Determining Intent in Senate Voting

Following up on my previous article, I downloaded the results from the Senate elections held in 2013 and processed the 50,131 below the line (BTL) ballots to determine if my ranking system was valid.

Results were worse than expected.It wasn’t a lot of work for me to process the 3 million+ lines because I used the following program:


# aggregate votes and preferences against candidates
# starting from line 3
# CandidateID,Pref,Batch,Paper
# build associative array on [CandidateID,Pref]
BEGIN {
        FS=","
}
{
        CID = $1 + 0
        pref = $2 + 0
        if ( NR >= 3 ) {
                tote[CID,pref] = tote[CID,pref] + 1
                if ( CID in Candy ) {
                        ;
                } else {
                        Candy[CID]++
                }
        }
}
END {
        # get candidateID
        for ( CID in Candy ) {
                printf "%s,", CID
                for ( pref = 1; pref <= 10 ; pref++ )
                        printf "%d,", tote[CID,pref]
                printf "\n"
        }

}

Once sorted by candidate ID, it produces the following total counts of each preference per candidate; for the first 10 preferences. There’s no need to go further as 6 vacancies ought to be filled well before the 10th is exhausted.

23179,659,173,381,1144,617,712,582,1594,687,1405,
23180,57,628,117,402,1116,562,687,635,1582,654,
23229,957,178,700,148,581,200,644,231,625,363,
23230,79,917,105,684,116,560,175,580,221,616,
23433,287,63,189,194,241,212,337,378,444,592,
23435,25,266,45,200,185,228,194,349,367,441,
23603,200,94,512,147,491,274,622,381,800,484,
23604,18,197,65,483,127,470,243,611,363,768,
23607,2254,601,940,517,956,554,989,879,1050,980,
23609,405,2108,251,908,465,934,477,1016,835,1050,
23705,442,78,344,383,315,578,297,586,354,821,
23707,43,410,59,356,347,323,572,289,580,368,
23870,1480,300,846,1249,988,949,853,1664,862,1798,
23879,158,1403,177,880,1218,939,908,895,1658,862,
23885,4936,982,2225,671,1447,939,1073,803,739,889,
23893,349,4602,935,2134,950,1511,713,1072,743,720,
23901,325,367,4438,1091,2216,816,1408,684,1031,715,
23909,166,213,534,4533,989,2175,657,1383,640,1084,
23916,221,425,312,424,4610,894,2038,574,1403,593,
23939,332,194,314,317,362,4697,734,2105,549,1443,
23963,362,112,325,200,608,296,496,500,613,588,
23967,12759,1621,2724,461,3915,521,2157,297,1361,266,
23970,26,354,82,315,202,589,270,505,502,595,
23975,1268,11801,1191,2229,783,4068,555,1930,324,1293,
23980,334,663,12270,717,2455,685,4204,431,1952,279,
24132,259,154,458,404,582,633,681,1086,893,1655,
24138,95,255,111,436,362,584,598,709,1072,884,
24208,142,43,200,328,388,496,346,893,611,1290,
24214,22,127,35,195,319,308,454,361,885,597,
24254,4280,597,907,1001,1136,730,2549,1538,1165,1305,
24258,125,2703,244,828,857,1079,764,2842,1446,1178,
24264,1634,277,682,193,593,208,622,309,720,405,
24266,189,1606,125,589,160,580,193,594,306,723,
24284,5271,1555,1853,5108,1346,2409,1490,1430,882,1248,
24289,2198,5490,1223,2368,4383,1247,2135,970,1347,778,
24299,491,1340,5808,977,1911,4971,1143,2220,952,1405,
24305,382,355,794,6345,852,1703,5085,1001,2244,878,
24321,428,104,1042,260,653,256,583,372,816,533,
24327,52,374,107,1037,180,616,231,548,371,803,
24351,364,125,619,191,596,245,611,374,747,577,
24356,37,338,94,614,162,568,223,619,380,762,
24486,422,75,290,119,574,168,947,373,733,384,
24487,84,31,193,88,281,121,344,165,484,239,
24488,8,72,34,179,71,261,105,328,151,465,
24701,551,212,454,212,434,292,643,567,922,871,
24705,77,505,94,464,169,411,292,639,559,926,
24710,125,53,277,90,407,130,485,203,794,282,
24712,16,123,45,253,69,390,122,457,198,784,
24717,603,111,479,133,390,169,370,344,426,391,
24719,35,430,84,479,124,391,161,359,343,432,
24728,49,31,171,69,244,142,332,308,342,385,
24732,8,50,33,157,62,215,107,317,225,332,
24742,374,87,278,162,411,196,540,350,569,491,
24743,40,345,77,271,132,404,183,517,340,603,
24792,1549,328,1231,1141,1128,976,934,1580,918,1662,
24795,140,1424,208,1241,1070,1066,973,961,1558,854,
24842,108,74,225,165,484,266,721,610,661,649,
24843,23,109,55,215,133,437,279,703,560,646,
25020,1127,239,858,571,734,737,848,1114,708,1433,
25023,106,1062,146,834,471,717,722,865,1092,704,
25026,509,163,482,1283,758,740,777,2358,1138,1882,
25027,66,500,104,529,1246,668,737,854,2359,1097,

Candidate 23967 scored the highest number of first preference votes (12759) with some distance in counts for lower preferences of other candidate. That candidate would fill one of the vacancies.

If however one follows the method I suggested previously, then the second vacancy would be filled by candidate 23980 with the most 3rd preferences (12270) being greater than those of candidate 23975 who received 11801 2nd preferences. That seems quite unfair, given the notional bias for second preference over a third!

Even more unfair when applying the previously proposed system which would abandon all those second-preference votes in the next round of vacancy filling.

It is worth testing the treatment all of the first 6 preferences equally; as if they were simply six X’s against candidates. The top 20 rankings would then be:

CID 1st 2nd 3rd 4th 5th 6th TOT
23967 12759 1621 2724 461 3915 521 22001
23975 1268 11801 1191 2229 783 4068 21340
24284 5271 1555 1853 5108 1346 2409 17542
23980 334 663 12270 717 2455 685 17124
24289 2198 5490 1223 2368 4383 1247 16909
24299 491 1340 5808 977 1911 4971 15498
23885 4936 982 2225 671 1447 939 11200
23893 349 4602 935 2134 950 1511 10481
24305 382 355 794 6345 852 1703 10431
23901 325 367 4438 1091 2216 816 9253
24254 4280 597 907 1001 1136 730 8651
23909 166 213 534 4533 989 2175 8610
23916 221 425 312 424 4610 894 6886
24792 1549 328 1231 1141 1128 976 6353
23939 332 194 314 317 362 4697 6216
24258 125 2703 244 828 857 1079 5836
23607 2254 601 940 517 956 554 5822
23870 1480 300 846 1249 988 949 5812
24795 140 1424 208 1241 1070 1066 5149
23609 405 2108 251 908 465 934 5071

Spewin’. That’s what candidate 23885 would be. “Left on the outer” even they received more first preferences than those who got in. But then; if there were only X’s on the ballot paper, and that’s that.

To reflect the notion of “higher preference” one requires a weighting to represent the value of preference as perceived by voters. Well there isn’t a robust one so one does what is done by the best economists and climate modellers and invents something that looks plausible. 🙂

As a first guess, one could weight the preferences by the position of the preference. i.e divide the second preference tally by 2, the third preference tally by 3, the fourth by 4, the fifth by 5 and the sixth by 6.

Similarly, one can weight them more severely by powers of 2 making each preference worth half of the next higher one; dividing the second preference by 2, the 3rd by 4, the fourth by 8, the fifth by 16 and the 6th by 32.

Comparing the results for the top 10-ranked:

CID 1st 2nd 3rd 4th 5th 6th Pweight Bweight
23967 12759 1621 2724 461 3915 521 15462.58 14569.09
23975 1268 11801 1191 2229 783 4068 8957.35 7920.94
24284 5271 1555 1853 5108 1346 2409 8613.87 7309.66
23885 4936 982 2225 671 1447 939 6782.32 6186.91
24289 2198 5490 1223 2368 4383 1247 7027.10 5857.66
24254 4280 597 907 1001 1136 730 5479.95 5024.19
23980 334 663 12270 717 2455 685 5539.92 3997.47
23893 349 4602 935 2134 950 1511 3937.00 3257.09
24299 491 1340 5808 977 1911 4971 4551.95 3009.91
23607 2254 601 940 517 956 554 3280.62 2931.19
24792 1549 328 1231 1141 1128 976 2796.85 2264.38
23870 1480 300 846 1249 988 949 2580.02 2089.03

Either weighting method looks fairer than a simple total.

Coincidentally, both weighting methods ranked the top 6 candidates in the same order. However, a difference creeps in at the 8th ranked.

The results are inconclusive. Largely because the intent of voters is difficult to determine; the preferences are individually subjective.

Weightings are to determine rankings are fundamentally arbitrary and subjective.

Oh yes; in case you’re wondering about the names of the candidates who’d have been elected by the 50,131 who bothered to vote below the line; out of the 1.35 million who turned out to vote:

Liberal 23885 JOHNSTON David
The Greens (WA) 23967 LUDLAM Scott
The Greens (WA) 23975 DAVIS Kate
The Nationals 24254 WIRRPANDA David
Australian Labor Party 24284 BULLOCK Joe
Australian Labor Party 24289 PRATT Louise

These weren’t elected anyway because too many ballot papers were lost and another poll had to be held.

I’ll leave the analysis of the effect of ticket preferences, invoked by voting above the line, on the notional results for another time.

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3 Responses to Determining Intent in Senate Voting

  1. Pingback: The Eee-Aws Have It | contrary2belief

  2. julian says:

    it’s all rather arbitrary anyhow.. and it’s still way better than what the americans do. (from my experience living there). once you start quibbling about “fair” then you are close enough.

    • Welcome back.

      I tried; in vain as you can tell; to figure out how one could determine voter intent in the preferential Senate voting method. Maybe that’s possible. More likely; the communications protocol is inadequate, not just in the counting of votes but in communicating to voters as to how their votes will be counted. This was touched on in the following article: The Eee-Aws Have It.

      The perception of fairness is important to sustain a democracy. Preferences in Senate votes make the “counting” process opaque to the majority of voters. Well, given the 60+ candidates in the ballot paper, if all had received and equal number of votes, the 1% is about what they’d have gotten.

      For the minority voting below the line (and thus notionally politically informed), picking the first (and last!) dozen or so in order of preference isn’t too difficult. It’s the 30 to 40 in the middle that’s the issue!

      Personally, I favour voters only needing to put a number against up to the first n candidates, where n is the number of positions to be filled. Such would eliminate the need for the above the line voting option and reduce the effect of preferences (and the trading done between parties and brokers before the election).

      Maybe it’s perversely appropriate to have Senators representing the State when they individually gained what could be vaguely perceived as approval from less than 1% of the electorate.

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