REFERENDUM RESULTS, ACTUAL AND POSSIBLE
A note by Eamon Henry. 22 July 2008

This short discussion offers a statistical (regression) analysis of the Irish (12 June 2008) Referendum results, of voting on the Lisbon Treaty. For a turnout of 53.1 percent, there was a NO vote of 53.4 percent, implying a YES vote of 46.6 percent.
Readers not familiar with statistical analysis are asked to accept “on faith” the results presented below via “Simple Regression” analysis of YES percentage as depending on TURNOUT percentage across all 43 constituencies. The next paragraph gives results in technical format. There follows a non-technical discussion. The actual Yes and Turnout percentages, by constituency, are given as an appendix table below, having been extracted by me from the Irish Times of 17 June 2008. The “Data Desk” software package has been used by me to give the regression results shown below.
I first present some simple results. Of all 43 constituencies, only 9 gave a Yes result above 50 percent. Of these 9, five were in the Dublin-Dun Laoghaire area, including Dublin South East constituency, which had a 61.6 percent Yes for a 49.6 percent Turnout. The regression results are as follows (and rather technical). For a fairly loose-fitting Rsquared of 15 percent, a highly significant (99 percent probable) positive coefficient emerged, namely an average 0.779 percent Yes extra for every 1 percent extra Turnout. This coefficient has a “standard error” of 0.289. Based on an assumed “Normal distribution” background, we can have about 95 percent probability that in repeated referenda of similar voter behavior, a lower limit Yes connecting coefficient is given by the average coefficient 0.779 stated above less twice the standard error value 0.289, that is a value 0.201 (given by 0.779 less twice 0.289). What this means in practice will be explained in what follows, as illustrating how to project or estimate results for non-voters supposedly voting.
We first apply the regression average coefficient to the non-voters supposedly going out to vote, as per each extra 1 percent of the electorate (across all constituencies). Call this the “naïve” assumption. A connecting coefficient of 0.779 rounded to be 0.8 indicates that an extra 5 percent turnout would give an extra 4 percent Yes. In other words, 58.1 percent turnout (actual 53.1 plus 5.0) would yield 50.6 percent Yes (actual 46.6 plus 4.0), namely a Yes majority.
By contrast, let us apply a “lower-limit pessimistic” connecting coefficient of value 0.201, as derived above. To obtain an extra 4 percent Yes would now require an extra 20 percent Turnout , via connecting coefficient now only about 0.2. In other words, a 73.1 percent turnout (actual 53.1 plus 20.0) would yield 50.6 percent Yes (actual 46.6 plus 4.0), namely a Yes majority.
It is clear that a larger (than 0.2) assumed connecting coefficient would require a smaller (than 73 percent) turnout to obtain a Yes result larger than 50 percent. These results are interesting, in providing some “parameters” regarding possible voter behavior in a repeat performance.

Appendix: Lisbon Treaty Irish Referendum (12 June 2008) Results by Constituency.

Constituency Yes Percent Turnout Percent
Meath East 50.9 50.7
Laois Offaly 56.0 54.3
Kildare North 54.6 51.5
Clare 51.8 52.5
Dublin North 50.6 55.3
Dublin NorthCentr 50.6 61.1
Dublin SouthEast 61.7 49.6
Dublin South 62.9 58.4
Dun Laoghaire 63.5 58.8
Dublin West 47.9 54.5
Dublin NorthWest 36.4 52.9
Dublin NorthEast 43.2 57.2
Dublin Central 43.8 48.8
Dublin MidWest 39.6 51.7
Dublin SouthCentr 39.0 51.6
Dublin SouthWest 34.9 53.6
Donegal NorthEast 35.3 45.7
Donegal SouthWest 36.6 46.5
Sligo Leitrim 43.3 52.6
Cavan Monaghan 45.2 53.4
Louth 51.9 53.4
Mayo 38.3 51.3
Roscommon.Sth. Leitr 45.6 56.9
Longford West Mth 46.3 51.4
Meath West 44.5 51.9
Galway west 46.1 50.00
Galway East 46.9 49.8
Wicklow 49.8 60.8
Tipperary North 49.8 58.5
Limerick East 46.00 51.4
Carlow Kilkenny 50.0 50.9
Kildare South 48.5 48.7
Limerick West 44.6 51.8
Wexford 44.0 52.8
Kerry North 40.4 51.3
Tipperary South 46.8 55.4
Waterford 45.7 53.4
Kerry South 42.6 53.1
Cork North West 46.1 55.6
Cork East 43.0 50.6
Cork South West 44.4 55.3
Cork South Central 44.9 55.0
Cork North Central 35.6 53.4