A third party can flip an election without winning a seat

In a hypothetical country, each of 10 districts elects one lawmaker, and the party with the most votes wins. In Race 1, only Purple and Yellow run, and Purple wins six districts to Yellow’s four. In Race 2, a third party, Green, wins 30% of the vote in each district, taking more votes from Purple than from Yellow. Green’s entry into the race flips the winning party from Purple to Yellow, which now wins a majority of seats. Green does not win a single seat.