====================================================================== Voting Systems FAQ ====================================================================== This Voting Systems FAQ is in four parts. The 1st part describes various voting systems, the 2nd part describes some concepts to do with voting systems, and the 3rd part describes which system is in use in various countries. The 4th part is a list of further reading material. When I am not sure of something I have marked it with "(?)". Your comments are appreciated, particularly information about voting systems used in other countries. FAQ maintainer: phil@vision25.demon.co.uk Version: version 2.5, 5-Jun-97 This document is available on the World-Wide Web at ---------------------------------------------------------------------- List Of Changes ~~~~~~~~~~~~~~~ 3-Jun-97. version 2.5 Added results of French and Canadian elections. Added commentary about Condorcet from AJ Smith. ---------------------------------------------------------------------- Table of Contents ~~~~~~~~~~~~~~~~~ PART 1: Some voting systems explained - First Past The Post (FPTP) - Run-Off Voting - Single Transferable Vote (STV) - Single Non-transferable Vote (SNTV) - Single Transferable Proportional Vote (STPV) - Alternative Vote (AV) - Supplementary Vote (SV) - Approval Voting - Party List systems (PL) - Additional Member System (AMS) - Mixed Member System (MMS) - Condorcet PART 2: Concepts relating to elections and voting systems - Gerrymandering - Splitting the vote - Tactical voting PART 3: Voting systems used in various countries - Australia - Canada - France - Germany - Ireland - Israel - Japan - Malta - New Zealand - South Africa - United Kingdom - United States of America PART 4: Further reading ====================================================================== PART 1: Some voting systems explained ====================================================================== First Past The Post (FPTP) ~~~~~~~~~~~~~~~~~~~~~~~~~~ This is the simplest system. Each voter votes for one candidate. The candidate they prefer. The candidate with the most votes is elected. FPTP can also be used to elect multiple candidates for a constituency in some local elections. Each voter gets N votes where there are N people to be elected. The voters must use each vote on a different candidate; they cannot put all their votes on the same candidate. The N candidates with the most votes are elected. COMMENT: FPTP has the advantage of being the simplest possible system. It has the disadvantage that when only one person is being elected, this system doesn't guarantee to elect a popular candidate; if two candidates (call them A and B) have similar views, this might "split the vote" that they get, allowing a third candidate (C) to be elected, even though the supporters of A and B all prefer A and B over C and together they are more numberous than C's supporters. AV is an attempt to rectify this problem. ---------------------------------------------------------------------- Run-Off Voting ~~~~~~~~~~~~~~ In this system, voting takes place in two rounds. The first round is a FPTP election. If no candidate gets a majority of the vote in the first round, a second round is held, with only the candidates who did well in the first round standing. This system is used in France, where the rule is that any candidate who got more than 12.5% in the 1st round is allowed to stand in the second. COMMENT: If people have the same preferences in both rounds, then Run-Off voting is an inferior form of AV (it is like SV in that respect). However, because of the time gap between the two rounds, voters have the opportunity to change their mind about who they wish to vote for. ---------------------------------------------------------------------- Single Transferable Vote (STV) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This is a system for electing multiple candidates in a constituency. Each voter marks '1' against the candidate they most like, '2' against their next favourite, and so on until they have no preference for the remaining candidates. The highest preferences for each candidate are counted. If any candidate has more votes than the Quota, they are elected. The Quota is calculated as: Quota = int(V/(N+1)) + 1 where: V = number of votes N = number of candidates to be elected int() = convert to integer, rounding down The rationale for this formula is that the quota is the smallest number of votes such that the candidate is certain to be within the top N candidates. If someone is above the quota, the additional votes above the quota are reallocated to the other candidates according to the voters' lower preferences. This is done by giving each vote of the candidate a fractional value according to the fraction that the candidate was above the quota. (In Ireland they use the simpler, but less precise, system of simply picking a bunch of the candidate's ballot papers at random and using those for reallocation.) If no-one is above the quota, the candidate with the smallest number of votes is eliminated, and their votes are reallocated to other candidates. When votes are reallocated, if the voter has expressed no further lower preferences, their vote is discarded. This procedure is continued until all N candidates are elected. ---------------------------------------------------------------------- Single Non-transferable Vote (SNTV) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This is a cross between FPTP and STV. Each voter has one vote, and can vote for one candidate. The N candidates with the most votes are elected. ---------------------------------------------------------------------- Single Transferable Proportional Vote (STPV) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This is like STV except: 1. there is no quota 2. In a constituency with N seats, the lowest-polling candidate is dropped (and their votes redistributed) until there are only N candidates remaining. These N candidates are then elected. 3. each elected candidate gets a number of votes in parliament equal to the number of people electing them. COMMENT: STPV is more proportional than STV. STV has to round up to the nearest 1/N in an N-member constituency, which is obviously less proportional than giving each elected member a weighting exactly proportional to their support. Also STPV is better for smaller parties: because there is no quota, a party with less than 1/(N+1) of the vote is more likely to get representation with STPV than STV. ---------------------------------------------------------------------- Alternative Vote (AV) ~~~~~~~~~~~~~~~~~~~~~ This is the same as STV, except that only one candidate is to be elected. The procedure for counting the votes is the same, except that there is no reallocation of surplus votes. At least one institution in the world uses 'weighted AV' - that is, votes which are transfered at the nth preference do so at x^n times their actual weight, where x (a number between 0 and 1) is the 'weight'. According to Paul Martin (paul.martin@nuffield.ox.ac.uk), "this is a candidate for the most lunatic voting scheme". COMMENT: Altough AV is better than FPTP, it doesn't guarantee to pick the candidate that most voters prefer to every other candidate. Consider if there are 3 candidates, X, Y and Z. 35% want X. 2/3rds of these have Z as their second choice and the other 1/3 have Y. 34% want Y. 2/3rds have Z as 2nd choice, and the other 1/3rd have X. 31% want Z. Half prefer X as their second choice, and the other half prefer Y. In an AV poll, X would win, even though most voters prefer Z to X. In fact, most voters also prefer Z to Y. So even though most people prefer Z to any of the other options, it is not chosen. This is why some people consider Condorcet to be a better system than AV. In a Condorcet poll, Z would win, because it the the only option that most voters prefer in a pairwise comparison with all the other options. ---------------------------------------------------------------------- Supplementary Vote (SV) ~~~~~~~~~~~~~~~~~~~~~~~ A cut down version of AV, recommended by the Plant Commission and possibly invented by Peter Kellner. SV is the same as AV except that voters may express only up to two preferences (ie 1st pref and 2nd pref) rather than completing the list. Your second preference is a 'supplementary vote'. COMMENT: Allowing just 2 preferences is entirely arbitrary. I see no advantages of SV over AV. SV has been described as "the second most lunatic [voting system] I have ever come across". (comment by Paul Martin in uk.politics.electoral) ---------------------------------------------------------------------- Approval Voting ~~~~~~~~~~~~~~~ Each voters is allowed to vote for as many, or as few, of the candidates they like. The candidate with the most votes wins. The advantage of this system is that it favours popular independents, the big disadvantage is that it is non-proportional. Tactical voting is possible in the system, such as not voting for a candidate you approved of, to stop him from beating a candidate you approved of even more. COMMENT: I think approval voting is inferior to Condorcet in that it only allows the candidates to be put into one of two grades, whereas Condorcet allows the candidates to each be graded in relation to the others. Condorcet and AV allow voters to do the same thing as approval voting, but in a more sophisticated way. ---------------------------------------------------------------------- Party List systems (PL) ~~~~~~~~~~~~~~~~~~~~~~~ Each party makes out a list of candidates. Each voter votes for a party lsit. Each party is then allocated MPs in proportion to haw many people have voted for it. Sometimes the MPs are allocated according to the order they appear on the party's list. Sometimes voters can influence the order. Some PL systems have a threshold, so that if a party gets a lower proportion of the votes than this, it is allocated no seats at all. The purpose of this is to discourage small parties. Parties won't qualify for whole numbers of seats -- they will theoretically be entitled to eg 34.72 seats or 19.14 seats -- so how are the surplus seats allocated? Two approaches are commonly used -- the Hare system, under which the surplus seats go to the lists with the largest number of surplus votes; and the de Hondt system, under which the surplus seats go to the lists with the highest average vote per seat. The de Hondt system is more widely used (including Israel, where it is known as the Bader-Ofer method, although they have also previously used the Hare method). These systems are best explained using an example. Consider an election for 10 seats where there are 4 parties who got these votes: A 5200 B 2400 C 1500 D 900 Total votes = 10000 Under Hare, A in entitled to 10*5200/10000 = 5.2 seats B = 2.4 seats C = 1.5 seats D = 0.9 seats The whole numbers are allocted, giving A 5, B 2, C 1 and D 0 seat. Two seats are unallocated so they go to the two highest remainders, in this case D (0.9) and C (0.5). So the final allocation is: A 5 B 2 C 2 D 1 Under de Hondt, the following algorithm would be used: 1. for each party, calculate rep := numVotes/(numSeats+1) 2. give an extra seat to the most underrepresented party (ie the one with largest rep). 3. if any seats remain unallocated, goto 1. So, in our example, to start with, no seats are allocated. The party with the largest number of votes is A, so give it a seat: Party Votes Seats rep A 5200 1 2600 B 2400 0 2400 C 1500 0 1500 D 900 0 900 A's divisor is now 2, so its rep is 5200/2 = 2600 which is still the highest, so it gets allocated a second seat: Party Votes Seats rep A 5200 2 1733 B 2400 0 2400 C 1500 0 1500 D 900 0 900 Now B has the highest rep, so it gets a seat: Party Votes Seats rep A 5200 2 1733 B 2400 1 1200 C 1500 0 1500 D 900 0 900 And so on, until all the seats are allocated. This process can be shown more concisely as a table: Seats: 0 1 2 3 4 5 6 Divisor: 1 2 3 4 5 6 7 A: 5200 2600 1733 1300 1040 867 743 B: 2400 1200 800 C: 1500 750 D: 900 450 The final allocation of seats is: A 6 B 2 C 1 D 1 Systems like de Hondt which use successive divisors are collectively known as "Saint-Lague" systems. Other sets of divisors are possible, such as the series 1, 3, 5, ... which is used in Norway and Denmark. ---------------------------------------------------------------------- Additional Member System (AMS) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This is used to describe any composite system where some candidates are elected in individual constituencies (as in FPTP, STV, AV etc) and other candidates are elected according to some formula in order to make the *total* repesentation proportional. Compare with Mixed Member Systems). It is also used more specifically to describe the electoral system used in Germany (see the entry for Germany below). ---------------------------------------------------------------------- Mixed Member Systems (MMS) ~~~~~~~~~~~~~~~~~~~~~~~~~~ In this kind of system, there are in effect two separate elections for two separate classes of seats (typically one using single-member constituencies and one using party lists). The outcome of one election has no bearing on the outcome of the other one. The result is a hybrid assembly with some degree of proportionality, but where proportionality is by no means guaranteed. The difference between AMS and MMS is that in AMS the allocation of list seats conterbalances the constituency seats gained, whereas with MMS the number of list seats a party gets is not affected by the number of constituency seats it gets. ---------------------------------------------------------------------- Condorcet ~~~~~~~~~ This is partly electoral system, and partly a way of thinking about preference electoral systems that elect one candidate. The Condorcet winner in such an election is the candidate who when compared in turn with each of the other candidates, is prefered to them. It is not guaranteed that they will be any candidate to whom this applies, so any Condorcet electoral system must have a way of resolving such results. One way is to define the 'top cycle' to mean that candidates are said to be in the 'top cycle' if each of them will beat all candidates outside the top cycle in pairwise competition but not all the candidates inside the top cycle. Then the winner can be chosen by having an AV election between the top cycle candidates. Another way would be to choose the candidate in the top cycle who in the pairwise contest that they do worst in, they lose by the least amount. This can be best explained by way of illustration: In an election there are 3 'top cycle' candidatess. Considering only preferences between these candidates, 41 voters voted X 1st, Y 2nd, Z 3rd 33 voters voted Y 1st, Z 2nd, X 3rd 22 voters voted Z 1st, X 2nd, Y 3rd In pairwise comparisons: X: against Y = 41+22-33 = +40 (ie X won by 40 votes) against Z = 41-33-22 = -14 (ie X lost by 14 votes) Y: against X = -40 against Z = 52 Z: against X = 14 against Y = -52 So X wins, because his worst result (-14) is less bad than Y's or Z's worst results (-40 and -52 respectively). The choice of a winner from any candidate within the top cycle is to some extent arbitrary, in the sense that there are good reasons for picking any of them. COMMENT: There are good reasons to regard the Condorcet criterion, when fulfilled, as the best test of who should win: so if there is a Condorcet winner, then a system for selecting one winner ought to win it. On this view, AV is not as good as the Condorcet scheme, because there are circumstances in which it will fail to pick the Condorcet winner. OTOH, other people (such as A J Smith, ) have argued that if an option is unknown, or obscure, it is rational to expect that it is average in its value. Therefore obscure parties, parties without a clear identity, parties the voters are ignorant about, are likely to appear in the middle of people's preferences. The Condorcet criteria gives too much weight to people's middle preferences. If a party has a few first preferences, but is middling on the rest of the ballot papers it could well mean that the public knows very little about the party, and it has negligible positive support. Yet that party would be well placed to be the Condorcet winner. ====================================================================== PART 2: Concepts relating to elections and voting systems ====================================================================== Gerrymandering ~~~~~~~~~~~~~~ This is the practice of fixing the result of an election by altering electoral boundaries to favour one side. It is named after Elbridge Gerry. When he was governor of Massachusetts, he redrew the boundaries of the electoral districts to give an advantage to his own party. Gilbert Stuart, the artist, looking at a map of the new distribution, with a little invention converted one district in Essex County to a salamander and showed it to Benjamin Russell, editor of the Boston Sentinel. "Better say a gerrymander" said Russell, and the name caught on. Altering boundaries did not hinder Elbridge Gerry's political career -- he was Vice-President from 1812 until his death in 1814. His name was pronounced with a hard "g" (rhymes with "got"), so we've all been pronouncing it wrongly all these years. Gerrymandering is a lot easier to do in some electoral systems than in others. The easiest system is FPTP. AV is similar. Gerrymandering is harder with STV, but it is possible when the number of members per constituency is small, ie 3 or less. It is not possible to do when there are a large number of members per constituency, unless you either know the proportion voting for each party accurately in advance, or you make the number of voters per MP smaller in districts where your supporters live (which is usually illegal). Gerrymandering is pretty much impossible in a list system or STPV. ---------------------------------------------------------------------- Splitting the vote ~~~~~~~~~~~~~~~~~~ Consider a FPTP election with these votes cast: A 10000 B 7000 Now consider if another candidate, A1, stands, who has views very similar to A, and thus attracts a lot of A's supporters. The result might be: A 5500 A1 4500 B 7000 So B wins, even though support for A's policies is greater. A1 is said to have "split the vote". It is because of situations like this, and to avoid the necessity for tactical voting, that AV is considered better than FPTP. ---------------------------------------------------------------------- Tactical Voting ~~~~~~~~~~~~~~~ Tactical voting occurs when votes vote in any pattern other than their true preference, because doing this allows them to better influence the result of the election in their favour. Consider a FPTP election with these votes cast: A 10000 B 9500 C 2000 Most people voting for C happen to greatly prefer B over A. There is no way C can win the election, but if some of C's supporters switch to voting for B instead of C, then B can win instead of A. Obviously, C's supporters would prefer C to win, but if this cannot happen, then B is better than A. If enough of C's supporters know that this is like likely result, they might decide to vote tactically for B. ====================================================================== PART 3: Voting systems used in various countries ====================================================================== Australia ~~~~~~~~~ The House of Representatives (the lower house of parliament) is elected by AV. The Senate (the upper house) is elected by STV. However, because each state gets the same number of members elected to the senate, this does not provide for proportionality -- nor is it intended to. However, within each state these is rough proportionality, within the constraint that 6 STV members are elected by each state at a time. ---------------------------------------------------------------------- Canada ~~~~~~ FPTP is used in all elections. Results of general election held on 2 June 1997: Party Votes %age Seats %age ~~~~~ ~~~~~~~~~ ~~~~ ~~~~~ ~~~~ Lib 4,924,465 38.4 155 51.5 Ref 2,489,877 19.4 60 19.9 PC 2,421,532 18.9 20 6.6 NDP 1,421,408 11.1 21 7.0 BQ 1,370,188 10.7 44 14.6 Others 211,677 1.6 1 0.3 Total 12,839,147 ---------------------------------------------------------------------- France ~~~~~~ A two-round run-off system is used, both for parliamentary elections, and for electing the President. The French system allows any candidate with more than one-eighth of the vote to continue into the second round in elections for the lower chamber. Only the top two candidates are allowed into the run-off in the presidential election. It is usual for candidaes to withdraw in favour of some other candidate in the second round of parliamentary elections: Usually, the PS, PCF and Vert candidates withdraw in each others' favour. (left grouping) The UDF and RPR candidates withdraw in each others' favour. (right grouping) The FN never withdraws. Sometimes the left or right grouping will withdraw in favour of the other to beat the FN. The most recent election was in 1997. The 1st round was held on 25 May, and the 2nd round on 1 June. Final results of the 2nd round: Party: Députés: ~~~~~~ ~~~~~~~~ PC 38 PS 240 PRS 12 Divers Gauche 21 Ecologistes 7 Sans Étiquette 1 --- 319 RPR 135 UDF 108 Divers Droite 14 --- 257 Front National 1 Second Round - Votes ~~~~~~~~~~~~~~~~~~~~ Votes %age ~~~~~~~~~ ~~~~ Parti Socialiste 9,950,039 38.9 Parti Communiste 963,915 3.8 Ecologists 414,871 1.6 Assorted Left 1,058,437 4.1 Rassemblement pour la Rep 6,057,761 23.7 Union Dem de France 5,374,563 21.0 Assorted Right 360,247 1.4 National Front 1,434,884 5.6 ---------------------------------------------------------------------- Germany ~~~~~~~ AMS is used. Half the MPs are elected by FPTP is individual constituencies. The other half are additional members elected to make the numbers in parliament proportional to how people voted. In general elections, each voter has two separate votes: a primary vote ("Erststimme") with is a vote for a specific candidate in a constituency FPTP election, and a secondary vote ("Zweitstimme") which is a vote for a party list. When allocating Additional seats, they are allocated so that the total number of MPs in parliament (including constituency seats) that a party gets it proportional to the number of secondary votes that party gets. So if two parties get the seme number of secondary votes, but one gets more constituency seats than the other, the one with more constituency MPs will get less additional MPs, to compensate. A threshold is applied to make sure there is not a profusion of small parties: a party must get at least 5% support nationally or win at least 3 constituency seats, to qualify for getting any Additional seats. The threshold doesn't apply to the representatives of the Danish- speaking (the "Suedschleswigscher Waehlerverband") minority in Schleswig-Holstein, because they have a special exemption. ---------------------------------------------------------------------- Ireland, Republic of ~~~~~~~~~~~~~~~~~~~~ STV is used for parliamentary and European Parliamentary elections. The last General Election was held in 1992. These were the results: Votes Seats % of TDs ~~~~~~ ~~~~~~ ~~~~~~~~ Fianna Fail 39.11% 68 TDs 41.0 Fine Gael 24.47% 45 TDs 27.1 Labour 19.31% 33 TDs 19.9 Progressive Democrats 4.68% 10 TDs 6.0 Democratic Left 2.78% 4 TDs 2.4 Others 9.64% 6 TDs(*) 3.6 (*) These were 1 Green and 5 Independents. ---------------------------------------------------------------------- Israel ~~~~~~ A Party List system is used for elections to the Knesset. There is a threshold of 1.5%, which is not a particularly onorous hurdle to overcome given that the Knesset has 120 members. The threshold has been increasing in recent years: up to and including the 1988 election it was 1%. For the 1992 election it was 1.25%. In Israel it is also permissible for two lists to make a pre-election surplus-votes arrangement, whereby the total vote for the two lists is used to determine the number of seats allocated to both parties in total, and only then are they allocated to the two parties. The Prime Minister is elected separately, by a two-round run-off. This system has only been used once, in 1996. The first round results were: Binyamin Netanyahu 1,501,023 50.5% Shimon Peres 1,471,566 49.5% There was no second round, because one candidate achieved a majority in the first round (as was almost inevitable given that only 2 candidates were standing). A good on-line source for Israeli electoral information is the Israel Foreign Ministry . A very good site is the Knesset On-line . Most of this is at the moment only available in Hebrew, but the English version is being worked on -- press the button marked "English". [Most of this information was supplied by Daniel Vulkan, ] For further information see "Political Dictionary of the State of Israel", edited by Susan Hattis Rolef and published by the Jerusalem Publishing House in 1993. ---------------------------------------------------------------------- Japan ~~~~~ Used SNTV until recently. I think they use a different system now, a form of MMS(?) ---------------------------------------------------------------------- Malta ~~~~~ STV is used. If a party gets more than 50% of the vote, but does not achieve a parliamentary majority, extra members are added until they do have a majority. ---------------------------------------------------------------------- New Zealand ~~~~~~~~~~~ Uses a system called Mixed Member Proportional (MMP). This is very similar to the German system. Each voter votes twice: once in a constituency FPTP election, and once for the national vote. The non-constituency MPs are chosen so that parliament as a whole is proportional to the national vote. A party must have 5% of the total vote or at least 2 constituency seats to gain any non-constituency seats. ---------------------------------------------------------------------- Norway ~~~~~~ Uses AMS. 157 MPs are elected from regional (county) party lists, with 8 additional members to achieve overall proportionality. The regional party lists use Saint-Lague with divisors of 1,3,5,... ---------------------------------------------------------------------- Russia ~~~~~~ Uses a form of MMS. Constituency MPs are elected by FPTP. Additional members are elected in proportion to a national list. ---------------------------------------------------------------------- South Africa ~~~~~~~~~~~~ Party List with no threshold. ---------------------------------------------------------------------- United Kingdom ~~~~~~~~~~~~~~ FPTP is used in all elections, except in in Northern Ireland where FPTP is used for parliamentary elections but all other elections (ie local elections and European Parliamentary elections) are decided by STV. Some local elections outside NI use FPTP in multi-member constituencies. A General Election was held on 1st May 1997. These parties managed to get seats in parliament: Votes Seats Votes/Seat ~~~~~~~~ ~~~~~ ~~~~~~~~~~ Labour Party 13551381 419 32342 Conservative Party 9590565 165 58125 Liberal Democrats 5243322 46 113985 Ulster Unionist Party 258349 10 25835 Scottish National Party 621154 6 103526 Plaid Cymru 161030 4 40258 Social Democratic & Labour Party 190814 3 63605 Sinn Fein 126921 2 63461 Democratic Unionist Party 107348 2 53674 Ind (Bell) 29354 1 29354 Ind Unionist (McCartney) 12817 1 12817 [Martin Bell stood as an Independent in Tatton. Robert McCartney stood as a United Kingdom Unionist in Down North.] A number of other Parties also stood for election, but didn't manage to win any seats: Votes ~~~~~~~~ Referendum 810778 UKIP 105850 Green 65997 APNI 62972 Socialist Labour 52516 Liberal 45166 BNP 35393 NLP 30165 Others 182304 The total number of votes cast was 31284196. COMMENT: it is a measure of FPTP's unproportionality that the Referendum Party managed to get more votes than most of the parties that got MPs elected (ie the SNP, UUP, SDLP, PC, SF and DUP) but didn't get a single MP. If PC can get 4 MPs on 161,000 votes, surely a party with over 800,000 votes should get some MPs too? is a good site for UK political information, including election results. ---------------------------------------------------------------------- United States of America ~~~~~~~~~~~~~~~~~~~~~~~~ FPTP is used for elections to the Senate and House of Representatives. Individual states choose their own voting systems for state legislatures, although most choose to use FPTP; a notable exception is in Cambridge, Massachusetts, where the city council and school board are both elected by STV. The President is elected by an electoral college: each state has a FPTP election to determine the electoral college representatives for that state. The candidate who gets the most votes gets all their representatives chosen. The electoral college then votes for the president. In theory, an electoral college representative has no obligation to vote for their candidate but in practise they almost always do. (This clause was put in the constitution as a safeguard to prevent an unsuitable person becoming president.) A consequence of this system is that the candidate with the most votes doesn't always become president. More information about the US electoral college system can be found at . ====================================================================== PART 4: Further reading ====================================================================== Comparative Electoral Systems, by Robert A. Newland. (Arthur McDowell Fund, 1982). Available from the Electoral Reform Society. Electoral Systems: A Comparative and Theoretical Introduction, by Alan Ware and Andrew Reeve (Routledge, 1992). Electoral Systems and Party Systems: A Study of Twenty-Seven Democracies, 1945-1990, by Arend Lijphart (OUP, 1994) Contains several chapters, appendices and notes explaining how different electoral systems work and what countries have used what. Political Dictionary of the State of Israel, edited by Susan Hattis Rolef (Jerusalem Publishing House, 1993). ---------------------------------------------------------------------- The Electoral Reform Society is on the web at: ---------------------------------------------------------------------- End of FAQ.