Harry Enten at Nate Silver's new 538.com site looks at why Arizona lawmakers are so much more conservative than Arizona voters:

But the legislature’s conservatism is out of step with the people it governs. Voters in Arizona are more in favor of abortion and gay rights than the nation as a whole, and only a few points more conservative on illegal immigration.1

The disconnect stems from the state’s long history of Republican voting habits and quirks in its electoral system, which together have led to an influx of legislators far more extreme than the voters who elected them.

Arizona is mostly Republican and has been for generations. Since 1952, no other state has voted for a Democratic presidential candidate fewer times. In 2012 exit polls, only Kansas showed a higher proportion of Republicans to Democrats when people were asked about their party identification.

But Republicanism is changing, and as the GOP has gotten more conservative, Arizona Republican voters have stayed a bit more moderate. According to exit polls taken during the 2012 presidential primary, Arizona GOP voters were no more likely to say they were very conservative or a member of the tea party than those in the average state. We’ve seen proof of that when they vote for president. In February 2012, Republican voters in Arizona sided overwhelmingly with the most moderate candidate remaining in the primary race: Mitt Romney. He crushed his conservative rivals Newt Gingrich and Rick Santorum by nearly 20 points.

Given all that, why do these hyper-conservative state legislators keep getting elected? Because the Arizona electoral system allows for extreme candidates to compete on an equal playing field with their more moderate competitors.

Enten puts at least part of the blame on Clean Elections and term limits.