The National University of Ireland (NUI) and Trinity College constituencies will be abolished under a plan to give all third-level graduates a vote in Seanad elections.

The Cabinet will shortly consider a Bill extending the university franchise to the graduates of all third-level institutions including the institutes of technology.

Under the terms of the Bill, the two existing three-seat university constituencies will go. Instead, one six-seat constituency will be established and all third-level graduates will be entitled to vote.

The Government plans to have the Bill debated in the Oireachtas before Christmas and passed into law in time to have the new constituency in place for the next election.

Immediately after the defeat of the referendum to abolish the Seanad, Taoiseach Enda Kenny promised to proceed immediately to implement a 1979 referendum decision to extend the university franchise.

In the referendum campaign to abolish the Seanad, all* of the six university Senators were prominent in the campaign for a No vote. NUI Senators Feargal Quinn, Rónán Mullen and John Crown, and Trinity Senators David Norris, Ivana Bacik* and Seán Barrett campaigned for a No vote on the basis that it would result in a reformed Seanad.

The Government’s decision to move immediately to reform the university seats in advance of any wider reform is likely to provoke a negative reaction from the existing university Senators.

However, Government sources say the fact that successive governments have ignored the 1979 decision by the electorate to widen the university franchise is the obvious first step in the reform of the Upper House.

Minister for the Environment Phil Hogan has prepared the legislation to extend the university franchise and he will seek the approval of his Cabinet colleagues for it in the next few weeks, possibly as early as today.

The university constituencies account for six of the 60 seats in the Seanad. Some 43 are filled by an electorate composed of county councillors, TDs and outgoing senators.

The electorate for the NUI was 102,000 in 2011. The NUI turnout in the Seanad election of that year was just 33 per cent. The Trinity electorate was 53,583 and the turnout was lower at 29 per cent.

One of the reasons for the low turnout is that the majority of graduates are no longer at the address they registered at and thousands of ballot papers go to the wrong address. Setting up an electoral register for the new constituency could be difficult given there are already problems registering NUI and Trinity College graduates.

About half of the third-level graduates in the country come from institutes of technology with another 15 per cent or so coming from the new university-level institutions. It means the electorate for the new constituency will be at least double the size of the existing one for the two three-seaters.

The 1937 Constitution specifies that six of the 60 seats in the Seanad should be filled by graduates of the then two existing universities, the NUI and Trinity College. Two three- seat Seanad constituencies were established by law after the enactment of the Constitution.

Both universities had previously held seats in parliament.

* This article was amended on Thursday, November 28th, 2013.