Arthur: I am your King.
Peasant woman: Well I didn't vote for you.
Arthur: You don't vote for kings.
Woman: Well how'd you become king, then?
Arthur: The Lady of the Lake, her arm clad in the purest shimmering samite,
held aloft Excalibur from the bosom of the water, signifying by divine
providence that I, Arthur, was to carry Excalibur. That is why I'm your king.
Dennis: Listen. Strange women lying in ponds distributing swords is no basis
for a system of government. Supreme executive power derives from a mandate from
the masses, not from some farcical aquatic ceremony.
Arthur: Be quiet!
Dennis: You can't expect to wield supreme executive power just because some
watery tart threw a sword at you!
Arthur: Shut up!
Dennis: If I went 'round sayin' I was an emperor just because some moistened
bint had lobbed a scimitar at me, they'd put me away!.
From the Monty Python and the
Holy Grail
In most political elections each of the citizens with a single vote for a political candidate (president, state representative, mayor …). The candidate with the highest number of votes wins the election. We call that “majority rule”. In this chapter we will discuss different procedures of counting votes for candidates. When only two candidates are in a race, “majority rule” is a good system of choosing the winner. However, when three or more candidates are running, there is no perfect way to decide an election.
When choosing only between two alternatives, the obvious voting procedure is as follows: each voter votes for one or the other choice and the alternative with the most votes wins. We call this procedure majority rule. Note that every vote is treated equally. That is, no single vote is more important than any other vote. If a single voter changes the vote from a losing alternative to a winning one, the outcome of the election would stay the same. And if every voter reversed his or her vote, then the outcome would be reversed as well.
The only potential problem with majority rule is a tie. In a two-way race ties are usually broken in some prearranged way prescribed by election procedures. For example, the following news story is an example how a tie was broken in a small town in New Mexico in 1998:
Quick
game of poker settles New Mexico mayoral contest
ESTANCIA, N.M. (March 5, 1998
11:18 p.m. EST) - Two candidates who tied in a vote for mayor of this small New
Mexico town settled their contest Thursday with a flip of a coin and a quick
game of five-card draw.
Incumbent James Farrington
and JoAnn Carlson each received 68 votes in the Estancia mayoral race in
central New Mexico Tuesday. According to the town's provision, the two had to
decide on a game of chance to break the tie.
"I wanted five card
draw, she wanted to roll the dice," said Farrington, a sandwich shop owner
who was appointed mayor 2 1/2 years ago. "So we flipped a coin to see what
game would be played. She lost the flip, we played five-card draw and I won
with ace high."
"I lost to a dumb deck
of cards," said Carlson. "It doesn't reflect the mandate of the
people, but that's what the state rules call for so that's how it was
done."
Carlson says she will contest
the result in district court Friday, saying Farrington is not a resident of
Estancia, but only has a business there.
However, the perils of the majority rule occur when more than two alternatives
are in a race, or when not every option is represented as an alternative with a
fair chance. For example:
·
In South Korea's 1987 presidential election, 2 liberals
faced the heir of a military dictatorship. The liberals got a majority of the
votes but split their supporters, so the conservative won under a majority
vote-counting rule. These rules elect whoever gets the most votes; 50% is not
required. The militarist party claimed a mandate to continue its repressive
policies. Defeated at the next election years later, its leaders were convicted
of treason for ordering the tragic shooting of pro-democracy demonstrators.
· In North Carolina, the plurality rules effectively deny representation to African-Americans. They have enough voters to totally fill 2 election districts. However, they are a 25% minority scattered over 8 districts. So for 100 years they won no federal representation. In the absence of fair representation many felt invisible as voters.
At the time the founding fathers wrote the U. S. Constitution, they had two choices: a direct election and a representative election. One of the concerns about the direct representation (an election in which the people elect the president directly by majority vote) was mostly technological: ability of presidential candidates to travel and establish presence in remote areas of the country. One of the logical outcomes of direct election could be a fragmentation of the country in regions, each with their own candidate. On the other hand, their concern with representative election (an election in which the representatives of the people elect the president) was the ability by the members of Congress to both accurately assess the desire of the people of their states and to actually vote accordingly. This could have led to elections that better reflected the opinions and political agendas of the members of Congress than the actual will of the people.
The Electoral College was established by the founding fathers as a compromise between election of the president by Congress and election by popular vote. The electors are a popularly elected body chosen by the States and the District of Columbia on the Tuesday after the first Monday in November (November 7, 2000). The Electoral College consists of 538 electors (one for each of 435 members of the House of Representatives and 100 Senators; and 3 for the District of Columbia by virtue of the 23rd Amendment). Each State's allotment of electors is equal to the number of House members to which it is entitled plus two Senators.
The electors meet in each State on the first Monday after the second Wednesday in December (December 18, 2000). A majority of 270 electoral votes is required to elect the President and Vice President. No Constitutional provision or Federal law requires electors to vote in accordance with the popular vote in their State.
If no presidential candidate wins a majority of electoral votes, the 12th Amendment to the Constitution provides for the presidential election to be decided by the House of Representatives. The House would select the President by majority vote, choosing from the three candidates who received the greatest number of electoral votes. The vote would be taken by State, with each State delegation having one vote.
A little math will tell you that the Electoral College system makes it possible for a candidate to actually lose the nationwide popular vote, but be elected president by the Electoral College.
In fact, it is possible for a candidate to not get a single person's vote – not one – in 39 states or the District of Columbia, yet be elected president by wining the popular vote in just 11 of these 12 states:
|
State |
Electoral Votes |
State |
Electoral |
|
California |
54 |
Ohio |
21 |
|
New York |
33 |
Michigan |
18 |
|
Texas |
32 |
New Jersey |
15 |
|
Florida |
25 |
North Carolina |
14 |
|
Pennsylvania |
23 |
Georgia |
13* |
|
Illinois |
22 |
Virginia |
13* |
* Either state could be the 11th state
A presidential candidate must win a majority – 270 – electoral votes to be elected. Since 11 of the 12 states in the chart above account for exactly 270 votes, a candidate could win these states, lose the other 39, and still be elected. Of course, a candidate popular enough to win California and New York will almost certainly win some smaller states, as well.
Has a presidential candidate ever lost the nationwide popular vote but been elected president in the Electoral College? Yes, twice.
In 1876 there were a total of 369 electoral votes available with 185 needed to win. Republican Rutherford B. Hayes, with 4,036,298 popular votes won 185 electoral votes. His main opponent, Democrat Samuel J. Tilden, won the popular vote with 4,300,590 votes, but won only 184 electoral votes. Hayes was elected president.
In 1888 there were a total of 401 electoral votes available with 201 needed to win. Republican Benjamin Harrison, with 5,439,853 popular votes won 233 electoral votes. His main opponent, Democrat Grover Cleveland, won the popular vote with 5,540,309 votes, but won only 168 electoral votes. Harrison was elected president.
In this section we will discuss different techniques selecting a winner of an election.
In many situations there are more than two alternatives in an election. In those situations, the most common voting procedure is to simply count the number of first places for each candidate (alternative). The candidate with the most first place votes wins the election. This voting procedure is called plurality voting, and is in effect in counting the plurality vote in U. S. Presidential elections. For example:
In 1968 presidential election, the race was between a Republican candidate Richard Nixon, a Democrat Hubert Humphrey and an Independent George Wallace. Even though none of the candidates won a majority (more than 50% of the votes cast), the winner was Richard Nixon who won 43.56% of the votes.
|
Richard Nixon |
Hubert Humphrey |
George Wallace |
|
31,785,480 |
31,275,166 |
9,906,473 |
|
43.56% |
42.86% |
13.58% |
In 1992 presidential election, the race was between a Democrat Bill Clinton, Republican George Bush and a Reform party candidate Ross Perot. The results of the election were as follows:
|
Total Votes |
Clinton |
Bush |
Perot |
|||
|
Cast |
Democrat |
Republican |
Independent |
|||
|
104,425,014 |
44,909,326 |
43.01% |
39,103,882 |
37.45% |
19,741,657 |
18.91% |
Therefore, Bill Clinton was elected president in 1992 with 43% of the vote.
An alternative way to select the winner would be to hold a runoff election between the top two candidates. In the case of 1992 election, the runoff would have been between Clinton and Bush, with Perot being eliminated. If we assume that Perot voters preferred Bush to Clinton by a two-to-one margin, as the polls at that time indicated, the voters would have chosen in the following way: Clinton 51,489,878 and Bush 52,264,987. In other words, Bush would have won the 1992 election.
In this example, George Bush was Condorcet[2] winner: he would have defeated both Clinton and Perot in one-on-one election.
Some countries (like France and Australia) employ the majority rule when determining the winner of an election. However, a critical difficulty with the majority formula is that, in a multiparty political system, the formula may produce an electoral deadlock if no candidate secures 50 percent of the total vote. In order to break such deadlocks a runoff election is required. This system thus ensures that the elected representative has the support of the majority of the voters. The majority formula is employed in Australia and France:
If no candidate secures a majority in the first round of the French National Assembly elections, another round of elections is required. In this second round, the candidate securing a plurality of the popular vote is declared winner.
In Australia voters rank the candidates on a preference ballot. A preference ballot is an ordering of the candidates from the best to the worst according to voter preference. If a majority is not achieved on the first round of elections, the weakest candidate is eliminated, and the votes of the weakest candidate are distributed to the other candidates according to the second preference on the ballot. This redistribution process is repeated until one candidate collects a majority (more than 50%) of the votes. This voting procedure is called sequential runoff or the Hare[3] method.
The Math club at Indiana University is holding an election for president. The candidates are Abe, Becky, Charlie and Diane. Each of the 17 voters ranks the four candidates in order of preference. The summary of this election is given in the preference table below. Each column shows a different ranking among the candidates, and the number at the bottom of the column specifies the number of voters who chose that particular ranking.
|
First |
Abe |
Charlie |
Diane |
Becky |
Becky |
|
Second |
Becky |
Diane |
Charlie |
Diane |
Charlie |
|
Third |
Charlie |
Becky |
Becky |
Charlie |
Abe |
|
Fourth |
Diane |
Abe |
Abe |
Abe |
Diane |
|
|
6 |
4 |
4 |
2 |
1 |
Using the plurality voting procedure, the winner of this election would be Abe with 6 = 35% first place votes. But is it really fair when 59% of the voters ranked Abe last on their preference ranking?
An alternative is to use the Hare method:
In the first round of election, the weakest candidate is Becky, with only 3 first place votes. She is therefore eliminated from the preference table:
First |
Abe |
Charlie |
Diane |
Diane |
Charlie |
|
Second |
Charlie |
Diane |
Charlie |
Charlie |
Abe |
|
Third |
Diane |
Abe |
Abe |
Abe |
Diane |
|
|
6 |
4 |
4 |
2 |
1 |
Combining the third and fourth column (which are now same), we have:
First |
Abe |
Charlie |
Diane |
Charlie |
Second |
Charlie |
Diane |
Charlie |
Abe |
Third |
Diane |
Abe |
Abe |
Diane |
|
|
6 |
4 |
6 |
1 |
In the second round of elections, the weakest candidate is Charlie, with only 5 first place votes, and is therefore eliminated:
First |
Abe |
Diane |
Diane |
Abe |
|
Second |
Diane |
Abe |
Abe |
Diane |
|
|
6 |
4 |
6 |
1 |
Combining the identical columns, we obtain the following preference table:
First |
Abe |
Diane |
|
Second |
Diane |
Abe |
|
|
7 |
10 |
Therefore, Diane wins this election with more than half of the first place votes in the last round.
Every year, the Associated Press polls seventy (70) sportswriters on a weekly basis beginning with the preseason poll, and progressing through the season. Each of the sportswriters ranks the teams according to her/his preference. Each first place team receives 25 points; the second place team receives 24; the third 23, and so on, while the 25th place wins 1 point. The team with the most points after all 70 rankings are counted is on top if the AP Top 25 College Football Poll. At the end of the 1999-2000 NCAA football season, the rankings were the following:
|
No. |
School |
Record |
Pts |
|
1 |
12-0 |
1,750 |
|
|
2 |
11-1 |
1,647 |
|
|
3 |
12-1 |
1,634 |
|
|
4 |
10-2 |
1,519 |
|
|
5 |
10-2 |
1,406 |
|
|
6 |
11-1 |
1,402 |
|
|
7 |
10-2 |
1,357 |
|
|
8 |
10-3 |
1,236 |
|
|
9 |
9-3 |
1,168 |
|
|
10 |
13-0 |
1,136 |
|
|
11 |
10-3 |
1,038 |
|
|
12 |
9-4 |
941 |
|
|
13 |
10-2 |
923 |
|
|
14 |
9-3 |
788 |
|
|
15 |
9-4 |
678 |
|
|
16 |
8-4 |
640 |
|
|
17 |
8-4 |
575 |
|
|
18 |
8-4 |
452 |
|
|
19 |
9-3 |
358 |
|
|
20 |
8-4 |