The House Republican minority succeeded Tuesday in delaying by at least two years the ability of Connecticut voters to decide if the state Constitution should be amended to increase the General Assembly’s discretion over the use of absentee ballots.

Connecticut is a rarity among the states: Its rules for absentee voting are among the most restrictive in the U.S., and they are enshrined in its constitution.

At issue Tuesday was a proposed constitutional amendment that would allow — not require — the legislature to authorize no-excuse absentee voting. Notwithstanding the experience elsewhere, Republicans said the change would invite large-scale fraud.