Chapter I democracy and its mathematical discontents 1 Choosing an Electoral System



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Figure: Boston Tea Party

While the French might have understood and theorized what constitutes ‘democracy’59 one should emphasize that ‘democracy’ as a modern concept and practice is a true child of the ‘Land Beyond the Pillars of Hercules.”60
Political mythology has it that The Fundamental Orders of Connecticut, adopted by the citizens of Hartford and neighboring towns on January 14, 1638, were the "first written constitution of a modern democracy."61 However, the commonwealths of the Puritans of yore were amalgams of theocracy, fierce individualism, and democracy. When the settlements at Portsmouth and Newport were united in 1641 they were declared to be
a democracy or popular government; i.e. it is in the power of the body of freemen orderly assembled, or the major part of them, to make or constitute just laws… and to depute from among

themselves such ministers as shall see them faithfully executed.62


Democracy did not extend to the natives, and attitudes towards French ways were not all favorable.
“Racial pride or prejudice had prevented any fraternization between the English settlers and the savages… The English were fundamentally farmers and home-builders… [T]he native for the English was neither business partner nor a military ally. He was, for the most part, a dangerous animal, like the panthers, wolves and wild-cats, or a nuisance like the stones and tree stumps, to be cleared away before advancing settlements. The French on the other hand, had no racial antipathy. They became brothers of the savages, lived with them and took Indian mistresses or wives. They were traders, adventurers, explorers, not settlers… The war begun in Europe in 1689 between two civilized nation was almost immediately echoed back from the American forests by the warwhoop of the savages. With much cruelty, parties of French and Indians fell on our settlements…” 63
Democracy rose in the pre-modern world as a reaction to ‘aristocracy’ and monarchial tyranny. Democracy was theoretical among the French who accepted the notion of the tyranny of the revolution. Among the Americans, Hamilton detested the French revolution and its ‘egalitarian’ creed.
“The French Revolution had broken out in 1789, and at first we all followed its course with enthusiasm. It was easy to get drunk on abstract liberty in the eighteenth century, and the French people seemed to be following in our footsteps. Washington had been in office but a few weeks in his second term when news arrived that caused a revulsion of sentiment among a large part of the Americans. The increasing bloodshed and the brutal violence of the French movement had culminated in cutting off the head of the King after the Declaration of a Republic, and France had declared war on England and Spain… These events killed the sympathy of many Americans…”64
Of American democracy, we find the critical note of John Stuart Mill,65
“The natural tendency of representative government, as of modern civilization, is towards collective mediocrity… In the false democracy which, instead of giving representation to all, gives it only to the local majorities, the voice of the instructed minority may have no organs at all in the representative body. It is an admitted fact that in the American democracy, which is constructed on this faulty model, the highly-cultivated members of the community, except such of them as are willing to sacrifice their own opinions and modes of judgement [sic], and become the servile mouthpieces of their inferiors in knowledge, seldom even offer themselves for Congress or the State Legislature, so little likelihood have they of being returned. Had a plan like Mr. Hare’s by good fortune suggested itself to the enlightened and patriotic founders of the American Republic, the Federal and State Assemblies would have contained many of these distinguished men, and democracy would have been spared its greatest reproach and one of its most formidable evils.”

Balinski and Young insist—not without merit—that all the methods of apportionment devised in Europe have some roots in the political history of the United States. The democratic ideal is enshrined in the U.S. Constitution. According to Article 1, Section 2,
“Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers, which shall be determined by adding to the whole Number of free Persons, including those bound to Service for a Term of Years, and excluding Indians not taxed, three fifths of all other persons. …
The Number of Representatives shall not exceed one for every thirty thousand, but each State shall have at least one Representative;”
The history of PR in Germany offers a vivid example of how democracy can give birth to its antithesis. It also offers a commentary on the limits of what constitutes “mathematical justice”. It was during the “Weimar Republic”66 and through the ballot-boxes that Hitler and his Social Nationalists came to power in the mid-1930s. Japan’s “Taisho democracy” of the mid-1920s gave rise to an era of mass politics which was used by the Japanese army to sell an imperial ideology with wide appeal. There is a strong correlation between democratization and the rise of belligerent nationalism and war.67


1 Patterns of Democracy: Government Forms and Performance in Thirty-Six Countries, Arend Lijphart, Yale University Press, New Haven, 1999.

2 See “Electoral formulas: A macroscopic perspective,” A. Blais & L. Massicotte, European Journal of Political Science 32: 107-109, 1997.

3 Polis is Greek for ‘city’. Compare with the Latin ‘Civitas’ and Arabic ‘Medina’. The "barbarians" of the Greeks (lit. the 'foreigners') dwelt "outside" the Polis and did not participate in its affairs.

4 See The Muqaddimah, in Franz Rosenthal’s translation, vol. I, Pantheon Books, New York, 1958.

5 Democracy in the United States, William Riker, Macmillan, 2nd Edition, 1965.

6 “Religion and the Third Wave,” Samuel Huntington, National Interest 24, 29-42.

7 The third wave: democratization in the late twentieth century, Samuel Huntington, University of Oklahoma Press, Norman, 1991, p. 9.

8 For a detailed description of all subsystems see “Electoral System Families” at the IDEA website http://www.idea.int/esd/systems.cfm. For a list of countries subscribing to a particular system see “The Electoral Systems of Independent States and Related Territories Worldwide” at http://www.idea.int/esd/data/world.cfm.

9 For example, 119 of 192 countries are classified in a study conducted by Freedom House in 1999 as “electoral democracies”. “…[L]iberal democracies—i.e. countries Freedom House regards as free and respectful of basic human rights and the rule of law—are 85 in number and represent 38 percent of the global population.” See, Democracy’s Century: A survey of global political change in the 20th century, Freedom House, December 7, 1999, www.freedomhouse.org/reports/century.html.

10 For example, Algeria, Morocco and Madagascar adopted PR, Niger and Tunisia adopted semi-PR forms, Djibouti and Gabon chose plurality, while Mali and Mauritania still use majority. All were French colonies which gained independences in the late fifties and early sixties.

11 See Exercise 7 in which women’s participation rates under each system are computed.

12 In the 2000 census, there were 35,305,818 Hispanics in the U.S., 16,907,852 of whom identify as “white”; 710,353 are “black or African American”, 14,891,303 are “some other race”, and 2,224,082 have “two or more races”. (US Census Bureau Release, April 1, 2000)

13 Women’s Underrepresentation and Electoral Systems, Wilma Rule, PS: Political Science and Politics, Vol. 27, No. 4 (1994), 689-692.

14 The International IDEA Handbook of Electoral System Design, Reynolds, Andrew; Reilly, Ben, The International Institute for Democracy and Electoral Assistance (IDEA), www.idea.int, Stockholm, 2002 Reprint, p. 30.

15 from data collected by the Inter-Parliamentary Union in 181 countries;

16 Women in National Parliaments website, www.ipu.org/wmn-e/world.htm.

17 See http://www.stortinget.no/english/history.html.

18 See http://www.sofia.mfa.no/Norway/Norway+at+a+glance/Norway+at+a+glance.htm.

19 See “Florida List for Purge of Voters Proves Flawed”, New York Times, 10 July 2004. http://www.nytimes.com/2004/07/10/national/10florida.html.

20 See “A Fair Voting System for South Africa” at http://www.fairvote.org/reports/1993/reynolds.html.

21 Comparing Proportional Representation Electoral System: Quotas, Thresholds, Paradoxes and Majorities, M. Gallagher, British Journal of Political Science, 22:4 (1992), 469-496.


22 Exercise 14 shows that these conditions are equivalent.

23 See Exercise 13.

24 Antigua & Barbuda uses a “First Past the Post” (FPTP) system to decide who gets elected. This is a plurality system and a legacy from British colonial times.

25 The alternatives were produced using various forms of proportional representation which will be described in chapters 2 and 3.

26 The Excel file works for any number of seats, up to 300 parties.

27 Data provided by Psephos Election Archive, http://psephos.adam-carr.net/countries/a/antigua/. Like most English speaking Caribbean countries, Antigua & Barbuda inherited the First-Past-The-Post (FPTP) system from Britain. The seat distribution displayed is that determined by this system. The alternatives were produced using PR.

28 Data also provided by Psephos Election Archive, http://psephos.adam-carr.net/countries/p/pakistan/


29 Data from Psephos Election Archive, http://psephos.adam-carr.net/countries/p/pakistan/


30 Democracy, from the Greek demos = people, kratos = rule. It is interesting to note that the literal meaning of kratos is town. This is why in the Middle Ages, Arab translations of Greek classics chose “medina jamiyah” for “democracy”; aristocracy was called “medina imamiyah”. The word “kratos” is still found in both Arabic and Hebrew under the meaning of “village” in the forms “Karyah” and “Kiryat” and can still be traced in the name of Carthage (Kart Hadasht=New City).

31 This expression was recently revived by U.S. Secretary of Defense Donald Rumsfeld who also appears on the board of directors of Freedom House.

32 Historians note that William Shakespeare failed to mention the Magna Carta in his historical play King John.

33 See the BBC:http://www.bbc.co.uk/history/timelines/england/stu_world_upside_down.shtml.

34 See for example the two volumes edited by Seymour Lipset, Democracy in Europe and the Americas, Democracy in Asia and Africa, Congressional Quarterly, Inc., Washington, D.C., 1998.

35 “Communal Democracy and its History”, A. Black, Political Studies, Vol. XVI (1997), 5-20.

36 “Primitive Democracy in Ancient Mesopotamia”, T. Jacobsen, Journal of Near Eastern Studies, Vol. 2, No. 3 (Jul. 1943), 159-172.

37 “Traces of Primitive Democracy in Ancient Israel”, C. Umhau Wolf, Journal of Near Eastern Studies, Vol. 6, No. 2. (Apr., 1947), pp. 98-108.

38 Puhrum seems to be an ancient ancestor of a public “forum”.

39 T. Jacobsen, opt. cit., notes the parallels between prehistoric Mesopotamia and the “primitive Teutonic tribes who overrun Western Europe”. W. J. Shepard calls “primitive democracy” a “rude form of democracy in which government was not differentiated no law clearly distinguished from religious or social custom.”

40 Their “amen” was a “primitive” form of the English “ye” and “nay”.

41 Quoted in “Domesticating Democracy: Culture, Civil Society, and Constitutionalism in Africa”, Maxwell Owusu, Comparative Studies in Society and History, Vol. 39, No. 1 (Jan. 1997), 120-152. Owusu notes that “Members of African societies sense their unity and perceive their common interests in symbols in the form of myths, proverbs, fiction, dogmas, ritual, sacred places and persons, and so forth; it is their attachment to these symbols which gives African societies their identity, cohesion and persistence. Some of these powerful symbols could be adapted to serve modern democratic governance…”

42 “From local assembly to national assembly,” History of Norway’s Storting, www.stortinget.no/english/history.html

43 “Occupational Versus Proportional Representation”, Paul H. Douglas, The American Journal of Sociology, Vol. 29 (1923), 129-157.


44 See ``The Guilds of Early Modern Augsburg'' by E. L Skip Knox; http://oit.boisestate.edu/sknox/dissertation/

45 Curia Regis is Latin for “Royal Council”.

46 “Medieval Origins of Constitutional Government in the West”, Brian M. Downing, Theory and Society, Vol. 18, No. 2 (Mar. 1989), 213-247.

47 Quoted in Downing, opt. cit.

48 “The place of politics in the philosophy of Ibn Rushd,” Erwin I. J. Rosenthal, Bulletin of the School of Oriental and African Studies, University of London, Vol. 15, No. 2 (1953), 246-278.

49 timocratic=rule by honor and military glory; from the Greek tīmē, value, honor + kratia, cracy; compare with the Arabic dhimmah, also honor.

50 plutocratia=rule by the wealthy.

51 The period corresponds to the years 1106-1145 AD. Almoravids, were Berber Moors who invaded the bulk of the Maghreb and Andalusia and controlled much of both from 1056 – 1147 AD.

52 “Jama`a” (lit. “the community”) stands for “Jamaat al-Muslimeen”, the Muslim populace as a whole.

53 See “Djumhuriyya”, in Encyclopedia of Islam, New Edition, Vol. II, E. J. Brill, 1965, 594-597.

54 “Republic” seems to have been the choice for the bulk of systems in the Islamic world. The word “jumhuriyah”, coined in the late 18th century by Ottoman scholars, derives from the Arabic “jumhur”, meaning mass or people. The respected British Lexicographer and Orientalist G. P. Badger chose “Hukm Jumhuri” as a translation of the word “democracy” in his An English-Arabic Lexicon (Reprinted by Librairie du Liban, Beirut, 1967). He translates “republic” as “Hukumah Jumhuriyah”, and explains “[this is] a commonwealth, [a] government by the election of the citizens”, pp. 223, 875.

55 French Revolution Research Collection, Oeuvres de Condorcet, publiées par A. Condorcet O'Connor et M. F. Arago, Tome Dixième, Paris, Firmin Didot Frères, 1847, pp. 84, accessed via gallica.bnf.fr

56 gallica.bnf.fr

57 Borda’s paper was translated into English by Alfred de Grazia. See “Mathematical Derivation of an Election System”, ISIS, Vol. 44 (1953), pp. 42-51.

58 A Short History of Electoral Systems in Western Europe, A. M. Carstairs, George Allen & Unwin, London, 1980.

59 Originally a “democrat” was one of the republicans of the French revolution. In the U.S., a democrat was an anti-federalist, or one who carried on the beliefs and practices of Thomas Jefferson. In the popular slang of 1890, a “democrat” is a “high four-wheeled cart, painted and varnished, with double seats, one behind the other.” See, The Oxford English Dictionary, 2nd Edition, Clarendon Press, Oxford, 1989, Vol. II.

60 The pillars of Hercules are a reference to the Strait of Gibraltar from Greek Mythology, and a reference to the perils of travels in the Mare Tenebrosum (The Atlantic Sea); the pillars appear today as the double bar of the dollar sign. See http://www.saudiaramcoworld.com/issue/199203/pillars.of.hercules.sea.of.darkness.htm.

61 The third wave : democratization in the late twentieth century, Samuel Huntington, University of Oklahoma Press, Norman, 1991.

62 Quoted in, “The Political Ideas of the Puritans, II”, Herbert L. Osgood, Political Science Quarterly, Vol. 6, No. 2 (Jun., 1891), 201-231.

63 The March of Democracy, James T. Adams, Vol. I, Scribner’s, New York, 1932, p. 44.

64 The March of Democracy, opt. cit., p. 178

65 On Liberty, Representative Government and the Subjection of Women, J. S. Mill, Oxford University Press, London, 1912 edition, 259-260.

66 After the city of Weimar.

67 “Democratization and the Danger of War”, E. D. Mansfield and J. Snyder, International Security, Vol. 20, No. 1 (Summer, 1995), 5-38.

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