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Weighted Voting

Weighted Voting. Part 3. Electoral College Map. This is an example of weighted voting. Need 270 out of 538 to win. Go here to see a poll of where the race stands today: http://www.realclearpolitics.com/epolls/maps/obama_vs_mccain/. Banzhaf Index.

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Weighted Voting

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  1. Weighted Voting Part 3

  2. Electoral College Map This is an example of weighted voting. Need 270 out of 538 to win. Go here to see a poll of where the race stands today: http://www.realclearpolitics.com/epolls/maps/obama_vs_mccain/

  3. Banzhaf Index • We’ve seen examples, where even though a voter has a positive weight, his or her vote may be completely useless to influence any election. • Example: The allocation of voting power in the original (six-member) European Common Market Council of Ministers made the smallest member (Luxembourg) a “dummy.” • So the weight of the voter is not necessarily a good representation of the influence he or she has on an election. • The Banzhaf Index is a better way to measure voting power. It is the number of distinct winning of blocking coalitions in which he or she is a critical voter.

  4. Review • Calculate the Banzhaf index for the committee with voting system [3 : 2,1,1]. • Answer: A = 6, B = 2, C = 2. • A has 60% of the power B has 20% of the power C has 20% of the power

  5. George Banzhaf III • Banzhaf is a law professor who introduced his powerindex in 1965 • He has fought for anti-smoking legislation, anti-junk food laws, “potty parity” and a number of other issues. • His power index was influential in a number of cases in New York state. • At first the courts tried to apportion the number of votes on its board of supervisors to match the Banhaf index. • This was hard to do, and after 25 years of lawsuits, the courts gave up and ruled in 1993 that weighted voting is inherently unfair.

  6. Electoral College • New Mexico has 0.93% of the electoral college votes. • But its Banzhaf index share is 0.91%. • Most other states have a share of the electoral college that is very close to the Banzhaf index share. • So fortunately the Electoral College has evolved in a generally fair way, from the point of view of the Banzhaf index.

  7. Experiment • What if California (55), Arizona (10), New Mexico (5), Texas (34) and Oklahoma (7) formed a country? • This would give us the system: [56 : 55,10,5,34,7] • We could do this by hand, but it would take a while. So we’ll use the Banzhaf calculator: www.math.temple.edu/~cow/bpi.html Banzhaf index: CA = 28 TX = AZ = NM = OK = 4 • Banzhaf power as a percentage: CA = 64% TX = AZ = NM = OK = 9% • Would the electoral college, assuming voting weights are based on populations, for such a country be “fair”?

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