Of the 50 state legislatures in the US, 49 are bicameral and only Nebraska's is unicameral.
The idea behind the two chambers of the federal Congress is, of course, to balance the need for representation of states (each state having equal representation in the Senate) and of the people at large with the "one person, one vote" principle (the number of representatives in the House depending on the state's population); thus the bicameral nature of Congress is easy to understand.
It is not the same with state legislatures, however. The existence of two chambers in the state legislatures only seems to bring expenditures and delays in legislating, with few benefits, as the state representatives and state senators are elected basically in a very similar manner.
My question is then: why haven't more states followed Nebraska's example and reformed their legislature into a unicameral body?
History of the Nebraska Unicameral (watch video)Among other factors, the video notes that only 18 of 100 representatives and 13 of 33 senators favored the measure. Nebraska now has 43 legislators, or about 1/3 the previous number. When the Scottish Parliament was replacing FPTP with STV for local elections, the main concern was the severance benefits for councilors who would not be elected under STV (e.g. an area with 3 Labour councilors might elect one Labour, and 2 from among SNP, LibDem, and Conservatives).
It was strongly supported by US Senator George Norris, a popular progressive. The election was in 1934 so that there could be an appeal to cost-cutting to people who were losing their farms.
Supposedly it got additional votes because of two other ballot measures to end Prohibition and legalize horsetrack gambling, both of which would have populist support and attract voters who ordinarily were not vested in the legislative process.
The final vote was 286K to 193K, but 100K did not vote, so maybe it just wasn't that big a deal either way to many voters. You would be quite atypical in your interest.
Supposedly there was some interest in switching to a unicameral legislature after the Supreme Court ruled that both houses must be apportioned based on population, but the average legislator would just be interested in muddling along. Eventually a court would impose redistricting, but it would be inappropriate for a court to make a radical transformation. After the new election with new districts, all the new legislators would be quite happy with the new system. Legislators from rural districts would fear that a unincameral legislature would reduce the number of legislators even more. Legislators from urban areas might agree that some were incompetent, but would not agree on which.
And many legislators might like the complexity of a bicameral system. All kinds of things can happen in a conference committee, and some may delight in understanding an unnecessarily complex procedure. If they are lawyers, and many legislators are, they make take pride in their understanding of arcane procedures.