Of course, this issue is not specific to the Tory party -- the same problem could arise with a Socialist Party candidate standing against a New or Old Labour candidate.
I conclude from this that an analysis of party support based upon first preferences alone is doomed to failure.
As an example, we consider the 1997 Irish General election[2]. The 166 seats for the Dáil are from 41 constituencies having 3, 4 or 5 seats each. In this analysis, we consider three categories for the first preference votes: those of Fianna Fáil (FF), those for Fine Gael (FG) and the others. It can reasonably be said that the 'others' does not represent a party, but if strict proportionality is obtained for FF and FG, then the others as a single group will also be represented proportionally. We return to this problem later.
Kestelman[3] considers several measures of proportionality. Here, we consider some of those measures as applied to each individual constituency and compare this with the actual result. The measures used here are the Loosemore-Hanby Index, Gallagher Index of Disproportionality, Sainte-Laguë Index and the Farina Index (all taken from the above paper).
Given a specific index, then one can determine the number of seats for each party which would give the closest fit with respect to that index. In fact, all the indices give the same result with one exception: the Sainte-Laguë Index gives a different result for the Dublin Central constituency. Ignoring this isolated value we have the table as follows:
Constituency Actual Best Fit(%) Comparison Carlow-Kilkenny (2,2,1) (2,2,1) 13.998 = Cavan-Monaghan (2,2,1) (2,2,1) 8.850 = Clare (3,1,0) (2,1,1) 7.452 FF to Other Cork East (2,2,0) (2,1,1) 16.773 FG to Other Cork North-Central (3,2,0) (2,1,2) 12.473 Two changes Cork North-West (2,1,0) (2,1,0) 24.912 = Cork South-Central (3,2,0) (2,2,1) 11.923 FF to Other Cork South-West (1,2,0) (1,1,1) 20.608 FG to Other Donegal North-East (2,0,1) (1,1,1) 17.801 FF to FG Donegal South-West (1,1,1) (1,1,1) 12.710 = Dublin Central (2,1,1) (2,0,2) 17.771 FG to Other Dublin North (2,1,1) (1,1,2) 16.756 FF to Other Dublin North-Central (2,1,1) (2,1,1) 4.487 = Dublin North-East (2,1,1) (2,1,1) 19.113 = Dublin North-West (2,0,2) (2,1,1) 15.808 FG to Other Dublin South (2,2,1) (2,1,2) 11.999 FG to Other Dublin South-Central (2,1,1) (1,1,2) 13.301 FF to Other Dublin South-East (1,1,2) (1,1,2) 4.042 = Dublin South-West (2,1,2) (1,1,3) 12.192 FF to Other Dublin West (2,1,1) (1,1,2) 11.492 FF to Other Dun Laoghaire (2,2,1) (1,2,2) 11.226 FF to Other Galway East (2,2,0) (2,1,1) 7.923 FG to Other Galway West (2,1,2) (2,1,2) 10.324 = Kerry North (1,1,1) (1,1,1) 19.729 = Kerry South (1,0,2) (1,0,2) 18.479 = Kildare North (1,1,1) (1,1,1) 9.214 = Kildare South (1,1,1) (1,1,1) 8.464 = Laoighis-Offaly (3,2,0) (3,1,1) 13.281 FG to Other Limerick East (2,1,2) (2,1,2) 9.015 = Limerick West (1,2,0) (1,1,1) 4.945 FG to Other Longford-Roscommon (2,2,0) (2,1,1) 15.181 FG to Other Louth (2,1,1) (2,1,1) 12.575 = Mayo (2,3,0) (2,3,0) 14.288 = Meath (3,2,0) (2,2,1) 3.803 FF to Other Sligo-Leitrim (2,2,0) (2,1,1) 15.211 FG to Other Tipperary North (2,0,1) (1,0,2) 24.890 FF to Other Tipperary South (1,1,1) (1,1,1) 11.361 = Waterford (2,1,1) (1,1,2) 14.951 FF to Other Westmeath (1,1,1) (1,1,1) 15.218 = Wexford (2,2,1) (2,2,1) 3.036 = Wicklow (2,1,2) (1,1,3) 13.758 FF to Other
The content of the table is best explained by taking an entry: say Waterford, with 4 seats. The Actual and Best entries give the seats in the order (FF, FG, Other). The Best entry is computed according to all the indices apart from the isolated result already noted. The Fit% figures are calculated from the formula:
Fit% = Sqrt(Sigma(S%-V%)2), which is related to the Gallagher index.
The last column gives the comparison between the actual and best entries in seats. For Waterford, a single change in the actual result by a FF seat becoming an Other seat would produce the 'best' result.
One can see from this result that 18 constituencies would remain unchanged if they gave the best fit to first preference proportionality. The major difference is that the two major parties have gained over the others -- the best fit giving 56 seats in the Dáil for 'others' against the actual number of 35.
Two constituencies are different from the others. In the case of Cork North-Central, a two seat change is needed from the actual result to get the best fit. The reason for this is a high level of transfers from the other candidates to the two major parties. The case of Donegal North-East is special because the difference in the actual and best does not involve an increase in the 'other' seats. The reason for this was a significant transfer from FG to FF in the actual election when an FG candidate was still available for transfers.
As would be expected, there is a wide variation in the Fit entries. Also, the Fit values decrease with increased constituency seats: an average of 15.7% for 3-seats, 12.8% for 4-seats and 10.7% for 5-seats.
The under-representation of the Other group is to be expected as many of those candidates are excluded early in the count with many transfers to the major parties (as well as to non-transferables). This effect clearly indicates the dubious nature of grouping all the parties other than the major two into one.
The conclusion from this analysis seems to be that there is little loss in proportionality due to the natural granularity of the STV system. The lack of proportionality compared to the first preferences is caused by the vote transfers. There is a capital T in STV.
In addition to the above analysis of granularity, the same data reveals a very close correlation between the indices used. This is gratifying, since they are clearly supposed to be measuring the same property. However, the correlations can be represented approximately in a graph as follows in which the indices are indicated by their initials and the distance between them increases with a lack of correlation. From this it appears that the Loosemore-Hanby Index is centrally placed which reinforces Kestelman's support for that index.
Correlation graph
