A unified primary (or top-2 approval+runoff) is an electoral system for narrowing the field of candidates for a single-winner election, similar to a nonpartisan blanket primary, but using approval voting for the first round, advancing the top-two candidates, allowing voters to confirm the majority-supported candidate in the general election.
Comparison to other primary systems
In the US, most primary elections are party-specific: voters select a political party, either as part of the voter registration process or at the ballot box, and may vote only for candidates sharing that same party affiliation. These primary systems use plurality voting, where each voter may express a preference for one candidate per office. The candidate in each party receiving the most votes advances to the general election. Voters not affiliated with a major political party may or may not be able to participate in these primary elections, depending on jurisdictional rules, and candidates not affiliated with a major political party may be nominated to the general election by other processes such as minor party conventions or petition.
The non-partisan blanket primary (aka "jungle primary" or top-two primary) is a single primary election in which all voters may participate, and all candidates appear on the same ballot, regardless of party affiliation or lack of party affiliation. The top two most-voted candidates (even if members of the same party) will appear in the general election. This is intended to allow non-partisan voters and candidates to participate, and to allow more moderate nominees in the general election (since voters from both sides of the spectrum can vote for them). However, the non-partisan blanket primary still only allows voters a single choice per office, and is therefore prone to the spoiler effect, where candidates espousing similar ideologies split votes, helping candidates with opposing ideologies (but fewer candidates) to win.
Like a blanket primary, the unified primary has only one primary election, in which all voters participate, and all candidates appear on a single ballot regardless of political party affiliation. Unlike a blanket primary, the unified primary uses approval voting in the first round, in which voters may express support for any number of favored candidates, which is intended to eliminate vote splitting and spoilers (since voters can support a partisan favorite and a moderate). The top two most-approved candidates will appear in the general election.
Analysis
Proponents posit that the Unified Primary system will increase voter choice by allowing all voters to participate equally in all stages of the election process, by allowing voters to express support for more than a single candidate, and by allowing all candidates to compete in a uniform election process, regardless of political party affiliation or lack of affiliation.
In contrast, FairVote, a national election reform non-profit that advocates instant-runoff voting, theorized that it is likely that general election races would have two finalists from the same major party in districts where a majority of voters affiliate with that party, and thereby reduce voter choice in the election that has statistically higher turnout than current primary elections.
Election method simulation of various voting systems indicate that an election system comprising approval voting in the first stage and a vote between the top two approved in the second stage is the highest-performing simple (unranked, unit weighted) two-stage voting system on the criteria of Bayesian regret and propensity to elect the Condorcet winner. These simulations confirmed early election science research that found that the most efficient simple two-stage voting system allows two or more votes in the first stage and a single vote between two candidates in the second stage.
Unlike single-round Approval voting, the Approval+Runoff method fails independence of clones, because any time the second-most approved candidate wins the runoff, if a clone of the most-approved candidate is introduced, then the runoff will be only between the most-approved candidate and their clone, preventing the second-most approved candidate and any of their clones from winning.
Usage
St. Louis
The STL Approves campaign sought to adopt the same system (though they refer to it simply as "approval voting") in St. Louis city elections (Mayor, Comptroller, President of the Board of Aldermen, and Alderman).
Originally called St. Louisans for Ranked Choice Voting, the campaign switched to advocating for approval+runoff, primarily due to learning that St. Louis and St. Louis County voting machines are incompatible with IRV.