What is the best voting method? Paradoxes abound

Texas Christian University math professors Efton Park and Rhonda Hatcher examined the efficacy of various voting methods from a mathematical probability standpoint at the February meeting of the Women’s Policy Forum.

The husband-and-wife team analyzed the outcomes of various voting procedures to see which would produce the most accurate representation of voters’ ballots.

Plurality voting – The most familiar and common form of voting – whoever gets the most votes wins. Although this may seem fair, sometimes outcomes don’t reflect the desires of the electorate. An example, Park explained the 1998 Minnesota gubernatorial race that produced Jesse Ventura’s victory.  A virtually even split of votes between Norm Coleman (R), Hubert Humphrey III (D), and Jesse Ventura (I) allowed Ventura to win the election with less than 40 percent of the vote.

Plurality with a runoff – Another variation on the most common form of voting, requires a runoff between the top vote getters if one candidate doesn’t win more than 50 percent of the ballots. Even this method can go awry. In 1991, in the Louisiana gubernatorial race among Buddy Romer, the incumbent, Edwin Edwards, a former governor who had been convicted of corruption and resigned, and challenger and independent David Dukes, KKK and white supremacist, produced a runoff. Edwin Edwards and David Duke received 34 percent and 32 percent of the votes respectively. The choices left to voters were the crook or the white supremacist, producing a Sophie’s Choice runoff.

Ranked choice voting or Instant runoff – This is an increasingly popular election method that asks voters to rank contenders in order of preference. Minneapolis, San Francisco and many college campuses used this form of forced ranking. Ballots are initially counted to see who has the most votes. If a candidate has more than 50 percent of the vote, that person wins. If not, person with the least first rankings is eliminated. Votes for that candidate are moved to the remaining candidates that ranked the highest. This process continues until one candidate has more than 50 percent of the votes or there is a tie. Downside to this approach, as demonstrated by the speakers, is that it is possible for the candidate without a plurality to win.

According to Hatcher, voters desire monotonicity and freedom from irrelevant alternatives. Monotonicity means that if one or more voters raise a candidate in their ranking while leaving all other candidates in the same relative positions, then that candidate never does worse. Plurality voting with a runoff and ranked choice voting both violate this theory. Freedom from irrelevant alternatives means that if a group of voters prefer Candidate A over Candidate B, then adding or removing other candidates should not change the group’s preference for A or B. Every method discussed violated this rule.

Weighted voting systems – Unequal number of ballots awarded based on size or population. Examples are shareholders’ votes, NCAA Division 12 , United Nations Security Council, and Electoral College. Measuring voting power in this system depends on critical players who can determine the outcome of any vote. In the electoral system, states can become critical players based on their ability to sway election outcomes.

Only one ranking voting system adhered to these four conditions:

*Voters can choose any preference ranking

*Every candidate can win

*Is montone

*Free from irrelevant alternatives

A dictatorship!

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