Electoral Disproportionality and Bias under the Alternative
Vote: Elections to Australia’s House of Representatives
RON JOHNSTON and JAMES FORREST
THIS PAPER IS TO APPEAR IN
AUSTRALIAN JOURNAL OF POLITICAL SCIENCE
Not to be cited without
the authors’ consent
ABSTRACT: Studies of electoral disproportionality and bias under Australia’s alternative
electoral system have mainly relied on the two-party preferred (2PP) vote totals for all
electorates, irrespective of whether these are needed to determine the election outcome there.
We argue that separate analyses should be undertaken for two groups of electorates – where
the determination is made using the first-preference (FP) votes and where the 2PP
redistributed votes are needed because no candidate wins a majority of FP votes, illustrating
this with an analysis of the 2007 House of Representatives
The Alternative Vote (AV) system used for elections to the Australian House of
Representatives poses particular problems for analyses of electoral disproportionality
and bias. Most analysts have used data on the two-party preferred (2PP) vote totals in
each electorate (i.e. after preferences have been distributed) as their measure of party
strength. This almost entirely eliminates candidates of small ‘minor parties’ and
presents a false impression of the strengths of the two main party blocks. It also
misrepresents the situation in well over half of the electorates at some recent contests
where the outcome is determined on the first preference (FP) votes. We argue that
disproportionality and bias in the two groups of electorates should be analysed
separately, illustrating this using the 2007 House of Representatives’ election
In evaluating the seats:votes relationship, analysts of AV contests can use either FP
votes, or 2PP votes after the reallocation of preferences; since 1983 the 2PP vote has
been determined for every electorate, irrespective of whether the result was
determined at the FP stage. Standard practice has been to use the 2PP totals. In his
detailed analyses of Australian electoral biases, for example, Jackman (1994, 323)
claimed that ‘[t]he number of first preference votes a party receives is often a
misleading indicator … [of a party’s electoral strength], since seats are decided after
distributing preferences’. However, his contention that ‘2PP provides convenient
summaries of the electoral strengths of the main partisan groupings’ (Jackman 1994,
324) had already been countered by Rydon (1986), who argued that ‘publication of

School of Geographical Sciences, University of Bristol and Department of Environment and
Geography, Macquarie University, respectively. We are grateful to Galina Borisyuk for providing
SPSS code with which to calculate all the bias estimates.
the full distribution of the preferences … may have served a useful purpose in
underlining the limited usefulness of ‘two-party preferred’ because ‘there is no one
simple method of handling election results. Methods must be devised to meet
different purposes and in the light of electoral competition’. This paper follows
Rydon’s argument.
An additional complication in the Australian context is the nature of the party system.
Most commonly-used bias measures are best suited to situations where two parties
predominate (Borisyuk, Johnston, Thrasher and Rallings 2008). Australia has a
variant of that situation: the left-of-centre has a single dominant party – the Australian
Labor Party (ALP) – but the centre-right has two – Liberal and National. The latter
have long operated as a Liberal-National Coalition (LNC),1 but in some electorates,
where a retiring member from one of the parties is not seeking re-election, each may
field a candidate, potentially splitting the centre-right vote. Such situations have been
relatively rare recently (in 2007 only eight electorates had both Liberal and National
candidates), but they need to be incorporated into analyses of disproportionality and
bias.
Evaluating Election Outcomes Under AV
The core of the problem of evaluating disproportionality and bias in Australian House
of Representatives election results is illustrated in Table 1. The first block gives each
party’s 2007 percentages of all FP and 2PP votes cast, and seats won. (All ‘Other’
parties are combined.) If FP votes are the standard against which seat allocation is
contrasted, the Liberal Party achieved almost proportional representation, National
was somewhat over-represented, the ALP substantially over-represented, and the
other parties very substantially under-represented. If 2PP votes are the comparator,
the LNC is slightly under-represented and the ALP slightly over-represented
(seat:votes ratios of 0.93 and 1.06 respectively) and the ‘Others’ proportionally
represented. If we follow Jackman and others in preferring the 2PP standard, the
result was fairly proportional.
Using the 2PP votes also misrepresents ‘Other’ parties whose candidates were
eliminated in all but three electorates used in the final determination. Moreover, using
either the FP or 2PP vote counts for all electorates confounds the situation, as
illustrated by the lower two blocks which separate the 75 electorates determined on
FP votes from the other 75 where 2PP totals were the determinant. In the former, all
three ‘main’ parties, but especially the ALP, were over-represented and the ‘Others’
massively under-represented. In the 75 seats won on the 2PP votes, on the other hand,
the levels of over- and under-representation were much smaller. The outcome shown
in the first block is thus a net effect which confounds two very different sets of
outcomes.
Use of the AV system, with seats decided on either FP or 2PP votes, together with the
small number of seats where both Liberals and Nationals field candidates – produce at
least six analytical scenarios (Table 2). The first, analysing 2PP votes across all
electorates, ignores ‘Other’ parties. The next two are also unsuitable, because the
1
In 2008, the two parties merged in the state of Queensland, a decision that may stimulate similar
mergers in other states and nationally.
2
result is determined in many electorates only after distribution of the 2PP votes. The
fourth option is also flawed: combining the votes for the two LNC parties could see
them ‘winning’ a seat on the FP votes which neither could on its own.
The fifth analyses the situation in electorates where the result is determined on FP
votes only, and the two coalition parties are treated separately but where the coalition
partner with the largest FP total is treated as the LNC’s main party. The sixth analyses
only those electorates where 2PP votes are used for the final determination (which in
all but two cases involved both ALP and LNC candidates). These two separate sets of
results are, in effect, the ‘real’ situation.
Clear differences across these six scenarios are shown by the Gallagher (1991) leastsquares disproportionality index values (Table 3). Those based on 2PP vote shares –
options 1 and 6 – are on average only about one-third of those based on FP vote
shares; when all parties are included, disproportionality is much greater than when
only the final two parties (ALP and the LNC in all but three electorates) are deployed.
In our preferred scenarios, 5 and 6, disproportionality was much greater in the 75
electorates where the result was determined using FP votes (scenario 5) than in the
other 75 where 2PP totals were deployed (scenario 6).
Measuring Bias
A growing literature explores the degree of bias – or partisan asymmetry (Grofman
and King 2007) – in election results. Whereas studies of disproportionality focus on
deviation from a proportional representation norm, those of bias are concerned with
whether such disproportionality affects all parties equally. Some attempts to evaluate
bias use the actual election result (Grofman, Brunell and Campagna 1997; Blau
2001); others create a notional election result, based on the actual outcome but
changing the relative performance of the two main parties to estimate the result if the
votes cast had been distributed differently across the parties, but in the same relative
proportion in every electorate. We use the latter approach.
The procedure developed by Brookes (1959, 1960) takes the election result and, using
a uniform swing, reallocates votes from one party to another in every electorate to
produce a notional election outcome. A wide range of swings can be evaluated
(Johnston, Pattie, Dorling and Rossiter, 2002); we concentrate on one – equal vote
shares. The procedure establishes how many seats each party would obtain in a
notional election where both have the same percentage votes share (i.e. each winning
half of the national total). Bias is presented as the difference between their two seat
totals – with the implicit assumption that with equal vote shares in an unbiased
situation they should get equal seat allocations.
Brookes’ procedure decomposes the estimated bias into various generating factors, of
which the most important are differences between electorates in their number of
electors and proportion of abstentions, and inter-party differences in the efficiency of
their vote distributions. In Australia, compulsory voting renders the abstentions
component redundant and frequent redistricting to achieve electoral equality means
that malapportionment is largely irrelevant (Medew, 2008). This leaves the efficiency
component as the likely bias generator. It is generally interpreted as a function of the
proportion of a party’s votes that are effective – i.e. win it seats. The larger the
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proportion either ‘wasted’ (i.e. cast in electorates where it loses) or ‘surplus’ (i.e. cast
in electorates it wins by large majorities) the smaller the proportion that are effective.
Bias favours the party with the largest effective vote share (Johnston, Pattie, Dorling
and Rossiter 2001).
Bias in Australia’s House of Representatives Elections
Table 3 shows the estimated bias at Australia’s 2007 election for each of the six
scenarios in Table 2: a positive figure indicates bias favouring the LNC; a negative
figure indicates pro-ALP bias. Also indicated is the size of the efficiency component.
(The other components, as anticipated, are close to zero and so omitted. Where the
efficiency component is larger than the total bias figure, one or more of the other
components indicates bias in the opposite direction.) Following Jackman, the first
scenario indicates a pro-LNC bias; if the two main blocks had equal shares of the 2PP
votes, the LNC would have had a majority in the House. The second and third
scenarios – using the FP votes in all electorates – suggest a similar outcome. The ALP
won the election, in both votes and seats, but may not have done so if the contest had
been somewhat closer because its votes were apparently less efficiently distributed
across all electorates than the LNC’s.
We argue that this is a misleading conclusion, however, contending that the fifth and
sixth scenarios provide the most realistic approach to bias estimation. These indicate
an intriguing outcome. In the 75 electorates where the result was determined on the
FP votes, there was a pro-ALP bias of 8 seats, whereas in the other 75, where 2PP
votes determined the outcome, a similar bias favoured the LNC. In both cases the
efficiency component predominated.
This last finding suggests that the geography of support for the two voting blocs
differentially favoured them in the parts of the country where they prevailed. Table 4
categorises electorates by the stage at which the result was determined, which party
would have won them in a notional election with equal vote shares, and the estimated
margin of victory then. The first two columns show a clear difference in the 75 seats
determined on FP votes (one of which was won by an ‘Other’ party). Almost all with
the LNC as victor would have been won by very large margins – meaning it gleaned
many surplus votes but there were relatively few wasted votes for ALP – whereas
many where the ALP candidate was the estimated winner had smaller majorities: the
ALP had a more efficient vote distribution, hence a pro-ALP bias there. In the 74
electorates won by one of the blocks at the 2PP determination, on the other hand,
there were not only many more marginal seats (suggesting that the distribution of
preferences tends to ‘close the gap’ between the two) but that the LNC would have
won many more highly marginal contests than the ALP – hence a pro-LNC bias there.
To provide a longer-term perspective, similar analyses have been undertaken for the
previous five elections (Table 5). The ALP won a legislative majority in 1993 and
2007 with the LNC victorious in the other four. In 1998, however, the LNC victory
was based on a tie in the percentage of FP votes and an ALP plurality on 2PP votes.
(In the 50 seats won on FP votes, ALP got 46 per cent of those votes, compared to 36
per cent for the LNC parties, the ALP winning 32 of the seats and the LNC only 18.
In the 98 districts won on the 2PP votes, the shares of the votes were ALP 47 and
LNC 51; the seats were allocated 34:63 respectively.)
4
The bias estimates vary considerably, not only across elections but also according to
the scenario employed. Focusing on the fifth and sixth, these show that – with the
exception of 1998 – the party that won the election overall experienced a bias in its
favour in the electorates where the determination was at the FP stage (scenario 5). The
LNC achieved a very substantial bias in its favour at three such contests, averaging 30
seats (out of totals ranging from 62 to 87), whereas the ALP’s two victories in 1993
and 2007 generated much smaller biases (-2 and -8 respectively). At the 2PP
determination, under scenario 6, those two ALP victories overall were achieved
despite substantial biases favouring the LNC, whereas the four LNC victories were
associated with minimal bias at that stage of the translation of votes into seats.
The 1998 election appears to be an anomaly, with a pro-ALP bias according to
scenario 5. The ALP and LNC were tied in their vote share in the relatively small
number of electorates determined on FP votes, and this was insufficient to counter the
lack of any bias to either bloc in the electorates determined at the 2PP stage. The LNC
won the election because the ALP’s advantage in the small number of FP-determined
districts was insufficient to deliver it enough seats for victory overall, especially as
there was no bias in the two-thirds of the electorates where the result was determined
on the 2PP votes (for further details on those earlier elections, see Johnston and
Forrest 2009).
A general trend thus emerges. Across the electorates, the relatively marginal seats
tend to swing between the two main party blocs. When a party wins the election
outright, this usually involves winning almost all of those marginal districts which are
determined on FP votes, benefiting that party in the bias calculations. There is much
less bias in districts determined with the 2PP votes, however, largely because – as the
detailed analyses of 2007 suggested – neither party had a substantial advantage by
winning most of the (larger number of) marginal districts The degree to which a party
benefits from the efficiency of its voter distribution is therefore a function of two
factors: its margin of victory in the FP-determined districts and the proportion of the
electorates with the result being determined at that stage. Hence the 1998 outcome: in
a very tight contest, the ALP benefited from a substantial bias in the FP-determined
seats where it tied with the LNC, but these formed only a relatively small proportion
of all districts and could not counter the LNC’s victory in the large number of districts
where the 2PP votes were deployed.
Conclusions
We have argued against the conventional wisdom that disproportionality and bias in
Australian election results should be studied using only 2PP vote totals. A substantial
number of electorate results at recent House of Representatives’ contests are
determined on FP votes, with one candidate gaining an outright majority. So we have
analysed the 2007 results using FP votes for those electorates where the result was
determined without the distribution of preferences, and 2PP votes for the remainder.
This analysis identified a substantial pro-ALP bias in the FP group of 75 electorates.
Its votes were more efficiently distributed there, because many of the electorates it
won were more marginal than those won by the largest party in the LNC coalition. In
contrast, there was a pro-LNC bias in the 75 electorates where the 2PP votes were
5
used to determine the outcome because the LNC won more marginal contests at that
stage than the ALP. Extending the analysis to the five preceding elections showed that
the party which won most votes in electorates determined at the FP stage benefited
from bias generated by the efficiency of the vote distribution – substantially so in the
case of the LNC at three of those contests.
Treating all electorates as if they were won at the 2PP stage thus produces a
misleading indication of the extent and direction of disproportionality and bias in
Australian House of Representatives’ election results. The procedure adopted here
provides a much more realistic indication of those features, and throws considerable
light on how the AV system operates.
6
References
Blau, A. 2001 ‘Partisan Bias in British General Elections.’ In British Elections and
Parties Review 11 eds. J. Tonge, L. Bennie, D. Denver and L. Harrison London:
Frank Cass, 46-65.
Borisyuk, R., Johnston, R., Thrasher, M. and Rallings, C. 2008 ‘Measuring Bias:
Moving from Two-Party to Three-Party Elections.’ Electoral Studies 27: 245-256.
Brookes, R.H. 1959 ‘Electoral Distortion in New Zealand.’ Australian Journal of
Politics and History 5: 218-223.
Brookes, R.H. 1960 ‘The Analysis of Distorted Representation in Two-Party, Single
Memberr Elections.’ Political Science 12: 158-167.
Gallagher, M. 1991 ‘Proportionality, Disproportionality and Electoral Systems.’
Electoral Studies 10: 33-51.
Grofman, B., Brunnell, T. and Campagna, J. 1997 ‘Distinguishing Between the
Effects of Swing Ratio and Bias on Outcomes in the U.S. Electoral College, 19001992.’ Electoral Studies 16: 471-487.
Grofman, B. and King, G. 2007 ‘The Future of Partisan Symmetry as a Judicial Test
for Partisan Gerrymandering after LULAC v. Perry.’ Electoral Law Journal 6: 2-35.
Jackman, S. 1994 ‘Measuring Electoral Bias: Australia, 1949-93.’ British Journal of
Political Science 24: 319-357
Johnston, R.J. and Forrest, J. 2009 ‘Geography and Election Results:
Disproportionality and Bias at the 12993-2004 Elections to the Australian House of
Representatives.’ Geographical Research 47: (in press).
Johnston, R.J., Pattie, C.J., Dorling, D.F.L. and Rossiter, D.J. 2001
‘Disproportionality and Bias in the Results of the 2005 General Election in Great
Britain: Evaluating the Electoral System’s Impact.’ Journal of Elections, Public
Opinion and Parties 16: 37-54.
Johnston, R.J., Rossiter, D.J., Pattie, C.J. and Dorling, D.F.L. 2001
‘Disproportionality and Bias in the Results of the 2005 General Election in Great
Britain: Evaluating the Electoral System.’ Journal of Elections, Public Opinion and
Parties 16: 37-54.
Johnston, R.J., Rossiter, D.J., Pattie, C.J. and Dorling, D.F.L. 2002 ‘Labour Electoral
Landslides and the Changing Efficiency of Voting Distributions.’ Transactions of the
Institute of British Geographers NS27: 336-361.
Medew, R. 2008 ‘Redistribution in Australia: The Importance of One Vote, One
Value.’ In Redistricting in Comparative Perspective eds. L.R. Handley and B.
Grofman. New York: Oxford University Press, 97-106.
7
Rydon, J. 1986 ‘”Two-Party Preferred”: the Analysis of Voting Figures Under
Preferential Voting’, Politics 21: 68-74.
8
TABLE 1. The Results of the 2007 General Election to the Australian House of
Representatives.
Votes %
FP
2PP
All electorates
Liberal
36.6
National
5.5
LN Coalition
42.1
ALP
43.4
Other
14.3
Electorates won on FP votes
Liberal
36.8
National
4.0
LN Coalition
40.8
ALP
43.4
Other
15.8
Electorates won on 2PP votes
LN Coalition
ALP
Other
Seats
Number
%
46.4
52.3
1.3
47.5
51.0
1.5
S:V Ratios
FP
2PP
55
10
65
83
2
36
7
43
55
1
1.00
1.22
1.03
1.27
0.09
29
4
33
41
1
39
5
44
55
1
1.05
1.33
1.08
1.34
0.07
32
42
1
43
56
1
0.93
1.06
1.00
0.90
1.10
0.87
FP – first preference votes; 2PP – two-party preferred votes; S:V %seats/%votes
9
TABLE 2. Possible Scenarios for Analysing Bias in AV Elections
Scenario
1.
2.
3.
4.
5.
6.
Electorates
All
All
All
FPd
FPd
2PPd
Votes
2PP
FP
FP
FP
FP
2PP
Treatment of Coalition
LN vote combined
Largest party in coalition there
LN combined
LN combined
Largest party in coalition there
LN combined
Key: FPd – electorates where result determined on the FP votes;
2PPd – electorates where result determined on the 2PP votes;
D – Gallagher Least Squares Index of Disproportionality
10
TABLE 3. The Gallagher Least Squares Disproportionality Index, Estimated Bias,
and the Efficiency Component of that Bias, at the 2007 General Election to the
Australian House of Representatives in each of the scenarios Identified in Table 2.
Scenario
1
2
3
4
5
6
Disproportionality
4.4
17.1
16.9
19.0
15.3
6.7
Bias
7
4
10
-8
-8
9
Efficiency
6.2
2.9
8.9
-8.3
-8.1
8.9
For bias and efficiency a positive figure indicates pro-LNC bias; a negative
figure indicates pro-ALP bias.
11
TABLE 4. The Marginality of Electorates that would have been Won by each Party in
the Notional 2007 Election to the Australian House of Representatives with
Equal Vote Shares.
Determination by
Seats won by
0-5%
5-10%
10-15%
15-20%
>20%
FP
LNC
0
0
0
4
29
2PP
ALP
0
5
4
9
23
LNC
16
11
6
2
6
12
ALP
8
9
13
0
3
TABLE 5. The Results and Bias Estimates for Australian House of Representatives
Elections, 1993-2007
Election
1993
1996
1998
2001
Vote %
FP
LNC
44
47
40
43
ALP
45
39
40
38
2PP
LNC
49
52
48
50
ALP
51
45
50
48
Seats
LNC
65
94
80
82
ALP
80
49
67
65
Stage at which election determined: electorates
FP
84
82
50
62
2PP
63
66
98
87
Bias by scenario*
1
5
2
24
3
2
1
5
5
-12
3
5
-3
19
3
4
-12
28
-14
19
5
-2
28
-11
24
6
16
-3
0
-3
2004
2007
47
38
42
43
52
46
46
52
87
60
65
83
87
63
75
75
6
-2
11
40
39
2
7
16
10
-8
-8
9
* A positive figure indicates pro-LNC bias; a negative figure pro-ALP bias.
13