Every person whose name appears in the Electoral Register last published before the date fixed for the election and every person whose name appears in the European Union Electoral Register and who in either case has not, following the publication of the said Electoral Register or the said European Union Electoral Register, been convicted of any offence connected with the election of members to the House of Representatives or with the election of members of Local Councils or with the election of members of the European Parliament shall be entitled to vote in elections of members of the European Parliament.