus be difficult to amend, electoral system change often only involves new legislation and can thus be subject to manipulation by unscrupulous majority.

Even with each voter casting exactly the same vote and with exactly the same number of votes for each party, one electoral system may lead to a coalition government or a minority government while another may allow a single party to assume majority control.

Conclusion:
While electoral systems are a vital component of any representative democracy, one should not overstate their importance. Do not determine the nature of party systems, or the type of government, majority or minority, single-party or coalition, in any country. Governmental outcomes are largely a function of the balance of party forces: the party system, in turn, is largely shaped by a country's political culture and social structure and by the electoral behavior of its citizens. However, the electoral system ... is a powerful intermediary force, modifying the competition among parties, distorting or faithfully reproducing the electoral preferences of the voters. Since elections are key institutions in modern democracies and provide the chief mechanism of political participation for most people, the means of translating individual votes into political representation is... an important factor in a country's political system[13].

End-Notes
[1]J.J O’Connor & E.F. Robertson THE HISTORY OF VOTING Mac Tutor History of Mathematics archive
[2]Miranda Mowbray & Dieter Gollmann (2007) Electing the Doge of Venice: Analysis of a 13th Century Protocol
[3]G. Hägele & F. Pukelsheim (2001) "Llull's writings on electoral systems", Studia Lulliana Vol. 3, pp3–38
[4] Apportionment: Introduction American Mathematical Society
[5]Proportional Voting Around the World FairVote
[6]Table of Electoral Systems Worldwide
[7]Table of Electoral Systems Worldwide
[8]Table of Electoral Systems Worldwide
[9]Table of Electoral Systems Worldwide IDEA
[10]Elections held in 1995 IPU
[11]Table of Electoral Systems Worldwide IDEA
[12]Nauru Parliament: Electoral system IPU
[13]Robert J. Jackson and Doreen Jackson, Politics in Canada, 2nd edition, Prentice-Hall Canada Ltd., Scarborough, Ontario, 1990, p. 501.