Many large newspapers in California are bemoaning the very low turnout in special U.S. House and legislative elections recently. Some newspapers are editorializing in favor of eliminating special elections for the legislature, and advocating that the Constitution be changed to let the Governor appoint legislators to fill vacant seats. See this Los Angeles Times editorial, and this Santa Rosa Press Democrat editorial.
The newspapers are correct that voter turnout in recent special elections has been low. Ever since the top-two rules were in force, starting in 2011, the median voter turnout in California special legislative and U.S. House elections has been 13.84%. The average has been 15.80%. There have been 19 special elections under top-two rules.
If one looks at special elections for U.S. House and legislature in the period just before top-two rules went into effect, one notes that the median turnout was 20.27% and the average turnout was 21.93%. That covers the special elections held in 2009 and 2010, and also the special election held January 4, 2011, because it was held under the old rules.
Thus, whether one uses the median turnout, or the average turnout, turnout is approximately one-third lower under the top-two rules than in the corresponding period of time before it went into effect. One reason for lower turnout is that top-two makes it impossible for minor party candidates to get into the run-off, if there is one. Under the old rules for special elections, which were blanket primary elections, the top vote-getter from each party went into the run-off, if there was one (and there usually was a run-off). This encouraged minor party members to run, because they could campaign for a longer period of time. Also, under the old rules, minor party members only needed 150 signatures to avoid paying the filing fee, but now they need either 3,000 or 1,500, depending on whether they are running for U.S. House/State Senate, or Assembly.
The new rules also discourage independent candidates. Under the old rules, they were always included in the run-off, if there was one. Also, under the old rules, they could have the word “independent” on the ballot; now they have the less-appealing “no party preference.” And under the old rules, write-in space was on the run-off ballot, but that is no longer true.
Minor parties sometimes did well in special elections, under the old rules. An American Independent Party nominee got 10.2% in the State Senate 37th run-off held June 8, 2010. A Peace & Freedom Party nominee got 8.45% in the State Senate 26th run-off held May 19, 2009. A Green got 6.2% in the Assembly 72nd run-off on January 12, 2010. A Libertarian got 5.2% in the US House 32nd run-off on July 14, 2009.
The calculations above do not include the two instances in which a special election was held simultaneously with a regularly-scheduled general election, because obviously the turnout for that special election was unusually high simply because it was held on a regular election day.