Voter Dropoff in LowsSalience Elections

Voter Dropo¤ in Low–Salience Elections
Richard Sinnott
University College Dublin
Dublin, Ireland
[email protected]
Christopher H. Achen
Department of Politics
Princeton University
Princeton, NJ 08544
[email protected]
April 30, 2008
Arend Lijphart has revived interest in the social class interpretation of Herbert Tingsten’s
(1937) “law of dispersion,”by which lower turnouts result in more socioeconomically biased
Lijphart refers to the law as “clear, strong, and well known” in the United
Indeed, we demonstrate that a generic version of Tingsten’s Law follows from
a standard probit model of voter turnout with constant coe¢ cients, so that we can give
a modern interpretation and derivation of Tingsten’s claim.
Surprisingly, however, we
show that neither in the U.S. nor in Europe do turnout data give much support to the
Lijphart’s social class interpretation of the law.
We argue that previous enthusiasm for
Tingsten’s Law has resulted from a misinterpretation of Tingsten’s data, and that his law
holds, though not Lijphart’s version of it. In the modern era, Tingsten’s Law may be seen
at its clearest in the behavior of inexperienced voters like the young, not the disadvantaged.
Low voter turnout means unequal and socioeconomically biased turnout.
This pattern is so clear, strong, and well known in the United States that it
does not need to be belabored further....There is, however, abundant evidence
of the same class bias, albeit usually not as strong, in other democracies.
–Arend Lijphart (1997, 2), APSA presidential address
Reviving a thesis due originally to Herbert Tingsten (1937, 230-231), Arend Lijphart (1997)
has suggested that low salience elections make it harder for those with low resources to get
to the polls, thereby increasing social class and income bias in the active electorate. Thus,
for example, U.S. midterm electorates would be more biased toward the prosperous than
presidential electorates, and European Parliament electorates more biased than national
electorates. Most importantly, U.S. electorates would be more socioeconomically biased
than virtually all European electorates.
The potential consequences are dramatic. By shifting the median voter position toward
more prosperous citizens, biased turnout might move social policy to the right.
example, low American midterm turnout would help account for Republican success in
Congressional elections. More importantly, the small American welfare state relative to
those of Europe would be explained in part by low American voter turnout among the
Moreover, weak representation of the American poor might be no accident. If turnout
has large consequences, the prosperous might have noticed the relationship and done something to hold turnout down. Some left–wing scholars have come to see American registration requirements and diminishing turnout as a century–long e¤ort in which elites “have
exerted themselves to forge and maintain electoral institutions that have kept the franchise
limited to those who were at least somewhat better o¤” (Piven and Cloward 1988, 254).
This research was partially supported by a research leave to the second author from the Department
of Politics, Princeton University. Thanks are owed to Je¤ Herbst for arranging the leave time. We
have bene…ted from numerous helpful suggestions and corrections from many colleagues, especially Larry
Bartels at Princeton, and from all the members of the Multi-Level Elections Project. The second author
also wishes to thank Arend Lijphart for taking time nearly four decades ago to chat about voting rules
with a student who was foolishly not enrolled in his class but had come to his Berkeley o¢ ce hours anyway.
The grant money for the multi-country survey research and aggregate data analysis was provided by the
Fifth Framework of the European Union. We express our thanks to all these people and organizations.
Of course, remaining errors are our own. The order of the authors’names was determined randomly.
Far from being a trivial issue, therefore, voter turnout might be the key to fundamental
features of national political life and a source of substantial cross–national di¤erences in
governmental structures.
In summarizing the evidence, Lijphart (1997, 1) begins robustly, presenting two propositions as beyond doubt:
. . . as political scientists have known for a long time, participation is highly
. . . as political scientists have also known for a long time, the inequality of
representation and in‡uence are not randomly distributed but systematically
biased in favour of more privileged citizens –those with higher incomes, greater
wealth, and better education –and against less advantaged citizens.
In presenting further support for his thesis, Lijphart (1997, 2-3) cites a great many
other studies, beginning with Gosnell (1927) and extending through the contemporary
period, which demonstrate the “general rule that the voting frequency rises with rising
social standard” (Tingsten 1937, 155). Lijphart cites Lipset (1960, 182): “The better
educated vote more than the less educated; . . . higher status persons more than lower.”
Lijphart (1997, 3) then adds, after reviewing similar …ndings from a many other scholars,
“More than three decades later, these conclusions are clearly still valid.”
Lijphart is undoubtedly correct here. Indeed, no one is likely to dispute the claim that
the more prosperous and the more advantaged vote more often in virtually every election
in virtually every country. Most of the facts cited in Lijphart’s article have this character.
The problem, unfortunately, is that this evidence has no bearing on Tingsten’s Law.
What Tingsten argued was a di¤erent and stronger proposition: Turnout biases get worse
as turnout declines.
As Lijphart’s (1997, 1) puts it, “. . . over time, the level of voting
participation and class inequality are strongly and negatively linked.” As we will show,
Lijphart gives only fragmentary and unpersuasive evidence for this proposition, the heart
of his argument.
In short, Lijphart argues that Tingsten’s Law holds in a wide variety of countries and
that its policy consequences are substantial, even grave. The evidence for it, he says, is
well known and overwhelming. Following Tingsten (chap. 4), Lijphart (1997) is driven to
proposing compulsory voting as a solution to the biased electoral outcomes in the United
States. On this view, Tingsten’s Law deserves a good deal more attention from political
scientists than it has yet received.
Using American and European data, we show that Tingsten’s Law does not hold in
modern electorates.
We develop a simple model that shows why the law once held for
European electorates (though not for the reasons usually supposed), and why it no longer
holds. Finally, we argue that we will need more theoretical sophistication about turnout
before we can understand class biases at the polls.
The Linear Probit Model and Tingsten’s Law
Tingsten (1937, 230) states his “law of dispersion” this way: “the dispersion (the di¤erences) in regard to participation in an election or within a certain group, is smaller the
higher the general participation is.” Tingsten had already shown in earlier chapters that
when the overall participation rate was 90% or more in various European elections, for example, both the middle class and the workers participated at high percentage rates not too
di¤erent from each other. On the other hand, when participation was much lower, larger
gaps in participation percentages tended to open up. Some of the e¤ects he discussed are
quite large. For instance, the fraction of workers in the Prussian electorate doubled (from
15% to 30%) as overall turnout rose from 18% to 30% in the 1893-1913 period. Put the
other way around, worker turnout drops in low salience elections in this period were fully
…ve times as large as those of the upper classes (Figure 1).
A di¢ culty with his argument occurs when turnouts are large, as Tingsten immediately
recognized following the passage just cited. In that case, the rules of arithmetic essentially
guarantee his law. For example, if an electorate turns out at a 95% rate, and if manual
workers are 50% of the population, then as a mathematical certainty workers have to be
participating at 90% or more. If the middle class participates more than the workers, the
participation gap between them cannot exceed ten percentage points, no matter what. By
contrast, if the overall participation rate is 50%, much larger gaps are possible. On this
interpretation of Tingsten’s Law, then, his result is not a social science discovery, but a
fact of arithmetic.
The ‡oor and ceiling e¤ects in percentage data create pseudo–e¤ects and bedevil statistical interpretation. Hence for several decades now, turnout has been studied, not with
percentages, but with the probit or logit models that have been developed since Tingsten
Researchers think of these models as closer to the actual processes at work in
dichotomous data such as turnout, in which people either vote or do not. For example, we
often suppose that turnout varies according to the perceived visibility and importance of
the campaign (“campaign intensity”), but that workers have less time to follow politics, or
less education, or weaker social networks, or less stake in the contest between two middle–
class candidates. If the e¤ect on workers is additive (i.e., subtractive), then conventionally,
we would analyze survey data on turnout with a simple, linear–in–variables probit model
like this one:
yi =
1 (Campaign
Intensity) +
2 (Worker)
+ ui (i = 1; :::; n)
where Campaign Intensity is a measure of the salience of the election to the populace, and
Worker is a dummy variable indicating whether the observation pertains to a manual worker
(1 = worker; 0 = non–worker). The dependent variable yi is an unobserved continuous
measure of the respondent’s willingness to vote or utility from doing so, ;
unknown parameters to be estimated, and ui is the disturbance term, assumed to have
a standard normal (Gaussian) distribution independent of the right–hand–side variables.
For simplicity, we suppress listing other variables in‡uencing turnout, so that the variable
Worker is meant to capture a descriptive fact, not necessarily a causal e¤ect.
Now, letting yi be the survey respondent’s turnout decision (1 if he or she voted, and
0 otherwise), we assume:
yi =
1 if yi
0 otherwise
It follows by standard textbook logic that:
Pr(yi = 1) =
(:) is the (cumulative) distribution function of the standard normal curve and
1 (Campaign
Intensity) +
2 (Worker).
This is the setup researchers use when they model turnout with probit analysis. As
is well known, the logit model is very similar, virtually indistinguishable in practice, apart
from a change of scale for the coe¢ cients.
Now the advantage of probit and logit models, as any econometrics text will explain,
is that they abolish the ‡oor and ceiling problem for dichotomous data.
By stretching
the ends of the scale, they make small percentage changes near 0% and 100% equivalent to
larger changes near 50%. And of course, this corresponds to our substantive understanding
of politics, in which raising a voter’s turnout probability from 50% to 55% is much easier
than raising it from 90% to 95%.
To view Tingsten’s Law in contemporary perspective, then, we need to know the e¤ect
of changes in Campaign Intensity on turnout by Workers and Non-Workers. For expositional convenience in the following hypothetical examples, we will assume that everyone
who is not a worker is middle class, so that there are just two groups in the population. Furthermore, we take
< 0, so that workers are always less inclined to vote. As
Campaign Intensity declines, how do the relative proportions of workers and middle class
citizens in the electorate change?
Now the …rst thing to understand is that the necessary calculation cannot be done
simply by comparing percentage drops from one election to the next, as Tingsten did
originally. As a hypothetical example, suppose that the workers and the middle class are
each half the population. Suppose that the middle class vote at a 90% rate in presidential
elections, while the workers vote at only a 50% rate. Then the middle class will enjoy the
ratio 9:5 in the presidential electorate, meaning that they make up 64% of the population.
Now suppose that in midterm elections, the middle class votes at a 78% rate, a drop of
12 percentage points. The workers turn out at a 40% rate, a drop of only 10 percentage
points. In percentage terms, therefore, middle class dropo¤ has been higher. However,
the middle class will now predominate by the ratio 78:40 in the midterm electorate, or
66%. Thus the midterm electorate is more socioeconomically biased than the presidential
version. Yet the middle class percentage dropo¤ is larger.2
What this example shows is that dropo¤s are relative to their starting points. A drop
of 12 percentage points from 90% is a drop relative to the starting position of 12/90 =
13.3%, while a drop of 10 percentage points for the workers is a relative drop of 10/50 =
20%. Thus workers have dropped less in absolute terms, but more in relative terms, and
they have lost ground. And of course, this makes sense: If all groups dropped the same
relative proportion from presidential to midterm elections, obviously their representation
in the electorate would be unchanged. It is the percentage dropo¤ relative to prior levels
that determines whether socioeconomic bias goes up or down.
To determine whether Tingsten’s Law is consistent with the simple linear version of
the probit model, therefore, we want to examine changes in Pr(yi = 1) as a function of
Converting to the probit or logit scale does not change this result. The 12% middle class dropo¤
remains larger on those scales than the 10% dropo¤ of the workers–in fact, it becomes proportionately even
larger–while still increasing the over–represenation of the middle class bias of the resulting electorate. Thus
converting to probit and logit does not evade the problem.
Campaign Intensity. Moreover, the computation needs to be done relative to the starting
value. For an in…nitesimal drop or rise, therefore, the absolute value of the proportionate
change is:
Relative Drop
@ Pr(yi = 1)[email protected](Campaign Intensity)
Pr(yi = 1)
= @ ( + 1 (Campaign Intensity) + 2 (Worker))[email protected](Campaign Intensity)= (z)
(z)= (z)
where (z) is the density of a standard normal curve at the point z =Campaign Intensity:
The issue now is whether Relative Drop falls as the vote total rises, or equivalently,
whether the partial derivative of Equation (4) with respect to z is negative. Rather than
take a further partial derivative, however, we note that (z)= (z) is closely related to the
inverse Mills ratio, (z)=[1
(z)]; which is well known in econometrics, since Heckman’s
(1976) work, as the mean of a lower–truncated normal distribution. That is, letting E be
the expectation operator for a standard normal distribution, we have3 :
E (xjx
z) =
x (x)dx
But since the mean of the lower–truncated distribution is obviously a positive, strictly
increasing function of the truncation point z, it follows that:
@[ (z)=[1
(z)][email protected] > 0
This inequality may also be demonstrated, though at somewhat greater length, by customary calculus methods.
Then by standard properties of a symmetric distribution, (z)=[1
(z)] = ( z)=[ ( z)],
which obviously has the same derivative as (z)=[ (z)] but with the sign reversed. Hence
Equation (6) implies that @(Relative Drop)/@z = @[ (z)=[ (z)][email protected] < 0; meaning that the
larger the proportion of the vote with which one begins, the smaller the proportionate drop
If x is the argument of a normal distribution truncated from below at z, then make the change of
variable y = x2 =2; and the proof follows easily.
when Campaign Intensity falls. But of course, that is Tingsten’s Law.
What we have shown, then, is that the standard probit models we use to study turnout
imply Tingsten’s Law. If socioeconomic status helps get people to the polls and if our probit
models are correct, then lower turnout electorates should be more biased socioeconomically.
It is not too hard to show that the same is true if our logit models are correct: Tingsten’s
Law follows in that case as well.
Thus we have a happy coincidence: Our standard statistical models imply a striking
…nding buttressed by “clear, strong, and well known” facts. Nearly all political scientists
favor large turnouts, most of us like our scienti…c evidence and our familiar linear statistical
models, and many of us express sympathy for the disadvantaged. When it turns out that
all these proclivities are compatible with Tingsten’s Law, the mind comes to rest.
Europeans and Europhiles generally, for whom this conceptual package also implies that
Europe is a much better place than the United States in this regard, the temptation to
acquiesce will be nearly irresistible.
That is what the political science profession as a
whole has done.
Just How Strong Is the Evidence?
Nearly drowned out by our conventional work habits and our political predilections, though,
the tiny voice of scienti…c caution raises a question: Is Tingsten’s Law actually true? After
all, the linear statistical model with which we derived it has no theoretical backing. It is
merely familiar because our canned computing packages make it easy to use.
Moreover, the empirical evidence is very thin. Tingsten’s own investigation remains
extremely impressive, but of necessity, he focused on inexperienced voters in new democracies more than 75 years ago, a group that is of limited relevance in the major democracies
(We return to this point below.)
In the contemporary work Lijphart cites, the
crucial di¢ culty is that correlations between social class and voter turnout, of which Lijphart makes so much, are simply irrelevant to Tingsten’s Law. Their relationship was well
known in Tingsten’s time, and announcing them would not have been newsworthy. Rather,
his law says that those correlations strengthen as turnout declines. (In calculus language,
Tingsten’s Law concerns @ 2 Individual [email protected] Class @National Turnout, not what
most of Lijphart’s evidence bears on, namely @Individual [email protected] Class.) Similarly, Lijphart quotes a good deal of evidence about how forms of participation other than
voting are unequal, but however regrettable, that, too, is irrelevant to the point at issue.
Apart from the immaterial evidence in Lijphart’s article, only Rosenstone and Hansen
(1993, 228-248) actually bear on Tingsten’s Law. Their …rst item of evidence, taken from
the American National Election Studies, compares elections between 1952 and 1988:
When [relatively] many citizens turn out to vote, they are more representative of the electorate than when fewer people vote. . . . Class equality4 in
participation was greatest in the high-turnout elections of the 1960s and least
in the low turnout elections of the 1980s. As turnout declined between 1960
and 1988, class inequalities multiplied (Rosenstone and Hansen 1993, 238 and
However, that relationship turns out to be almost entirely driven by two extreme
elections in 1960 and 1988–the …rst with heavy working–class turnout stimulated (pro and
con) by John Kennedy’s Catholicism, and the latter with working–class turnout depressed
by the chilly technocratic Democratic candidate, Michael Dukakis. Neither year’s pattern
has much to do with the forces Tingsten identi…ed.
Without those two elections, the
relationship in the other conventional eight cases vanishes, with no evidence for Tingsten’s
The second way Rosenstone and Hansen assess the impact of turnout on inequality in
the electorate is by comparing average midterm and presidential elections during the same
period. Here they …nd that the typical 15 percentage point drop between these two types
of American elections has only a small e¤ect when voter resources are measured by income,
and virtually none at all when it is measured by education. For example, suppose that the
upper …fth of the population turn out at 80% in presidential elections while the lowest …fth
is at 50%. Then let the two sides drop to 65% and 35% at the midterm, with intermediate
income groups dropping at rates in between. Then the upper …fth has increased from a
61.5% share of the two groups at the presidential election to 65% at the midterm— a 3.5
percentage point di¤erence at the extremes of the income distribution, with even smaller
di¤erences in between. Translated from the index they use (Rosenstone and Hansen, 1993,
Appendix F), this change is the same size as Rosenstone and Hansen …nd with respect to
income in American elections. The education e¤ect they discover is only about one …fth
as large— meaning less than a percentage point change in the above example, if indeed the
Lijphart has “inequality” here for “equality,” but this is obviously a typo. We have corrected the text
to match Rosenstone and Hansen’s original language.
e¤ect is statistically signi…cant at all.
Thus all these e¤ects are quite small, well below
the dramatic gaps Tingsten found.
Since Tingsten, these two investigations by Rosenstone and Hansen constitute the sum
total of the “clear, strong, and well known” relevant evidence cited in Lijphart’s article,
which he argues “does not need to be belabored further.”Now of course, the fact that we are
presented only with small amounts of mixed evidence need not mean that no relationship
exists. But it surely does call for cautious interpretation. Before resting on our ideological,
partisan, and national loyalties, therefore, we might look a bit further. That is what we
propose to do next.
Does Tingsten’s Law Hold in the U.S.?
To muster evidence for Tingsten’s Law, the …rst step is to avoid cheap comparisons across
continents. Yes, the percentage turnout di¤erences across social classes are larger in the
U.S. than in the average European country, and yes, turnout is lower in the U.S. than
in Europe generally, so that yes, those two variables correlate nicely.
Regressions run with two data points always …t very well indeed.
Indeed, R2 = 1:
But for persuasive
arguments, we have to do better.
Hence we turn to comparisons within continents and within countries, beginning with
the U.S. To an unusual degree, we may con…ne ourselves to purely descriptive relationships.
For Tingsten’s Law makes no causal claims. It simply says that, as an empirical fact, when
turnout declines in a political system, so does representation of the disadvantaged— for
whatever reason. Thus we construct no elaborate statistical models to control for myriad
causal factors in voting; they are o¤–point.
The issue is simply the trivariate empirical
relationship: How does the relationship between social class and individual turnout change
as national turnout varies?
Lijphart moves back and forth among various de…nitions of socioeconomic status, including education, but in our view, whatever the true causal patterns, it is the descriptive
absence of the poor that is the policy–relevant concern, not absence of the less educated.
A good many prosperous people in many countries are only modestly educated, and some
of the well educated have very modest incomes. When college dropout William Gates, the
world’s richest man, manages to vote, while some underfunded humanities graduate student, living in a garret with her master’s degree, does not, few of us would regard Gates’s
vote as a victory for the proletariat.
Thus we begin with income. The data throughout this section are taken from the
Current Population Survey (CPS) conducted by the American Census Bureau. It achieves
a response rate of more than 90% in a survey very little contaminated by other political
questions, so that these are the best available data on American electorates. Figure 1
con…rms the well known income gradient with respect to recent voter turnout, both for
the midterm election of 1998 and for the presidential election of 2000. There are at least
5000 observations at each data point here, so the percentages are very reliable. Clearly,
the prosperous vote more often.
But does Tingsten’s Law hold?
That is, are the proportionate dropo¤s in turnout
from the presidential to the midterm election larger for the poor, as Tingsten’s Law implies? Figure 2 shows the evidence from Figure 1, recoded in a form appropriate to testing
Tingsten’s hypothesis.
If Tingsten’s Law holds, this …gure should show a substantial
downward slant from left to right. Indeed, the lowest category of income (on the left) is a
few percentage points higher than the others, but even if we were to emphasize its modest
impact, it has relatively few people in it— fewer than 10% of the population. The majority
of the working class are elsewhere.5 Otherwise the relationship is quite ‡at, possibly even
trending upward, thereby disadvantaging the prosperous.
The poor are disadvantaged
in American elections, but they do not become more disadvantaged when turnout falls.
Overall, there is certainly no evidence here supporting Tingsten’s Law.
Lijphart (1997) and Piven & Cloward (1988) continue a long American tradition of
blaming registration requirements for imposing unnecessary burdens on the poor. However,
the state of North Dakota has no registration requirements, and thus requires no action
by individuals to qualify themselves for the ballot, paralleling the automatic European
registration that most reformers favor. Thus speculation about the impact of abolishing
registration rules can be replaced by simply taking a good look at North Dakota turnout
by income class to see whether that income gradient weakens or disappears.
We show
their turnout by income class in Figure 3 for the presidential election of 2000, along with
the national relationship. (There are more than 150 respondents in each cell except for the
…rst two and the last categories, which have more than 80 apiece.) Obviously, the gradient
with respect to income is substantial in North Dakota. In fact, the slope is steeper than
the U.S. average. Getting rid of registration has strengthened the class bias, not weakened
This chart illustrates the danger of comparing just the top and bottom categories of a distribution.
Rosenstone and Hansen (1993, 293-294) remark that, though they used a related procedure, taking the full
distribution into account is “more sophisticated,” even when, as often, it makes little di¤erence.
it. Clearly, registration is not the only problem keeping the poor from the polls in the
U.S. Here again is a sign that the way we think about voter turnout is fundamentally
We can also assess whether Tingsten’s Law holds in North Dakota. Figure 4 shows the
proportionate dropo¤ by income group from the 2000 election to the 1998 midterm election
by income class. (Categories with fewer than 100 respondents are dropped.) Again there
is no evidence for Tingsten’s claim.
If anything, the e¤ect is reversed, with better–o¤
citizens perhaps exploiting the easy voting laws to get themselves disproportionately to
the polls in presidential years.
In Figure 5 we look at the state with the highest turnout level in the continental U.S.
(Minnesota) and compare it to the state with the lowest turnout (West Virginia).6
Tingsten is correct, the income gradient should rise more dramatically in low turnout
states than in high turnout jurisdictions, so that the West Virginia curve should be steeper
than the Minnesota curve. The relatively small sample sizes in some categories introduce
some noise to the graph, but no obvious Tingsten e¤ect is apparent. The curves are roughly
parallel. If the poor do better in Minnesota relative to the turnout of the prosperous, the
e¤ect is not large.7
To check whether a low income, low turnout state like West Virginia might be obeying
Tingsten’s Law, the better strategy is not to compare it with Minnesota (which it does
not much resemble!), but rather to compare it to itself.
Figure 6 gives the percentage
dropo¤ of 1998 turnout as a fraction of 2000 turnout for the various income classes in West
Virginia. This time the curve is completely unambiguous: No Tingsten e¤ect appears.
The states with the apparently highest and lowest turnout rates in the 2000 election, as judged by the
CPS survey, are Alaska and Hawaii. However, both samples are quite small (fewer than 1000 respondents),
and both states are disconnected from the rest of the U.S., expensive to sample well, and unusual in other
ways, presenting di¢ culties of interpretation. Thus we have chosen to set them aside. We do not know
whether they …t Tingsten’s Law or not.
The lowest income category (less than $10,000 family income per year) has been dropped in both
states in both Figures 5 and 6 because there are fewer than 55 observations for it in Minnesota and fewer
than 110 for West Virginia. Nationally, they are a quite mixed group, disproportionately young, female,
and Latino, with students, welfare recipients, domestic workers, immigrants, institutionalized citizens, and
others, jointly amounting to fewer than 10% of the population in most states. Left in, this category would
show the West Virginia curve continuing downward, while the Minnesota curve is relatively ‡at at that
point. This again supports the possibility that there is a small e¤ect at the very bottom of the curve,
though it is di¢ cult to be certain. On the other hand, the upper category in West Virginia has fewer
than 100 observations, so that the apparent catching up to Minnesota in that category (which supports
Tingsten’s Law and seems to belie our argument) may easily be just sampling noise. However, we have
left that category in the graph due to its importance in the debate.
The prosperous drop out just as much as the middle ranks, who drop out just as much as
the poor. Low turnout elections do not make the class bias of the electorate worse in West
Checks of other states were also done, with the same general …nding.
Sample sizes
vary, as do the intensity of midyear elections, so that di¤erent states give slightly di¤erent
results, some undoubtedly due to sampling variation and some not. But as Figure 2 shows,
on average no such e¤ect exists.
Because we regard education as less relevant than income, we discuss it only brie‡y
In the U.S. as in most democracies, the young are better educated than the old,
and turnout is strongly correlated with age. The young drop out more at midterms, and
since they are better educated, this gives an arti…cial midterm drop at the upper end of
the education scale, prejudicing the data in our direction and against Tingsten’s Law. To
get a fair and meaningful test, therefore, we examine dropo¤ from presidential to midterm
elections by education just among the young electorate (those 18-24 years old), where age
is controlled, the dropo¤ rates are the largest in the population, and thus where the success
or failure of Tingsten’s Law should be easiest to detect. Figure 7 gives the result, with each
cell having at least 700 observations except for those with exactly 12 years of education
and those with a graduate degree.
(Those two cells have fewer than 100 respondents
and should be treated with much greater caution, though they could be dropped without
changing the conclusion.). Again the relationship is essentially ‡at, with no substantial
tendency for dropo¤ to fall with greater education. Those who did not …nish high school
(the …rst two groups) fall the farthest, but those with graduate degrees are just a few
percentage points behind them. It is the middle groups that drop the least, an e¤ect not
predicted by any theory.
But all the di¤erences are small, as the chart shows.
American midterm electorates simply are not better educated on average than presidential
electorates, contrary to what Tingsten’s Law would lead us to expect.
Again the lowest income category is absent from this chart, and there the apparent dropout was larger.
The problem, though, is that 2000 turnout in this category was just 36%. Small changes in the 1998
turnout rate therefore have very large e¤ects on the dropo¤. The sample rate for 1998 was 16%, making
the drop from 36% look enormous in percentage terms. However, if the drop had been 24% instead of 16%,
the percentage dropo¤ would have …tted smoothly into the chart shown in the text. With the sample size
available, the di¤erence between 16% and 24% is twelve people. Hence we decided to be consistent with
the previous graph and drop this lowest category. Again, however, there may be a hint here that there is
a small Tingsten e¤ect at the very bottom of the income scal— in the lowest 8 or 10% of the population.
It is worth remembering, though, that there is clearly no such e¤ect for the great majority of the working
In summary, the evidence we have examined in the American case is one–sidedly against
Lijphart’s argument. The working class is clearly disadvantaged in American electorates,
but there is no tendency for them to be more disadvantaged in low–turnout elections,
neither when registration requirements are in place nor when they are not. Nor is there
any evidence that education works di¤erently than income. Lijphart’s arguments do not
…t the contemporary United States.
Does Tingsten’s Law Hold in Europe?
As our sources of evidence for tackling this question we resort to three major surveys that
o¤er distinctive perspectives on the problem. The three surveys are the 2002 European
Social Survey (ESS), the 1994 Eurobarometer European Parliament Election Survey and
the 2002 Irish Quarterly National Household Survey (QNHS).
The ESS data allow us to test Tingsten’s law of increasing dispersion and Lijphart’s
rendition of it ("the level of voting participation and class inequality are strongly and negatively linked") across 22 countries and more than 38,000 respondents. Graphical analysis
of the relationship of turnout to occupation, education, and subjective assessment of household income shows a modest correlation— the di¤erence in turnout between the highest
and lowest points on these socioeconomic scales ranges from 10 points (in the case of education ) to 14 points (in the case of occupation). But as we have repeatedly noted, evidence
of this kind of relevant for discussions of electoral bias, but not for Tingsten’s Law.
One key question for the law of dispersion is: What is the fate of these di¤erences when
we compare countries with di¤erent levels of turnout? According to the Tingsten/Lijphart
thesis, the di¤erences (i.e. the inequalities) should be much stronger in low-turnout countries. Figures 8-10 provide scant support for this proposition. In the case of occupation,
the range in the highest-turnout countries goes from 10 to 19 to 15 and back up to 21
as countrywide turnout declines from 80% and over down to 60% and under— a possible
rising relationship, but not a consistent one. And this pattern is the best of the lot for
Tingsten’s Law. In the case of education (Figure 9), the di¤erences are smaller than for
occupation, and the trend is inconsistent (12 to 8 to 9 to 18). And in the case of subjective
assessment of household income, there is no evidence of a strengthening of the relationship
between socioeconomic inequalities and turnout as we move from the highest to the lowest
turnout countries (Figure 10).
Because it is conducted in all countries at more or less the same time, the ESS su¤ers
from the disadvantage that the question on turnout was asked with varying lapses of time
from the date of the national election in question. Our next source of evidence— the 1994
Eurobarometer European Parliament Election Survey— overcomes this problem to some
extent in that it provides a measure of self–reported dropo¤ based on a survey conducted
immediately after a low salience election that occurred at the same time in all the countries
involved. This can be expected to reduce the error that might be involved in respondents’
recall of whether they voted. Tables 1 and 2 show the relationship between dropo¤ in the
European Parliament election of 1994 and education and occupation respectively (again
excluding countries with compulsory voting). It is clear that there is some relationship:
Dropo¤ is less likely among those with the highest level of education and those with professional and managerial occupations. However, the relationship is slight – a matter of
seven or eight percentage points from one end of the occupational/educational spectrum
to another.
The Irish QNHS survey allows us to look at both education and political knowledge
as causes of turnout and voter dropo¤.
However, as Table 3 for Ireland shows, the
relationship between voter dropo¤ and education is non-monotonic and weak.9
And as
Table 4 shows, the relationship in Ireland between occupation and either turnout or voter
dropo¤ is erratic, with manual workers voting less and dropping out frequently, but also
with farmers, generally poorly educated and poorly paid, voting as often as the professional
and managerial class. Again, Lijphart’s argument fails to predict data well.
The QNHS data do suggest something else of real importance for Tingsten, however.
First, They show that the level of political information (measured by frequency of reading
about politics/current a¤airs in a national newspaper) is a more powerful, monotonic
predictor of turnout than either occupation or education. Turnout is 63 per cent among
those who pay no attention to politics/current a¤airs in a national newspaper, compared
to 89 per cent among those who read about politics/current a¤airs in a national newspaper
everyday (see Table 5). More importantly from the point of view of this paper, the rate of
dropo¤ declines from 30 per cent among those paying no attention to politics and current
a¤airs to 9 per cent among those who pay such attention everyday (Table 5) .10 Of course,
social class and education are somewhat correlated with political engagement in Ireland,
Voter dropo¤ was measured in the QNHS by the response "voted in some of them", to the question
"Thinking about all types of elections –local, Dáil, presidential and European –that have been held since
you became eligible to vote, would you say that you voted in all or almost all of them, voted in some of
them, voted in none of them, etc. . . ").
We believe that survey non-response does not change this …nding. See the appendix.
but not very strongly in Ireland. This table suggests that it is political engagement, not
social class, that is fundamental to understanding turnout.
We can summarize the evidence from the European surveys by noting …rst that
the data from the …rst (2002) round of the European Social Survey provide scant support
for the key proposition that, as the level of turnout in a country falls, the relationship
between voting and socioeconomic status strengthens. Focusing directly on the issue of
voter dropo¤, the 1994 Eurobarometer evidence likewise shows only very modest socioeconomic disparities. Then, in the case of Ireland, a very large scale survey indicated that
the relationship between lower socioeconomic resources and either turnout as such or voter
dropo¤ is very modest.
This brings us to the question of the impact of knowledge and political information.
Our …rst pass at this issue using Eurobarometer failed to show the kinds of contrasts that
were evident in the American data. However, both turnout and dropo¤ showed substantial
contrasts across levels of political knowledge and, even more so, across levels of political
engagement in the Irish case.
Similar analyses we have done elsewhere show just the
same e¤ect in American data (Achen and Sinnott 2009, chap. 12). In sum, we …nd that
Tingsten’s Law is best applied, not to social class as Lijphart suggests, but rather to levels
of political engagement.
In our view, that is closer to Tingsten’s own views, since he
applied the argument to gender di¤erences, which are unrelated to class.
In the …nal
section, we explain where this result brings us out in understanding both Tingsten and
If we are correct, the Lijphart thesis needs considerable amendment and reinterpretation
before it can be incorporated into the body of standard …ndings about voter turnout. We
have reached two conclusions: First, if the resource model of turnout is correct, Tingsten’s
Law will hold. Second, we have demonstrated that if our standard models for turnout are
correct, Tingsten’s Law follows as a mathematical consequence. What we have also found,
however, is that Tingsten’s Law holds only erratically. Sometimes lower turnout elections
reduce the representation of the poor and the less educated. Sometimes they do not. It
follows that both our standard ideas about turnout and/or our standard ideas about how
to model it statistically also hold only erratically. One of us has written elsewhere on the
dangers of too little graphical analysis, too many unjusti…ed linearity assumptions, and
too little use of formal theory (Achen 2002). The costs of all three are much in evidence
in the political science literature on voter turnout.
Although we have given only brief evidence here about where the profession has gone
wrong in studying turnout, we have suggested that the problem lies with what is sometimes
called the resource model of voter turnout. On this view, voting is expensive in one sense
or another, and so people need (…nancial and cognitive) resources to get to the polls.
Naturally, when voting becomes more di¢ cult in lower–turnout elections, it is those with
fewer resources who drop out. This plausible sounding story has been proposed by a great
many scholars for a century, and it fuels the policy concerns raised by Piven & Cloward
and by Lijphart, quoted in our Introduction. The di¢ culty with that viewpoint may be
simply stated: Once one looks at more than the broadest and roughest correlations, the
resource model just does not work very well in explaining data.
The failure of the resource model is also the reason why the recent reforms of American
registration statutes has had so much less impact than scholars expected in the studies
Lijphart cites. Reducing the price of a good will not raise sales if people don’t want to
own it.
Making registration easier will not raise turnout for people with no interest in
voting, especially if, as in the U.S., the citizenry is asked to go to the polls far more often
than in Europe, and if they …nd painfully lengthy ballots there when they arrive (Hanmer,
The more powerful explanatory variable lies elsewhere.
As has long been known in
the U.S., income is not as strong a predictor of turnout as education, education is not as
strong as knowledge, and knowledge is not as good as political engagement. Resources in
any usual sense are not the right causal variable. Instead, as Merriam and Gosnell (1924)
said long ago, it is the engaged and concerned who vote, and the disengaged who stay
home. The Irish evidence we presented and the American evidence we cited indicate that
political engagement remains the key factor explaining turnout.
Income and education
are correlated with engagement, but very imperfectly. No wonder, then, that Tingsten’s
Law applied to income or education categories predicts only weakly, if at all.
Readers who have quickly skimmed the rest of this paper may be imagining at this
point that our skepticism about Tingsten’s Law means that we also deny the socioeconomic bias in American electorates. That inference would be quite mistaken. Of course,
the disengaged are disproportionately poor and less educated, and so on our view of the
problem, the serious policy problem of biased electorates remains. However, it is not our
topic here. To repeat what we said earlier, one does not want to confuse Tingsten’s Law,
which concerns @ 2 Individual [email protected] Class @National Turnout, with the issue of
biased electorates, namely @Individual [email protected] Class.
Our research bears only
on Tingsten’s claim, namely that low turnout makes the bias in electorates worse.
…nd that it does not do so reliably or powerfully, and that it often fails.
Why then the consistent …nding in Tingsten (1937) that his law holds?
We have
returned to his data, recalculating his turnout …gures by social class and assessing the
proportionate dropo¤ as turnout falls in the manner of this paper, and there is no doubt
that the great man had the story right.
his time, Tingsten’s Law held widely.
We give one such example in Figure 11.
But is well to remember that his data bear on
the …rst part of the 20th century, where working class voters were casting ballots for the
…rst time. Inevitably, they had not yet reached full engagement with the political system.
By contrast, middle classes had generally been enfranchised earlier. Hence in Tingsten’s
time, and this is our key point, social class proxied powerfully for political engagement. If
engagement is the key variable, we would expect Tingsten’s Law to apply dramatically well
to social class distinctions then— but much less importantly now.
This conclusion is strengthened when other tables in Tingsten’s book are examined.
Older women, newly enfranchised late in their lives in this period and thus probably not
as engaged as experienced voters, often show the greatest dropo¤ when turnout falls, just
as our view would predict. Similarly, the greatest drop from presidential to midterm elections in the contemporary U.S. occurs among young, well–educated voters, who are engaged
enough to be reached by high–stimulus presidential campaigns, but lack the party identi…cation strength that would get them to the polls in the low–stimulus midterm elections
(Achen and Sinnott 2009, chap. 2).
In sum, Tingsten’s Law makes good theoretical and empirical sense when applied to
the right variable, namely political engagement. In Tingsten’s time, political engagement
was strongly correlated with social class, due to the recent enfranchisement of the workers.
Powerful e¤ects ensued, easily mistaken as causal, especially by those inclined to see social
class as the driving force in politics. But it was a case of correlation not implying causation.
We conclude by noting once more that Lijphart recommends compulsory voting as an
American cure for the perils of Tingsten’s Law. Holls (1889) made the same recommendation a century earlier. Nothing happened then, and barring some dramatic developments
we cannot foresee, nothing will happen now.
The idea …ts American political culture
poorly. Nonetheless, Lijphart’s article has set o¤ a very useful debate. Though we disagree about with his …ndings and his suggested cure, we have no doubt that his work has
helped set in motion the explosive recent increase in turnout research, and that that body
of work will eventually lead to successful policy proposals for raising voter turnout.
Appendix: Does Non-Response Bias Our Findings?
Almost all analyses of the socioeconomic correlates of turnout face the objection that the
real relationship between turnout and class fails to emerge in surveys with large nonresponse rates. The failure, the argument goes, is due to the fact that participation in
the survey is itself a¤ected by the same factors that a¤ect turnout and, accordingly, is
strongly socioeconomically biased. The result is that the number of people with working
class occupations, low education and low income is substantially reduced in the sample data
by comparison with the population data. Accordingly, the relationship between turnout
and class, education and income is much weaker in the sample data than it is in the
population, an argument that permits researchers to hold fast to the view that turnout is
very substantially biased but, because of the biased-response-rate problem, we just can’t
see it. In this way, the proposition that voter participation is strongly class-related is
rendered immune to critiques based on the evidence from most sample surveys.
The QNHS study provides an opportunity to test the central assumption of the foregoing argument, namely that participation in surveys on voting is strongly socioeconomically
biased. Normally, this assumption is impossible to test because the refusal to participate
occurs right at the outset of the interaction with the potential respondent and no data on
class, education etc. are collected for that case. However, because the QNHS is primarily
a population survey and is conducted by the o¢ cial governmental statistical agency (the
Central Statistics O¢ ce), the response rate to the core element of the survey that contains
all the socio-demographic data is in excess of 90 per cent). It is only when the interviewer
comes to the add-on political module in the survey and asks the respondent "Can I ask you
some questions relating to voter registration, arrangements for voting and voter participation?" that refusals and a fall in the response rate (to 60 per cent) become a problem.
However, in the QNHS case, the problem is also an opportunity in that it allows us to
test the hypothesis that response rates are socioeconomically biased to an extent that is
su¢ cient to prevent the real socioeconomic bias in the population appearing in the survey
data. Table 6 presents a test of this hypothesis focusing on the link between participation
in the survey and level of education. The results are very clear. There is no relationship
whatsoever between willingness to participate in the QNHS voter module and level of education and, accordingly, no basis for the argument that biased response rates in surveys
mask the real relationship between lower socioeconomic resources and turnout.
[1] Achen, Christopher H. 2002. Toward a New Political Methodology: Microfoundations
and ART. Annual Review of Political Science 5: 423-450.
[2] Achen, Christopher, and Richard Sinnott, eds. 2009. Voter Turnout in Multi–Level
Systems. Book manuscript.
[3] Gosnell, Harold. 1927. Getting Out the Vote. Chicago: University of Chicago Press.
[4] Hanmer, Michael J. 2004. From Selection to Election and Beyond:
the Causes and Consequences of Electoral Reform in America. Doctoral dissertation,
Political Science, University of Michigan.
[5] Holls, Frederick W. 1889. Compulsory Voting. American Political Science Review 1
(Apr.): 586-607.
[6] Lijphart, Arend. 1997. Unequal Participation: Democracy’s Unresolved Dilemma.
American Political Science Review 91,1 (Mar.): 1-14.
[7] Merriam, Charles E. and Harold F. Gosnell. 1924. Non-Voting: Causes and Methods
of Control. Chicago: University of Chicago Press.
[8] Piven, Frances Fox, and Richard A. Cloward. 1988. Why Americans Don’t Vote.
New York: Pantheon.
[9] Rosenstone, Steven J., and John Mark Hansen. 1993. Mobilization, Participation, and
Democracy in America. New York: Macmillan.
[10] Tingsten, Herbert. 1937. Political Behavior. London: P. S. King.
Figure 1: US Turnout by Income, 1998 and 2000
turnout fraction
under $10K
over $75K
Figure 2: 1998 Turnout Drop (as Fraction of 2000 Turnout) by Income
turnout drop
under $10K
over $75K
Figure 3: 2000 Turnout by Income, North Dakota and U.S.
turnout fraction
North Dakota
under $10K
over $75K
Figure 4: North Dakota Proportionate Turnout Dropoff 1998 vs. 2000
under $10K
over 75K
Figure 5: 2000 Minnesota and West Virginia Turnout by Income
turnout fraction
$10K to $15K
Figure 6: 1998 West Virginia Turnout Dropoff (as fraction of 2000) by Income
dropoff fraction
$10K to $15K
Figure 7: 1998 Turnout Dropoff (as fraction of 2000) among Americans 18-24
turnout dropoff
9-11 yrs
12 yrs
HS degree
some coll
Figure 8: Turnout by occupation in non-compulsory voting countries controlling for countrylevel turnout
Senior officials, managers and professionals
Technicians and associate professionals
Service and sales workers
Skilled agricultural and fishery workers
Craft and related trades workers
Plant and machine operators
Manual labourers
80% or more
occupation within country-turnout bands
Below 60%
Figure 9: Turnout by educational level in non-compulsory voting countries controlling for
country-level turnout
Lower secondary or second stage of basic
Upper secondary
Post secondary, non-tertiary
80% or more
educational level within country-turnout bands
Below 60%
Figure 10: Turnout by level of net household income (1=low) in non-compulsory voting
countries controlling for country-level turnout
80% or more
Below 60%
household income (1=low) within country-turnout bands
DROPOFF * five category educ variable Crosstabulation
Voted both
Voted natnl only
Abstained both
five category educ variable
up to 14
DROPOFF * Respondents occupati on Crosstabul ation
Voted both
Voted natnl only
Abstained both
Respondents occupation
other white
DROPOFF * Knowledge new four levels (0=1) Crosstabulation
Voted both
Voted natnl only
Abstained both
Knowledge new four levels (0=1)
Figure 11: Upper Class vs. Working Class Turnout Ratio, Prussia 1893-1913
turnout ratio of upper class to workers
national turnout