Wentworth 2018 – Phelps dominates the preference flows

Update (23 Oct): I’ve included a graph of the estimated preference flows (after a slight tweak to the analysis).

With the Australian Electoral Commission (AEC) counting of Wentworth 2018 nearing its end, we can look at the preference flows to David Sharma and Kerryn Phelps. For this analysis, I took the data from the 35 regular polling places (booths; not pre-polls, hospital teams, or postals), and examined how many of the primary votes for the other candidates went to Sharma versus Phelps when the preferences were distributed.

For example, for the Bondi Surf booth, Sharma got 375 primary votes and 449 votes in total after the flow of preferences (i.e, 74 preferences from voters for the other candidates). For the same booth, Phelps got 459 primary votes and 779 votes in total (320 preferences other voters – more than 4 times the number of preferences as Sharma).

The flow of preferences to Phelps was not as strong in other booths. For example, in Rose Bay Central, Phelps only got about twice as many preferences as Sharma. The differences in the flow of preferences can be largely explained by voters tending to have different voting patterns in the different booths. Voters at the Bondi Surf booth had a greater propensity to vote Green and Labor as their first preference (15% and 10.5% of voters). In Rose Bay Central, candidates for these parties only got 5% of  the primary vote.

In a single electorate, it might be reasonable to assume that voters who preference a particular candidate first will have a similar tendency to preference the two leading candidates. That is, Greens voters might tend to preference Phelps over Sharma. While voters for another candidate might tend to preference in a different way.

With the AEC data available, we can build a statistical model to estimate the degree to which voters for each of the candidates preferenced Sharma ahead of Phelps. This can be analysed as a basic regression model. We use the number of primary votes to each candidate in each booth as the explanatory variable (ignoring Sharma and Phelps because they don’t receive preferences from their primary votes), and the number of preferences received by Sharma as the response variable. The coefficients for this regression estimate the proportion of voters for each candidate who preferenced Sharma over Phelps.

Some candidates received very few votes, so it is difficult to estimate the preference flows from voters for those candidates using this method. However, it is clear that voters for the Greens, Labor and the independent candidate Licia Heath tended to preference Phelps (Phelps was estimated to receive about 80-100% of preferences from these voters).

 

 

Estimated preference flows to Sharma versus Phelps for voters for other Candidates in the Wentworth by-election. The dot is the estimate, with the bars representing the 95% credible estimate.

In contrast, voters for the other independent candidate Angela Vithoulkas appeared to flow towards Sharma; the analysis estimated Sharma won most of the preferences from Vithoulkas voters.

However, the Greens, Labor and Heath won the vast majority of primary votes that did not go to Sharma or Phelps, so with those voters preferencing Phelps over Sharma, Phelps dominated the preference battle, winning by 4 to 1. At this point it seems to be enough to get her over the line.

Finally as an aside, the fit of the model is quite good. The correlation between the number of preferences received by Sharma and the fitted value in the statistical model is 0.99.

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For those interested, here are the data and BUGS code that I used in the analysis:

model
{
  for (i in 1:35) # for each booth
  {
    m[i] <- b[1]*CALLANAN[i] + b[2]*KANAK[i] + b[3]*HIGSON[i] + b[4]*GEORGANTIS[i] + b[5]*MURRAY[i] + b[6]*FORSYTH[i] + b[7]*ROBINSON[i] + b[8]*GUNNING[i] + b[9]*VITHOULKAS[i] + b[10]*DOYLE[i] + b[11]*LEONG[i] + b[12]*HEATH[i] + b[13]*KELDOULIS[i] + b[14]*DUNNE[i]

    Sharma[i] ~ dnorm(m[i], p)
  }


  for (i in 1:14)
  {
    logit(b[i]) <- d[i]
    d[i] ~ dnorm(0, 0.1) # I(0,1)
  }
  p ~ dgamma(0.001, 0.001)
}

#Initial values for the MCMC
list(p=1, d=c(0,0,0,0,0,0,0,0,0,0,0,0,0,0))

#Data
Total[] Sharma[] CALLANAN[] KANAK[] HIGSON[] GEORGANTIS[] MURRAY[] FORSYTH[] ROBINSON[] GUNNING[] SHARMA[] VITHOULKAS[] DOYLE[] LEONG[] HEATH[] KELDOULIS[] PHELPS[] DUNNE[]
515 120 10 169 12 3 192 5 2 13 1032 36 15 10 29 7 724 12
165 37 7 40 5 1 71 0 1 7 635 11 3 6 9 2 282 2
399 76 4 161 5 3 147 0 1 5 333 15 10 13 20 6 360 9
1370 243 17 614 15 4 468 4 14 14 1087 42 26 32 75 18 1300 27
182 35 6 82 3 0 64 1 1 3 188 5 1 4 10 2 256 0
514 106 12 150 12 5 228 2 5 6 657 16 10 20 31 4 534 13
473 104 11 158 10 6 192 2 4 15 557 12 11 16 18 10 418 8
370 81 8 127 8 3 128 3 5 4 400 15 8 9 36 6 380 10
248 49 1 89 3 0 96 1 2 7 257 7 5 5 17 7 248 8
394 74 7 183 4 1 129 1 0 5 375 12 3 10 25 9 459 5
596 95 7 204 12 0 230 0 3 3 430 6 4 12 100 4 489 11
539 83 5 175 12 3 237 2 1 1 480 7 15 10 62 3 599 6
268 38 6 99 4 1 112 0 1 3 189 3 1 11 14 6 294 7
365 69 9 110 4 0 170 0 1 9 404 8 2 9 37 1 355 5
261 72 5 82 13 0 90 4 5 10 887 15 6 3 15 7 487 6
245 36 3 86 3 0 97 0 2 1 162 12 3 4 27 4 320 3
507 125 9 138 16 0 209 4 4 15 1665 31 22 6 34 5 835 14
78 14 1 28 1 1 30 0 1 0 160 4 2 2 4 2 100 2
224 72 4 63 5 5 80 2 0 6 881 13 8 12 16 3 344 7
170 37 2 49 3 1 75 1 1 2 351 2 1 5 21 7 200 0
539 77 5 176 6 1 217 2 2 8 440 8 7 18 69 18 783 2
333 43 3 109 5 1 133 1 1 1 260 13 8 13 34 7 440 4
611 118 17 189 16 3 229 3 4 11 771 13 11 13 82 11 907 9
615 107 14 192 10 0 237 4 4 9 573 26 20 13 60 13 756 13
350 66 4 99 7 2 151 0 2 3 306 13 10 19 28 1 366 11
750 148 11 197 16 2 375 3 6 8 766 25 15 23 44 9 708 16
357 97 10 99 10 1 125 1 5 6 876 32 7 5 38 6 547 12
196 60 7 56 10 2 54 3 4 8 579 20 6 4 16 2 304 4
84 26 5 21 1 0 30 0 1 4 317 13 1 1 5 1 99 1
310 68 5 115 8 1 106 5 2 6 1007 19 6 8 20 3 437 6
178 36 4 65 10 0 60 4 1 2 352 4 3 3 16 3 234 3
625 138 8 199 15 4 260 5 4 9 545 27 12 11 51 7 583 13
268 54 6 90 1 0 103 1 1 6 344 11 8 8 24 5 325 4
341 71 6 92 11 2 127 3 4 5 584 16 3 8 48 7 456 9
216 34 4 50 9 0 101 0 2 1 340 7 0 2 31 6 327 3
END