Research on the effects of prepaid postage on voter participation in Switzerland found a modest increase in turnout between 1.1 and 1.3 percentage points.
Prepaid Postage Using Pre-stamped Envelopes to Affect Turnout Costs
Survey of State Cost Savings
Alaska’s Election Policy Work Group compiled research regarding five star vote-by-mail systems, including a survey of cost savings across a number of states
Investing 85 Cents per Voter to Increase Voter Turnout by 4 Percent
In this paper that examines the effects of prepaid postage on voter turnout in the Swiss Canton of Berne, researchers find that prepaid postage is associated with a statistically significant 1.8 percentage point increase in voter turnout. Overall, this amounts to 4 percent more voters participating.