Doesn’t Approval Voting violate “one person-one vote”?

This is a common misconception. The term “one person, one vote” comes from Supreme Court cases about district size. The cases involved unequal district sizes so that the weight of the vote for people in a less populated district was much greater than the weight of the vote for others in a more populated district.

The U.S. Supreme Court made the “one person one vote” rule explicit in Reynolds v. Sims (377 U.S. 533). The rule stated that no vote should count more than any other so that it has unequal weight. This unequal weight would violate the Equal Protection Clause of the Constitution.

This has nothing to do with the voting method itself or forcing people to use our choose-one voting method, plurality voting.

Voters using Approval Voting may not vote more than once for any candidate. The existing ‘design and construction’ of ballots, both paper and electronic, do not permit voters to vote more than once for any candidate or issue.

Proponents of Approval Voting do not seek a change here.
No candidate shall receive multiple votes from a single voter,
as is current law.

Jonathan Singer's Approval Voting bill HB17-1281 in 2017 was our last legislative attempt to instruct the Secretary of State to create rules and procedures for Approval Voting elections. Now in 2019 we are led to believe that the new administration of Jena Griswold has an interest in supporting alternative voting methods, including Approval Voting.
Local election supervisors in counties, cities/towns, and special districts need election rules from the Colorado Secretary of State.
Home Rule communities may already use Approval Voting without SoS rules, but find them valuable.
Approval Voting for Colorado seeks additional rules, not a change to existing rules.
Use of Approval Voting will be strictly voluntary by communities and districts that want to try it.