3-2-1 voting

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In 3-2-1 voting, voters may rate each candidate “Good”, “Acceptable”, or “Rejected”. It has three steps:

  • Find 3 Semifinalists: the candidates with the most “good” ratings. (If this is a partisan election, no two semifinalists may come from the same party).
  • Find 2 Finalists: the semifinalists with the fewest rejections.
  • Find 1 winner: the finalist who is rated above the other on more ballots.


Tennessee capital (center squeeze)

Tennessee's four cities are spread throughout the state

Imagine that Tennessee is having an election on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities, and that everyone wants to live as near the capital as possible.

The candidates for the capital are:

  • Memphis on Wikipedia, the state's largest city, with 42% of the voters, but located far from the other cities
  • Nashville on Wikipedia, with 26% of the voters, near the center of Tennessee
  • Knoxville on Wikipedia, with 17% of the voters
  • Chattanooga on Wikipedia, with 15% of the voters

The preferences of the voters would be divided like this:

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

The three most-endorsed are Memphis (42), Nashville (26), and ? (17), for a total of 85 voters who endorsed at least one of them. Of those three, the two least-rejected are Nashville (0 rejections) and ? (42 rejections). Of those two, Nashville is preferred by 68 to 32.

High school mascot (chicken dilemma)

Imagine an election for a high school mascot, in which the options are “Bulldogs”, “Lions”, “Tigers”, or “Knights”, with the following votes:

Faction size "Good" candidates "Acceptable" candidates "Bad" candidates
36 Bulldogs, Knights Lions, Tigers
4 Bulldogs Knights Lions, Tigers
35 Tigers Lions Bulldogs, Knights
25 Lions Tigers Bulldogs, Knights

The votes above lead to the following outcome:

Candidate "Good" ratings "Acceptable" ratings "Bad" ratings 2-way score
Lions 25 35 40
Tigers 35 25 40 55
Knights 36 0 56
Bulldogs 40 5 55 45

The semifinalists are Tigers, Knights, and Bulldogs. The finalists are Tigers and Bulldogs. The winner is Tigers.