Research and Politics
January-March 2015: 1 –5
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Combining forecasts is a well-established and powerful
method to increase forecast accuracy (Armstrong, 2001;
Clemen, 1989). The reason is that a combined forecast
includes more information than forecasts from any single
component method. In addition, the systematic and random
errors associated with individual component forecasts are
likely to cancel out in the combined forecast.
As has been demonstrated with the PollyVote for pre-
dicting US presidential elections, combining forecasts is
particularly beneficial if one can draw on component fore-
casts that use different methods and data. The PollyVote
averages forecasts within and across four different compo-
nent methods: polls, prediction markets, quantitative mod-
els, and expert judgment. Across the six elections from
1992 to 2012, the resulting combined forecast reduced the
error of a typical poll, model, and expert judgment by more
than half. Compared with prediction markets, the most
accurate component method, error was reduced by 16%
(Graefe et al., 2014b). Forecasts made on Election Eve
prior to the three elections from 2004 to 2012 missed the
final vote share on average by 0.6 percentage points. To put
this in perspective, the average error of the final Gallup poll
was more than three times higher (Graefe et al., 2014a).
This performance was achieved even though the
PollyVote did not include forecasts from vote expectation
surveys, also known as ‘citizen forecasts’, which were
recently shown to provide highly accurate forecasts of US
presidential election outcomes (Graefe, 2014). These sur-
veys simply ask respondents whom they expect to win.1
Accuracy gains of adding vote expectation
surveys to a combined forecast of US
presidential election outcomes
In averaging forecasts within and across four-component methods (i.e. polls, prediction markets, expert judgment and
quantitative models), the combined PollyVote provided highly accurate predictions for the US presidential elections from
1992 to 2012. This research note shows that the PollyVote would have also outperformed vote expectation surveys,
which prior research identified as the most accurate individual forecasting method during that time period. Adding vote
expectations to the PollyVote would have further increased the accuracy of the combined forecast. Across the last
90 days prior to the six elections, a five-component PollyVote (i.e. including vote expectations) would have yielded a
mean absolute error of 1.08 percentage points, which is 7% lower than the corresponding error of the original four-
component PollyVote. This study thus provides empirical evidence in support of two major findings from forecasting
research. First, combining forecasts provides highly accurate predictions, which are difficult to beat for even the most
accurate individual forecasting method available. Second, the accuracy of a combined forecast can be improved by
adding component forecasts that rely on different data and different methods than the forecasts already included in the
Combining forecasts, election forecasting, vote expectations, citizen forecasts, presidential research
LMU Research Fellow, Department of Communication Studies and
Media Research, LMU Munich, Germany
Andreas Graefe, LMU Research Fellow, Department of Communication
Studies and Media Research, Oettingenstr. 67, LMU Munich 80538,
570416RAP0010.1177/2053168015570416Research & PoliticsGraefe
2 Research and Politics
The aggregate responses are then used as a forecast of who
will win the election. If data on historical elections are
available, the aggregate responses can also be translated to
popular vote-share forecasts using simple linear regression
(Lewis-Beck and Stegmaier, 2011; Lewis-Beck and Tien,
Vote expectation surveys have been around at least as
long as scientific polling (Hayes, 1936), but have long been
overlooked as a method for forecasting election outcomes.
Although early work pointed to the accuracy of vote expec-
tations, these studies focused on identifying factors that
explain why most citizens are able to accurately predict
election outcomes (e.g. Lewis-Beck and Skalaban, 1989;
Lewis-Beck and Tien, 1999). Only recently have research-
ers begun to specifically study vote expectation surveys as
a method for forecasting elections (Lewis-Beck and
Stegmaier, 2011; Murr, 2011, 2014).
In a previous study, I compared the accuracy of vote
expectations to forecasts from polls, prediction markets,
quantitative models, and expert judgment (Graefe, 2014).
Across the last 100 days prior to the seven US presidential
elections from 1988 to 2012, vote expectations provided
more accurate forecasts of election winners and vote shares
than each of the four established methods. Compared with
polls, vote expectations reduced the error of vote-share pre-
dictions by 51%. Compared with prediction markets, error
was reduced by 6%. In other words, vote expectation sur-
veys appear to be the most accurate individual method for
forecasting US presidential elections available to date.
The present research note builds on this work and con-
tributes to knowledge on combining forecasts by analysing
(1) the relative accuracy of vote expectations and the
PollyVote and (2) the accuracy gains from adding vote
expectations to the PollyVote.
Method and data
Accuracy is analysed for forecasts of the national two-party
popular vote in the six US presidential elections from 1992
to 2012, the time period for which forecast data on both the
PollyVote and vote expectation surveys are available. The
absolute error, calculated as the absolute difference of the
predicted and actual national two-party popular vote of the
incumbent party’s candidate, was used as the measure of
Forecasts from the original four-component PollyVote
and vote expectations were obtained from publicly availa-
ble datasets at the Harvard Dataverse Network. These data-
sets provide daily forecasts of the national two-party
popular vote for each of the six US presidential elections
from 1992 to 2012.2 From these data, a new set of daily
forecasts was calculated by adding vote expectations as a
fifth component method to the original PollyVote. That is,
this new (five-component) PollyVote was computed by
averaging forecasts across five (instead of four) component
methods: (1) polls, (2) prediction markets, (3) quantitative
models, (4) expert judgment, and (5) vote expectations. For
more information on the calculation of the original
PollyVote see Graefe et al. (2014b). All data and calcula-
tions are available at the Harvard Dataverse Network.3
Figure 1 shows the mean absolute errors (MAE) of fore-
casts from vote expectations, the original PollyVote (with-
out vote expectations), and the new PollyVote (including
vote expectations) across the six elections from 1992 to
2012. Vote expectations were less accurate than the original
PollyVote for both long-term (90–70 days prior to Election
Mean absolute error (1992-2012)
Days to Election Day
New PollyVote (including vote expectations)
Original PollyVote (without vote expectations)
Figure 1. Mean absolute errors of forecasts from vote expectations, the original PollyVote (without vote expectations) and the
new PollyVote (with vote expectations), 1992–2012.
Day) and short-term forecasts (from 20 days prior to
Election Day). For medium-term forecasts (60–20 days),
however, vote expectations performed similar to – and
sometimes better than – the original PollyVote.
Figure 1 further shows that adding vote expectations to
the original PollyVote increases accuracy. Except for long-
term forecasts, the new five-component PollyVote provides
at least as – and usually more – accurate forecasts as the
original four-component PollyVote.
Figure 2 presents the same data in a different way by
showing the MAE of vote expectations and both PollyVote
versions across the remaining days in the forecast horizon.
That is, at any given day, the chart depicts the average error
that one would have achieved by picking one of the three
methods and relying on its forecast until Election Day. For
example, if one had relied on the vote expectation forecasts
starting 90 days before the election, an average error of
1.32 percentage points would have resulted. In comparison,
the corresponding error of the original PollyVote would
have been 12% lower (1.16 percentage points). In general,
the gains in accuracy by relying on the PollyVote rather
than vote expectations tend to increase as the election
comes closer. Furthermore, Figure 2 demonstrates the ben-
efit of adding vote expectations, as the error of the new
(five-component) PollyVote was consistently lower than
the error of the original (four-component) PollyVote. For
example, starting 90 days prior to Election Day, the MAE
of the new PollyVote was 1.08, which is 7% lower than the
corresponding error of the original PollyVote.
This research note provides empirical evidence in support
of two major findings from the forecasting literature. First,
combining forecasts from different methods that use differ-
ent data provides highly accurate forecasts, which are dif-
ficult to beat by even the most accurate individual method
available. Across the past 90 days prior to each of the six
elections from 1992 to 2012, the original PollyVote – which
averages forecasts within and across polls, prediction mar-
kets, quantitative models, and expert judgment, but does
not include vote expectations – missed the incumbent par-
ty’s final vote share on average by 1.16 percentage points.
This error is 12% lower than the corresponding error of
vote expectation surveys, which prior research found to the
most accurate method for the examined time period (Graefe,
Second, and more importantly, the accuracy of a com-
bined forecast can be further improved by adding compo-
nent forecasts that rely on a different method and different
data than the forecasts already included in the combination.
After adding vote expectations as a fifth component
method, the new PollyVote reduced the error of the original
four-component version by 7%, a substantial improvement
given the already very low forecast error. On average across
the 90 days prior to the six elections, the new five-
component PollyVote missed the final election result by lit-
tle more than one (i.e. 1.08) percentage point.
This performance was achieved by calculating simple
unweighted averages within and across forecasts of five
component methods. Calculating unweighted averages
may appear as a naïve approach to combining forecasts, as
it does not account for the component methods’ relative
accuracy. However, an early review of more than 200
papers showed that the simple average provides a good
starting point for combining forecasts, and is difficult to
beat by more complex approaches (Clemen, 1989). These
results still hold today, despite many efforts in search of
Mean absolute error across remaining
days to election (1992-2012)
Days to Election Day
New PollyVote (including vote expectations)
Original PollyVote (without vote expectations)
Figure 2. Mean absolute error of forecasts from vote expectations, the original PollyVote (without vote expectations) and the
new PollyVote (including vote expectations), calculated across the remaining day to election, 1992–2012.
4 Research and Politics
sophisticated methods for combining. The problem with
complex statistical procedures that aim to estimate compo-
nent weights from historical data is that they tend to per-
form poorly in situations with limited and messy data,
which are common in the social sciences. A recent example
is Ensemble Bayesian Model Averaging (EBMA), a method
that has been shown to perform well for combining fore-
casts in the data-heavy domain of weather forecasting.
However, when applied to problems with scarce and noisy
data, such as in economic and election forecasting, EBMA
provided less accurate forecasts than the simple equal-
weights average (Graefe et al., 2015).
When pre-specifying equal weights to component fore-
casts, analysts ignore the components’ relative accuracy.
Instead, they deliberately introduce a bias that reduces vari-
ance and thereby limits a model’s ability to explain given
data. At the same time, however, lower variance avoids the
danger of overfitting a model to historical data. Thus, low
variance can be beneficial when predicting new data, in
particular, in situations that involve much uncertainty. In
statistical theory, this relationship is known as the bias–
variance tradeoff (Hastie et al., 2001).
When forecasting presidential elections, for example,
uncertainty occurs due to ambiguity about the component
methods’ relative accuracy, external shocks (e.g. campaign
events), or the existence of noisy data. Calculating
unweighted averages across forecasts is a simple way to
account for such uncertainties or, in other words, to incor-
porate prior knowledge that prediction in the situation at
hand is difficult.
Differential weights can be useful if there is strong prior
knowledge about the methods’ relative accuracy. For exam-
ple, polls are well known to have little predictive value until
shortly before the election (Erikson and Wlezien, 2012).
Thus, it might be useful to assign lower weights to polls
early in the campaign and then gradually increase their
weight as the election comes closer, an approach that is
becoming standard practice in models that combine struc-
tural (fundamental) data and updated polls over time. For a
review of existing models see Lewis-Beck and Dassonneville
(2015), who also incorporate this prior knowledge about the
relative accuracy of polls over time to develop forecasting
models for French, German, and UK elections.
While combining is most powerful when aggregating
many forecasts that use a different method and different
data, the approach can also be used if fewer methods are
available. In a recent study, combining forecasts from three
methods (a quantitative model, prediction markets, and
polls) yielded accurate predictions of the 2012 US Electoral
College and senatorial elections, a situation in which data
are scarce (Rothschild, 2014).
Finally, the benefits of combining are of course not lim-
ited to US elections. In a recent validation test, the PollyVote
was used to predict vote shares of seven parties in the 2013
German federal election by averaging forecasts within and
across the four-component methods that were used in the
original US PollyVote. Across the 58 days for which fore-
casts from all four components were available, the com-
bined PollyVote forecast was more accurate than each
component’s typical forecast. Error reductions ranged from
5%, compared with a typical poll, to 41%, compared with a
typical prediction market (Graefe, 2015).
Since 2004, the PollyVote has demonstrated the benefits of
combining for forecasting the national vote in US presiden-
tial elections by averaging forecasts from four-component
methods. Combining is a simple and powerful strategy to
generate accurate forecasts. Combining forecasts from dif-
ferent component methods typically yields more accurate
predictions than the average (i.e. randomly selected) com-
ponent, and often outperforms even the best component.
Adding forecasts that use a different method and different
data to the combination can be expected to further improve
accuracy. Given the results of the present research note, the
PollyVote will add vote expectations as a fifth component
for forecasting the 2016 US presidential election.
Declaration of conflicting interest
The authors declare that there is no conflict of interest.
This research received no specific grant from any funding agency
in the public, commercial, or not-for-profit sectors.
1. For example, “Regardless of whom you support, and trying
to be objective as possible, who do you think will win the
presidential election in November (2008)–Barack Obama or
John McCain?” Gallup Poll, October 23–26, 2008.
2. The PollyVote data are available at http://dx.doi.org/10.7910/
DVN/23184. The vote expectations data are available at http://
3. The data and calculations for the present research note are
available at: http://dx.doi.org/10.7910/DVN/27967.
The replication files are available at: http://thedata.harvard.edu/dvn/
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