From Wikipedia, the free encyclopedia Weighted voting
Weighted voting
Weighted voting systems are voting systems based on the ing called cross-voting. Essentially, voters were round-
idea that not all voters are equal. Instead, it can be de- ed up in two voters’ rolls, with the A roll bearing re-
sirable to recognize differences by giving voters different quirements generally reached by the European-descend-
amounts of say (weights) concerning the outcome of an ed population, but only in a few cases by Africans. The
election. This is in contrast to normal parliamentary pro- B roll provided for many Africans and a few Europeans,
cedure, which assumes that each member’s vote carries but not all the adult population. Despite its limited size
equal weight. in terms of voters, the A roll played the major influence
This type of voting system is used in everything from in electing the 65 members of parliament, which was fur-
shareholder meetings, where votes are weighted by the ther bolstered by the lack of support to sign up for the
number of shares that each shareholder owns, to the B roll, and its much lower turnout. In 1969, cross-vot-
United States Electoral College. ing was abolished altogether in favor of a de jure seg-
regationist weighted voting system, in which the A roll
Historical examples (electing 50 seats) was reserved for Europeans, Coloureds
and Asians meeting higher property and education re-
quirements, and the B roll (electing eight seats) reserved
Ancient Rome for Africans meeting lower property and education re-
The Roman assemblies provided for weighted voting af- quirements. In its 1970 general election, about 50,000 A
ter the person’s tribal affiliation and social class (i.e. roll voters (essentially all white) elected 50 parliamen-
wealth). Rather than counting one vote per citizen, the tary seats, a little more than 1000 tribal chiefs elected
assemblies convened in blocs (tribes or centuries), with eight special seats, whereas the rest of the population
the plurality of voters in each bloc deciding the vote were to be content with the remaining eight seats.
of the bloc as an entity (which candidate to support or
whether to favor or reject a law, for instance). Men of
certain tribes and a higher social standing convened in
The mathematics of weighted
smaller blocs, thus giving their individual vote the effect voting systems
of many poor citizens’ votes. In the Plebeian Council,
where only the plebs could participate, these effects were A weighted voting system is characterized by three
somewhat relaxed, thus making the decision to grant its things — the players, the weights and the quota. The vot-
decisions (called plebiscites) the full force of law very con- ers are the players (P1 , P2, . . ., PN). N denotes the total
troversial (Lex Hortensia in 287 BC). number of players. A player’s weight (w) is the number of
votes he controls. The quota (q) is the minimum number
Sweden of votes required to pass a motion. Any integer is a possi-
ble choice for the quota as long as it is more than 50% of
In several Western democracies, such as Sweden pre-uni-
the total number of votes but is no more than 100% of the
tary Germany weighted voting preceded equal and uni-
total number of votes. Each weighted voting system can
versal suffrage, as well as womens’ suffrage, to different
be described using the generic form [q : w1, w2, . . ., wN].
extents. In Sweden, universal and equal male suffrage
The weights are always listed in numerical order, start-
to the lower house (Andra kammaren) was introduced by
ing with the highest.[1]
Arvid Lindman’s first cabinet, while voting for city and
county councils, which indirectly decided the composi-
tion of the upper house (Första kammaren), was graded The notion of power
along a 40-degree scale. Certain corporations also had
When considering motions, all reasonable voting meth-
votes of their own, thus multiplying the political
ods will have the same outcome as majority rules. Thus,
strength of its owners. Weighted voting was abolished in
the mathematics of weighted voting systems looks at the
Nils Eden’s reforms of 1918-19, when female suffrage was
notion of power: who has it and how much do they
also introduced.
have?[2] A player’s power is defined as that player’s abili-
ty to influence decisions.[3]
Rhodesia Consider the voting system [6: 5, 3, 2]. Notice that a
Under its 1961 Constitution, the British colony of South- motion can only be passed with the support of P1. In this
ern Rhodesia provided for a special form of weighted vot-
1
From Wikipedia, the free encyclopedia Weighted voting
situation, P1 has veto power. A player is said to have ve- be passed without the unanimous support of all the play-
to power if a motion cannot pass without the support of ers. Thus, P3 holds just as much power as P1.
that player. This does not mean a motion is guaranteed It is more accurate to measure a player’s power using
to pass with the support of that player.[1] either the Banzhaf power index or the Shapley–Shubik
Now let us look at the weighted voting system [10: power index. The two power indexes often come up with
11, 6, 3]. With 11 votes, P1 is called a dictator. A player is different measures of power for each player yet neither
typically considered a dictator if his weight is equal to or one in necessarily a more accurate depiction. Thus,
greater than the quota. The difference between a dictator which method is best for measuring power is based on
and a player with veto power is that a motion is guaran- which assumption best fits the situation.The Banzhaf
teed to pass if the dictator votes in favor of it. [1] measure of power is based on the idea that players are
A dummy is any player, regardless of his weight, who free to come and go from coalitions, negotiating their al-
has no say in the outcome of the election. A player with- legiance. The Shapley–Shubik measure centers on the as-
out any say in the outcome is a player without power. sumption that a player makes a commitment to stay up-
Consider the weighted voting system [8: 4, 4, 2, 1]. In on joining a coalition.
this voting system, the voter with weight 2 seems like he
has more power than the voter with weight 1, howev-
er the reality is that both voters have no power whatso-
References
ever (neither can affect the passing of a motion). Dum- [1] ^ Tannenbaum, Peter. Excursions in Modern
mies always appear in weighted voting systems that have Mathematics. 6th ed. Upper Saddle River: Prentice
a dictator but also occur in other weighted voting sys- Hall, 2006. 48–83.
tems (the example above).[1] [2] Bowen, Larry. "Weighted Voting Systems."
Introduction to Contemporary Mathematics. 1 Jan.
2001. Center for Teaching and Learning, University
Measuring a player’s power of Alabama. [1].
A player’s weight is not always an accurate depiction of [3] Daubechies, Ingrid. "Weighted Voting Systems."
that player’s power. Sometimes, a player with several Voting and Social Choice. 26 Jan. 2002. Math Alive,
votes can have little power. For example, consider the Princeton University. [2].
weighted voting system [20: 10, 10, 9]. Although P3 has al-
most as many votes as the other players, his votes will
never affect the outcome. Conversely, a player with just a
See also
few votes may hold quite a bit of power. Take the weight- • Plural voting
ed voting system [7: 4, 2, 1] for example. No motion can • Prussian three-class franchise
Retrieved from "http://en.wikipedia.org/w/index.php?title=Weighted_voting&oldid=461838159"
Categories:
• Voting systems
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