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# Borda count

The Borda count is a voting system devised by Jean-Charles de Borda (who was apparently preceded by Nicholas of Cusa [1]), used for single or multiple-seat elections. This form of voting is extremely popular in determining awards for sports in the United States. It is used in determining the Most Valuable Player in Major League Baseball, the national championship of college football, as well as many others.

### Procedures

A number n is selected; this number can be smaller than or equal to the number of candidates. Each voter lists their top n choices, in order of preference.

A first-place rank is worth n points, a second-place rank is worth n-1 points, down to an nth rank being worth 1 point. A candidate's score is the sum of the number of points they received. The highest-scoring candidate is elected.

If all candidates are to be ranked, the number of points given per candidate can be reduced by one (so that a first-place rank is worth n-1 points and the last-place ranks is worth no points at all). This variation has the property that the number of possible points per candidate will be between 0 and (c-1)*v inclusive, where c is the number of candidates and v the number of voters.

### An Example

Imagine an election to choose the capital of Tennessee, a state in the United States that is over 500 miles east-to-west, and only 110 miles north-to-south. Let's say the candidates for the capital are Memphis (on the far west end), Nashville (in the center), Chattanooga (129 miles southeast of Nashville), and Knoxville (on the far east side, 114 northeast of Chattanooga). Here's the population breakdown by metro area (surrounding county):

• Memphis (Shelby County): 826,330
• Nashville (Davidson County): 510,784
• Chattanooga (Hamilton County): 285,536
• Knoxville (Knox County): 335,749

Let's say that in the vote, the voters vote based on geographic proximity. Assuming that the population distribution of the rest of Tennesee follows from those population centers, one could easily envision an election where the percentages of votes would be as follows:

 42% of voters (close to Memphis) 1. Memphis 2. Nashville 3. Chattanooga 4. Knoxville 26% of voters (close to Nashville) 1. Nashville 2. Chattanooga 3. Knoxville 4. Memphis 15% of voters (close to Chattanooga) 1. Chattanooga 2. Knoxville 3. Nashville 4. Memphis 17% of voters (close to Knoxville) 1. Knoxville 2. Chattanooga 3. Nashville 4. Memphis

The results would be tabulated as follows:

` `
Borda Count Election Results
City First Second Third Fourth Points
Memphis 42 0 0 58 226
Nashville 26 42 32 0 294
Chattanooga 15 43 42 0 273
Knoxville 17 15 26 42 207

Nashville is the winner in this election, as it has the most points. Nashville also happens to be the Condorcet winner here, but this not necessarily always the case.

### Potential for Tactical Voting

The Borda count may encourage tactical voting. In the above example, voters from Memphis and Knoxville are encouraged to "compromise" by insincerely ranking their second-choice candidates (Nashville and Chattanooga respectively) over their first choices, because their first choices are unlikely to win. Voters from both Memphis and Nashville are encouraged to insincerely "bury" Chattanooga, the candidate most likely to challenge Nashville, while voters from Chattanooga and Knoxville are encouraged to insincerely rank Nashville lower for the same reason.

A similar criticism involves "bulleted voting", or voting for a single choice only, thus allocating no points to other choices. This is solved in part by institution of the "Borda Preferendum", which allocates a number of points for the first choice equal to the number of choices made. Thus, in the above example, a partisan for Memphis who listed only Memphis on her ballot would give one point to Memphis, while a voter who listed Memphis first and listed second, third, and fourth choices on the ballot would allocate four points to Memphis.

In addition to tactical voting, strategic nomination considerations reign supreme in the Borda count. Running multiple, similar candidates may enhance a party's chance of winning the election by increasing the point differences with opposing candidates, if the party is allowed to advance more than one candidate for consideration.