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Five seats in D´ail ´Eireann were available for election in the Meath constituency in the 2002 general election. Brady (Fianna F´ail), Bruton (Fine Gael), Dempsey (Fianna F´ail), English (Fine Gael) and Wallace (Fianna F´ail) were elected. A latent space model, incorporating the Plackett-Luce model for rank data, was fitted to the 64081 electronic votes over the range of dimensionsD= 1, . . . ,4. Proposal densities were fixed to be

N(0, σ2_v) = N(0,32)

N(0, σ_c2) = N(0,0.022).

The DIC and Pritchard et al’s criterion were computed (Table 8.6) to deter- mine the appropriate dimension for the latent space. DIC suggested D= 3 whereas Pritchard et al’s criterion suggested D= 2. Due to these contrasting results princi- pal components analysis was applied to the different dimensional configurations of Meath candidates.

Table 8.6: Model selection criteria values to indicate the optimal latent space model for the Meath constituency. Latent space models were fitted over the range of dimensionsD= 1, . . . ,4. Entries in bold indicate the best fitting model according to each criterion.

Dimension DIC Pritchard et al.

1 1263878 1229179

2 1209849 1224901

3 1193842 1559845

4 1224017 5538406

Table 8.7 shows the variation captured by each principal component when differ- ent dimensions of latent space model were fitted to the data. Both dimensionsD= 1 and D= 2 appear to summarize the data well in that each dimension accounts for more than one fifth of the total variance. When a three dimensional model was

fitted the additional principal component only accounted for 9% of the variance of the data.

Table 8.7: The proportion of the variance explained by each principal component computed for configurations of the candidates in the Meath constituency, for a range of dimensions. Principal components analysis was applied to the average candidate configuration only, as the main interest of this study lies in the relative locations of the candidates. Entries in bold indicate the models deemed as good models using a 20% minimum variance criterion.

Variances Dimension σ2 1 σ22 σ23 σ42 1 1 - - - 2 0.67 0.33 - - 3 0.65 0.26 0.09 - 4 0.57 0.28 0.10 0.05

Both the one dimensional and two dimensional configurations are analyzed to examine relationships between the electoral candidates.

One Dimensional Results

Figure 8.7 illustrates the one dimensional configuration of the fourteen Meath can- didates. Each candidate is represented by an abbreviation of their surname and political party as detailed in Table 2.4. It is immediately clear that party politics plays a large role in the electorates’ view of the candidates. The Fianna F´ail can- didates (Brady, Dempsey and Wallace) are located on the far right of the single dimension with the Fine Gael candidates (Bruton, English and Farrelly) located on the far left. Fianna F´ail and Fine Gael are the two largest (and rival) Irish politi- cal parties. The other candidates lie between the two poles created by the Fianna F´ail and Fine Gael candidates but closer to Fine Gael. Interestingly Ward, who is a Labour Party candidate, is located closest to the Fine Gael candidates — Fine Gael and Labour have a history of forming coalition governments (most recently from 1994–1997). Also of note are the narrow interval estimates for the estimated

candidate positions (mean ±2 standard deviations are shown). This suggests low uncertainty in the candidate locations in one dimension.

The one dimensional configuration of candidates within the Meath constituency is similar to that of Dublin North and Dublin West in that there appears to be a Fianna F´ail versus non-Fianna F´ail division. However again evidence of candidate driven preferences is apparent from the different order of the candidates located on the left of the dimension. In Dublin North and Dublin West the Fine Gael candidates were quite centrally located whereas in Meath the Fine Gael candidates are situated farthest from the Fianna F´ail candidates. Thus within each constituency the candidates themselves are driving voter preferences to some degree; if this was not the case the same party order would occur across the single dimension in each constituency.

Two Dimensional Results

Good acceptance rates of 32% and 15% were achieved for the voter and candidate positions respectively when a two dimensional model was fitted.

Figure 8.8 illustrates the final average position of each of the fourteen candidates in the Meath constituency. Each candidate is denoted by the abbreviations detailed in Table 2.4. Party politics are again demonstrated as the mechanism which drives this election. The first principal component separates candidates by their political ideals — the estimated positions shows a clear divide between Fianna F´ail and the other parties in the x-axis direction. The second principal component illustrates the presence of an ideological cleavage (left to right wing) of the candidates. For example, the Christian Solidarity Party espouse right wing conservative values and their candidate Redmond (Rd) is located highest in the second principal component. The plot also includes ellipses which show approximate 95% posterior set es- timates of each candidate location to represent the uncertainty in the estimated locations. The uncertainty associated with all candidate locations is low. Further- more, there is considerable overlap between candidates from the same party.

Dimension 1 0.0 0.2 0.4 0.6 0.8 1.0 Bt (FG) Eg (FG) Fr (FG) Wd (Lab) Oby (GP) Ob (Ind) Fz (Ind) Kl (Ind) Cl (Ind) Rd (CSP) Rl (SF) By (FF) Wl (FF) Dp (FF)

Fig. 8.7: The one dimensional configuration of the Meath candidate means, av- eraged over a Metropolis-Hastings algorithm, and their associated uncertainty (in- dicated by ±2 standard deviation intervals). Each of the fourteen candidates as detailed in Table 2.4 are denoted by an abbreviation of their surname and political party. Candidates from different parties are plotted in different colours. The mean acceptance rate for candidate locations was 35%.

0.6 0.8 1.0 1.2 1.4 4.6 4.7 4.8 4.9 5.0 5.1 PC 1 PC 2

By

Bt

Cl

Dp

Eg

Fr

Fz

Kl

Ob

Oby

Rd

Rl

Wl

Wd

(FF)

(FG)

(Ind)

(FF)

(FG)

(FG)

(Ind)

(Ind)

(Ind)

(GP)

(CSP)

(SF)

(FF)

(Lab)

Fig. 8.8: The two dimensional configuration of the Meath candidate means with their associated uncertainty. The candidate initials indicate their posterior mean positions and the ellipses are approximate 95% posterior sets which indicate the uncertainty in the candidate positions. Candidates from different parties are plotted in different colours. The position of each candidate and the ellipses are estimated by 65000 Metropolis-Hastings iterations (post burn-in), thinned after every 100th iteration.