Conditional Approval

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Conditional Approval or CdlA is a method devised by Kevin Venzke which simulates voters adding approval to candidates only as needed over a number of rounds.

Definition

  1. The voter submits a three-slot ballot (preferred, approved, and disapproved) where the last slot may be implied by not being rated elsewhere. Any number of candidates can be placed in any slot.
  2. First, count all the preferred votes only, and note that the winner on these votes has been a "leader" in a round.
  3. All ballots which disapproved the current leader, or any past leader, have their "approved" (middle-slot) votes upgraded to "preferred" for purposes of the previous step. (A preference can never be downgraded back to "approved.")
  4. Go back to the second step, count the votes in their new states, and identify the new leader, etc.
  5. Cease this process and elect the current leader when it happens that the current leader is the same as the previous leader.

Comments

CdlA is not monotone, similar to other methods of this sort. Experimentally it is quite close to MinMax(Winning Votes), and the situation with regard to burial strategies and deterrence is probably similar.

Example

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

Suppose that the voters place their first preference in the top slot and their second preference in the middle slot, leaving the bottom two preferences unvoted.

Initially, we count only the top-slot ratings, and Memphis has the most votes (42%) and is the first leader. In response to this, supporters of the other three cities all cast their middle-slot preferences, since they didn't give any rating to Memphis. This results in Chattanooga leading with 58%. Since the Memphis voters didn't rate Chattanooga, they cast their preference for Nashville. This brings Nashville's count up to 68%.

Chattanooga and Knoxville supporters didn't vote for Nashville, but they have already added their middle-slot preferences so nothing changes. Nashville can't lose the leading position and is thus elected.