Final answer:
The popular sovereignty in Kansas went wrong due to voter fraud and illegal vote counting by proslavery advocates. This led to the drafting of a proslavery constitution and the federal government not recognizing the votes of Kansas to come into the Union as a free state.
Step-by-step explanation:
The popular sovereignty in Kansas went wrong due to voter fraud and illegal vote counting. Proslavery Missourians crossed the border to vote in Kansas, resulting in the advantage of proslavery advocates winning the territorial elections through fraudulent means. This led to the drafting of a proslavery constitution known as the Lecompton Constitution, which was opposed by some, including Democratic Senator Stephen A. Douglas. The crisis deepened as the federal government refused to recognize the votes of Kansas to come into the Union as a free state and instead recognized a sham pro-slavery legislature.