A look at both congressional elections, and state legislative elections, in the two states that have used “top-two”, shows that when states switch to “top-two”, the ability of incumbents to be re-elected increases. Also, when a state switches away from “top-two”, the ability of incumbents to be re-elected declines.
Washington used a classic open primary in 2006, but switched to a “top-two” system in 2008. No congressional incumbent lost in either election year. For Washington state legislative races, in 2006, six incumbents were defeated (in Senate districts 6 and 44, and House districts 6-1, 23-2, 24-1, and 31-2). But in 2008, under “top-two”, five incumbents were defeated (in Senate district 2, and House districts 6-1, 6-2, 17, and 44). It is true that there isn’t much difference between six incumbents losing under one system, and five incumbents losing under another system, of course. Nevertheless, the fact that more incumbents lost under a non-top-two system than lost under the first “top-two” experience in Washington contradicts the extravagant promises made by supporters of “top-two” in California. These supporters assume that “top-two” will wash away the “extremists” in the legislature.
Louisiana’s experience is more dramatic. The first year Louisiana used “top-two” for its state legislative races, in 1975, only five incumbents were defeated, our of 144 races (Senate district 38, and House districts 45, 61, 99, and 100). Unfortunately I have not been able to get the data for 1971, the last year Louisiana used a closed primary for state legislative races, but I will continue trying.
In Lousiana Congressional races, during the years that state used “top-two”, out of 112 U.S. regularly-scheduled U.S. House races, only one incumbent was ever defeated (except that in 1992, when two incumbents were left without a district due to reapportionment and redistricting, two incumbents had to run against two other incumbents, so obviously two incumbents lost). No incumbent was defeated in the ten U.S. Senate races. But when Louisiana switched back to semi-closed primaries for Congress starting in 2008, two U.S. House incumbents (out of 7 districts) were defeated.