DUBLIN—Irish voters are preparing to shutter one of the two chambers of parliament in a referendum that will take place on Oct. 4, one of the few examples of austerity reducing the number of politicians.

Having survived in one form or another for an almost uninterrupted stretch of over 90 years, the parliament's 60-seat upper house now faces oblivion if voters decide by a simple majority to get rid of it. Opinion polls suggest that over 60% of those voting Friday will cast ballots for the 'Yes' proposition, sealing the fate...