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Approval voting is an alternate voting system which some people believe has many advantages over our standard first-past-the-post system. Instead of marking a single candidate, the voter marks every candidate of which they approve. This eliminates concerns about vote-splitting and spoilers, allowing more open elections with more than two viable candidates. It has the added advantages of being simple to explain, and easy to implement with existing voting machines.

Has any municipality or state in the US ever used approval voting? Have there been any concerted movements in that direction?

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Now they have:

Fargo, ND

Measure 1 was adopted in 2018 with 64% support:

changing the electoral system in the city of Fargo from plurality voting to approval voting, whereby voters may vote for any number of candidates they choose in local elections.

The first election using it was held in June 2020 for two city commissioners, with each receiving more than 50% approval.

St. Louis, MO

Proposition D was adopted in 2020 with 68% support:

Shall the City of St. Louis adopt an ordinance to:

  • establish an open, non-partisan system for elections to the offices of Mayor, Comptroller, President of the Board of Aldermen, and Alderman
  • enable voters to choose all the candidates they wish in the open, non-partisan primary
  • allow the top two candidates to then compete in a runoff general election?

The first primary using it was held in March 2021, for mayor and several aldermen (the other races only had 1 or 2 candidates).

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Illinois used to use Cumulative Voting for the State House until it was repealed in 1980. Cumulative voting allows a voter to split their vote or votes (the number of votes given to the voter is immaterial) across multiple candidates if they chose to vote for more than one candidate. It is statistically no different than picking several candidates in a first-past-the-post election and then randomly selecting one. I included this voting system as an example because some voters do not understand that it is no different that randomly choosing one of several desired candidates in a traditional first-past-the-post system, and these voters end up treating it like an approval voting system. So it does operate like an approval voting system, so long as the voters are uninformed and confused.

They still use this system in Peoria Illinois due to a racial discrimination court ruling, and even the electronic voting machine software had to be modified to support it.

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As a result of the 2016 elections, Maine has approved using a similar system called Ranked Choice for some statewide offices

How does ranked-choice voting work?

Instead of casting a ballot for a single candidate, the voter ranks all of the candidates by preference. So if there are four choices, the voter is asked to rank them one through four.

If no one wins a majority on the first round, the candidate with the fewest votes is eliminated. For voters, that means if the eliminated candidate was your first choice, then your second-choice vote will be applied in the next round of counting.

If your second choice is eliminated, your vote for third choice will be applied — and so on until someone wins a majority.

It's worth noting it here, since it's still rare for any state or city to use anything except traditional voting. Ranked Choice is not exactly the same, however

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    Ranked chive is significantly different from approval voting. RC is any one of several systems, all of which involve the voter ranking preferred candidates in order. "Instant runoff" is one variant of RC. In approval voting, all candidates are either approved or not approved by each voter, there is no ranking. – David Siegel Mar 5 at 17:35

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