This system bears surface similarity to the Open Primary/Top Two Primary adopted in California and Washington. Like those systems, in the unified primary all voters may participate, all candidates appear on the same ballot regardless of party, and the top two candidates advance. Of significant difference is that in the unified primary voters are allowed to express support for all favored candidates.
All of the criticisms of so-called "top two" systems are in fact attributable to the restriction of support for a single candidate in a field of many: similar candidates split votes, so if there are an unequal number of candidates representing various viewpoints, the results can be skewed by simple candidate participation. Because all candidates appear on a single ballot, the spoiler effect is magnified, which enhances the shut out of minor party and independent candidates. Name recognition becomes even more important, so candidates need to raise more money to compete.
By allowing voters to express support for all favored candidates, the unified primary solves the weaknesses inherent in current top two systems.