Janine A. Parry, Daniel A. Smith and Shayne Henry have written this article for Political Behavior.  Here  is the abstract:

Generally speaking, campaign-related contact motivates voters. One form of such contact not much explored in the voter mobilization literature is the petitioning for ballot initiatives that occurs with considerable frequency in about half the states and even more localities. Using newly-available data that allow us to match individual petition signers with their subsequent election behavior, we explore the role of having had a hand in a ballot measure’s qualifying stage in propelling individual voters to the polls. Specifically, we perform multivariate analysis on a random sample of 1,000 registered Arkansas voters, 1,100 registered Florida voters, and all 71,119 registered voters in Gainesville, Florida to measure the influence of petition-signing in spurring voter turnout. We find marginal effects in the statewide samples, but substantial and significant turnout effects in the Gainesville municipal election—an off-cycle, low-profile election. Furthermore, the effect of petition-signing—across all of our samples—is strongest among irregular, as compared to habitual, voters. These findings are in keeping with recent campaign mobilization experimental research and comport with previous findings on the “educative effects” of ballot measures on voter turnout.