A new rational choice model incorporating the institution of compulsory voting into the "Calculus of Voting" (1968). Compulsory Voting is a sure method of increasing voter turnout only if citizens face significant sanctions and enforcement, and at the cost of those who cast a ballot being on average more apathetic. Overtime it is likely that any potential partisan effects of compulsory voting are disappearing.

1. A Rational Choice Model of Compulsory
Voting
How does Compulsory Voting alter Riker and Ordeshook’s (1968) “Calculus of
Voting”? What is its impact on turnout and electoral outcomes?
Jonathon Flegg
j.c.flegg@lse.ac.uk
j.c.flegg@nus.edu.sg
London School of Economics and Political Science
10th May 2010
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2. A Rational Choice Model of Compulsory Voting
Since around 1960 steadily falling rates of voter turnout across most established democracies
have been interpreted by many as the cause of a “crisis of legitimacy” for democracy, and as
one of the key trends indicative of ensuing Crouch‟s (2004) apocalyptic “post-democracy”.
Arend Lijphart (1997), in his presidential address to the American Political Science
Association in 1996, provoked a wave of new discussion when he argued that this
“democratic dilemma” was becoming so critical that developed democracies need to consider
a raft of institutional changes to boost electoral turnout. The most controversial and
efficacious was the introduction of compulsory voting (CV). Democratic government is a
public good, argue proponents such as Lijphart, and to avoid the free-rider problem voting
should be treated as an enforceable duty and not a voluntary right. But is compulsory voting
really the answer to society‟s lack of enthusiasm for exercising its franchise? What can we
reasonably expect from compulsory voting, and does it introduce any partisan effects? While
leaving the normative debate to one side (see Lijphart (1997) for the case in favour and Lever
(2007) for the case against), this essay addresses these questions by building a rational choice
model of compulsory voting and testing its predictions.
The Calculus of Voting
Rational choice theories of electoral turnout begin by assuming that citizens make the
decision to vote or not vote based on rational self-interest. In the basic two-candidate model
proposed by Downs (1957), each voter considers their costs (Ci) of voting (for example, in
time waiting to vote or in petrol used to drive to the polling station) and weighs that against
the expected benefits (Bi) they might receive from the election of their preferred candidate
over and above that received from the alternative candidate. This internal process, where
citizen i will only vote if their expected utility (Ri) is positive, is often referred to as the
„Calculus of Voting‟ (Downs 1957; Tullock 1967; Riker and Ordeshook 1968):
Ri = pBi – Ci
While the expected benefits of a citizen‟s preferred candidate being elected can be and are
likely to be non-zero and positive, the actual utility of voting for the candidate is likely to be
zero as the probability that the individual citizen‟s ballot will determine the election is
essentially zero in large electorates. Hence rational voters should not vote because invariably
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3. pBi < Ci holds, where p equals the insignificant probability the individual voter will prove
decisive in an election (Downs 1957; Palfrey and Rosenthal 1983). Obviously, this prediction
made by costly voting models is an unsatisfying one for the simple observation that in all
democratic elections citizens always do turnout in numbers significantly larger than zero.
This contradiction has led some to declare it as the “paradox that ate rational choice theory”
(Fiorina 1989).
To save the Calculus of Voting from its own theoretical underpinnings, Riker and
Ordeshook (1968) recognising that for the citizen the act of voting may include utility in and
of itself. They incorporated a positive, civic duty (Di) term into the equation, where a citizen
would vote if their overall expected utility from voting (Ri) is positive:
Ri = pBi – Ci + Di
While not denying that certainly many citizens vote out of a sense of duty, the term is both
subjective and defies measurement, making it essentially a residual „black box‟ term. Critics
have candidly overstated the implications of this point, arguing that it strips the Calculus of
Voting of its analytical value because all the important “action” is found within this term that
cannot be usefully understood through rational choice theory (Barry 1970; Mueller 2003:
306). A fairer criticism, as alluded to by Aldrich (1993: 258), is that the duty term does not
add anything new of analytical value. While rational choice cannot explain where duty
comes from, the fact that it reconciles the equation to the empirics unleashes the rest of the
model to be used uninhibited in analysis. A useful analogy to macroeconomics would be the
role of total factor productivity in production functions despite essentially being, as
Abramovitz (1956) put it, a “measure of our ignorance”. Moreover cross-country analysis of
the Riker and Ordeshook equation with panel data can easily deal with the duty term
through fixed effects, if it is assumed to remain relatively constant within countries through
time.
The Institution of Compulsory Voting
While CV is not the norm for democratic countries, it is currently used in 29 countries,
around a quarter of all democracies. As can be seen from Table 1, half of the world‟s CV
systems punish abstainers with sanctions, around half have introduced the institution since
World War II, and just over half of all countries with CV are found in Latin America. In one
sense the term „compulsory voting‟ is a misnomer, as citizens are only required to attend the
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4. polls. A citizen is not required to cast a preference for a valid candidate, and in fact in a
number countries the option exists for those who prefer abstention to indicate “none of the
above” on their ballot. Additionally, all current CV systems have certain exceptions from the
legal obligation to participate, that may include overseas residence or temporary absence,
infirmity, literacy, or because of religious belief or practice.
Multiple types of sanctions are employed in CV systems. Most common is a simple fine for
those who do not participate, ranging from three Swiss francs in the Swiss canton of
Schaffhausen to a hundred euros or more in Luxembourg for the first offence and rising up
to as much as a thousand euros for repeated infringements. Some CV systems, rather than
apply monetary incentives, punish a non-voting citizen by withdrawing their franchise. In
Belgium if a citizen fails to vote in four elections over a fifteen-year period, they loose their
franchise for the following ten years. A number of Latin American countries such as Bolivia
and Brazil sanction non-voters by prohibiting them from holding a position in the public
sector, or withholding access to public services. In the extreme, sanctions for those who fail
to vote can include imprisonment. Following the 1993 federal election in Australia, 43 non-
voters who refused to pay a fine received prison sentences (Bennett 2005).
How does Compulsory Voting Alter the Calculus of Voting?
Making voting compulsory increases the costs of not voting, and therefore implicitly reduces
the overall opportunity cost of voting. A rational model of voting behaviour with CV must
somehow incorporate the non-zero costs of abstention into the overall cost term (Kato 2007;
Panagopolous 2008; Krasa and Polborn 2009). Crucially the assumption of costly abstention
relies on both significant sanctions and enforcement for citizens who fail to vote
(Panagopoulous 2008; Birch 2009). Specifically the cost of not voting will only be greater
than zero if there is a positive interaction between a non-zero sanction (CNV) and the
probability or strictness of that sanction being enforced (qi). Building from the Riker and
Ordeshook (1968) equation, if the true cost of voting under a CV system is C i = CVi – qiCNV,
then a citizen would choose to vote if their overall utility from voting (Ri) is positive:
Ri = pBi – CVi + qiCNV + Di
If the electorate is heterogeneous, with a continuum of duty values from zero (politically
apathetic citizens) to high (Di > CVi, citizens who value electoral participation and who
would vote even in the absence of compulsion), then rational citizens would vote if:
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5. CVi < qiCNV + Di
And at the apathy-limit (Di → 0) a rational citizen would vote if:
CVi < qiCNV
These findings are crucial as it explains the real observation of non-universal turnout under
CV systems. While CNV is a fixed sanction, CVi and qi have individual-level variation and are
heterogeneous across the electorate. Citizens may still abstain under a CV system if they
possess or can acquire a large CVi or a low qi.
The Effect of Compulsory Voting on Turnout
The rational model of CV makes a number of predictions that we can examine in the real
world.
Prediction 1: ceteris paribus, turnout can only be higher under CV compared with voluntary voting, as
the overall utility function of voting is increased by a positive value qiCNV.
The most obvious prediction of CV systems is that turnout will increase because of the non-
zero costs of abstention. This has been substantiated by a large number of empirical studies
that find turnout to increase by between seven to sixteen percentage points in established
democracies (Powell 1986; Jackman and Miller 1995; Franklin 1999; Birch 2009), and by
between eleven and seventeen percentage points in Latin America (Fornos et al 2004). The
size of the increase in turnout due to the introduction of CV has been shown to be mainly
determined by how low turnout is prior to its introduction (Hirczy 1994), and of course by
the severity of the sanction and level of enforcement.
Prediction 2: while turnout can only increase with CV, it will not achieve universal turnout as long as
there is individual-level variation in the values of CVi and qi.
Individual-level variation in CVi and qi within the electorate also ensures that CV systems are
not a „magic bullet‟ for achieving complete turnout. The formal institution of CV operates as
a legal mechanism and for enforcement purposes lacks the informational advantages of
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6. informal forms of coercive social or political mobilisation, such as was able to regularly
achieve turnout of 99.99% in the Soviet Union. Even when penalties are significant some
citizens will still have high costs to voting that will deter them from voting, such as being
overseas during an election. Other citizens may reduce their probability of receiving a
sanction. In Australia, infringements are detected through the electoral roll, and so many
who seek to avoid detection simply never register in the first place.
Prediction 3: increasing sanctions and increasing enforcement will increase turnout.
Prediction 4: because of the interaction effect between qi and CNV we can predict that increasing both
sanctions and enforcement will increase turnout in excess of the effect of increasing each individually.
Prediction 5: if qi or CNV or both are equal to zero then we can predict that turnout should be
indistinguishable from that of a voluntary voting system.
Taken together, predictions 3 to 5 would substantiate the channel by which greater turnout
is achieved. The interaction of sanctions and enforcement in CV systems has been a source of
recent research. Panagopolous (2008) has divided all CV systems into three categories for
severity of sanctions and strictness of enforcement: no/low (-1), moderate (0), and high (+1).
Using multivariate regression analysis Panagopolous found a positive and significant
correlation between level of penalty, level of enforcement, and their interaction term with
level of turnout, while controlling for economic growth, and electoral and legislative
systems. Moreover, CV systems with “no/low” sanctions and enforcement, such as Italy,
Mexico and Thailand, showed turnout that was not statistically different to those without
CV. In effect in these CV systems citizens have a compulsory duty to vote in an aspirational
constitutional provision, but in effect they remain non-enforced or without penalty. In the
recent volume by Birch (2009: 94) on CV, multivariate analysis failed to find any statistically
significant impact of CV on turnout until it was qualified as sanctioned CV, which was found
to be highly significant. The evidence to date appears to support the argument that CV
increases turnout primarily through non-trivial and enforced sanctions, and systems that
lack either sanctions or enforcement are in effect no different from voluntary systems.
Prediction 6: if in a CV system a citizen will vote if Di > CVi - qiCNV, ceteris paribus, we would expect
the mean duty of a voter, D V , to be lower than under voluntary voting, where citizens will vote for all
values that satisfy Di > CVi.

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7. According to my sixth prediction voters under CV, the average voter under a CV system
should have a lower sense of duty (or a greater sense of apathy) than the average voter
without compulsion. Apathy may be manifest by a higher degree of intransitivity or protest
in the ballot box. The counter argument to the prediction CV increases the average apathy
amongst voters is that CV may have positive spillover effects on increasing citizen‟s duty
and political participation (Lijphart 1997). Similarly it has been suggested that CV increases
party identification within the electorate (Mackerras and McAllister 1999). Regardless of
whether such spillover effects occur or not, the evidence suggests that they are still not
sufficient to reverse the prediction of lower duty among voters in CV systems. A number of
studies find CV to be associated with an increase in spoiled ballots (Power and Roberts 1995;
Mackerras and McAllister 1999; Reynolds and Steenberger 2006) and higher levels of
arbitrary voting, or “ballot order effects” (Power and Roberts 1995; Jackman 2001; King and
Leigh 2009). Invalid voting is especially common in CV systems in Latin America, where the
percentage of spoiled ballots has exceeded forty percent in a number of elections.
Partisan Effects of Compulsory Voting
Riker and Ordeshook (1968) did not make any predictions about potential partisan effects
from their rational model. While those who fail to vote under voluntary voting could be
expected to have a lower sense of duty or a higher cost to voting, they treated both as
exogenous and uncorrelated with omitted variables. However as long as the possibility
exists that the explanatory variables are correlated with omitted variables, the potential for
partisan effects exists.
In actuality the model can make an obvious case for partisan effects if the cost of voting, C Vi,
represents the citizen‟s opportunity cost of voting, then turnout would be negatively
correlated with income. CV therefore would have the effect of differentially inducing higher-
income citizens to the polls and boosting the proportion of votes received by the party or
parties they tend to support, typically regarded as right-wing parties. However this
disinterested high-earner interpretation comes into direct conflict with a large body of
literature that argues the exact opposite (DeNardo 1980; Pacek and Radcliff 1995; Lijphart
1997). They argue that CV systems actually tend to benefit left-of-centre parties because it
has the effect of differentially induce lower-income citizens to the polls, the exact part of the
income spectrum who are most likely to abstain under voluntary systems. Corollary theories
of this disinterested low-earner argument predict the introduction of CV to increase realised
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8. social democratic policies (McAllister and Mughan 1986; Nagel 1988; Pacek and Radcliff
1995), and government spending (Husted and Kenny 1997; Brookie 2008).
What is the Evidence for Partisan Effects?
While the disinterested low-earner argument suggests CV is an institution that benefits left-
of-centre parties, the actual record of how the institution was introduced seems to support
the former theory that higher-income citizens have a greater need for compulsory
inducement to the polls. In a multivariate regression analysis of 33 countries that adopted
CV between 1862 and 1998, Helmske and Meguid (2007) argued that the institution was
adopted because the contemporaneous expansion of suffrage and the burgeoning ranks of the
working class through industrialisation presented an acute electoral threat to incumbent
right-wing governments. A perception existed that organised labour were succeeding in
mobilising their core constituency to the polls through social coercion, a perception
crystallised in the growing strength of left-wing Labour parties within democratic
legislatures. To defend their incumbency, right-wing governments were compelled to induce
their “rich and content” middle-class supporters to the polls through introducing CV.
Helmske and Meguid (2007) substantiate their argument through showing the strong
explanatory power of right-wing incumbency, increasing vote shares of left-wing parties,
and the percentage of workers in industry (as a negative measure of the right‟s natural
electorate) in explaining episodes where and when CV was introduced. The history of CV
suggests that the existence of competing informal methods of achieving turnout, such as
social coercion, can significantly influence the direction of possible partisan effects.
Both the disinterested high- and low-earner arguments agree that CV impacts partisan
advantage specifically through an income channel. The veracity of the income channel
appears to be supported by empirical analysis. Firstly, party competition must be based on
socio-economic cleavages (Lipset 1960; Pacek and Radcliff 1995), or more specifically income
must have a determining effect on party support. There is a well-documented general
correlation between income and support for right-of-centre parties throughout all western
democracies, exception France where the Communists and Socialists receive higher support
among higher income voters (McCarthy et al 2009). Secondly, there must be a relationship
between income and turnout. The empirical support between income and turnout is even
more strongly documented (Blais et al 1996; Klingemann et al 1994), substantiating the
argument that voluntary voting is generally skewed towards representing a higher income
median voter than that of the median citizen.
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9. So if a distinct income channel exists in determining turnout, what can be said of the
partisan effects of increased turnout and introducing CV? The most often quoted finding is
Pacek and Radcliff‟s (1995) study that found turnout and turnout interacted with Powell‟s
(1980) index of class-politics are both positively correlated with the proportion of votes won
by left-wing parties. Hence increasing turnout increases the proportion of left-wing election
victories, and the effect is even more pronounced in countries where party competition is
divided along differences in class. This result however has come under fire from a large
number of more recent studies finding little or no partisan effect of turnout (van der Eijk and
van Egmond 2007; Fisher 2007; Pettersen and Rose 2007). Birch (2009: 128) finds the
introduction of sanctioned CV does not significantly affect left-wing votes when controlling
for overall level of political and economic development. On government spending Brookie‟s
(2008) regression analysis found that while a 1.0 percentage point increase in turnout was
associated with a 0.15 point increase in government spending, the effect of CV was
insignificant and had the wrong sign.
While Lijphart (1997) disinterested low-earner argument, supported by the empirics of
studies such as Pacek and Radcliff‟s (1995), remain the conventional wisdom with regards to
partisan effects of turnout, its critics have become increasingly strident in recent years.
There does seem to be a general trend towards particularly scant evidence for partisan
effects within countries with weaker socio-economic cleavages in party competition, such as
the United States and Canada. As Pacek and Radcliff (1995) themselves admitted, class-
consciousness is eroding overtime as a determinant of voting in most developed democracies,
and hence rendering any possible partisan advantage as increasingly impotent.
The evidence from partisan effects from introducing CV, to the extent that it might be
separate from simply increased turnout, is even less compelling. There is absolutely no
conclusive evidence to date that CV introduces any partisan effects. One explanation may
have to do with the relatively large standard errors generated by the limited dataset
available, for example Birch‟s (2009) study found sanctioned CV increased the share of left-
wing party support by 3.75 percentage points, but the associated standard error was a hefty
6.25. At a minimum the historical record shows that the introduction of CV systems was tied
to the perceived existence of partisan advantage, which is in itself a form of argument in
favour of their existence. But overall the evidence is scant at best. The fact that establishing
not just the direction of partisan effects but their very existence validates Riker and
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10. Ordeshook‟s (1968) original approach of treating the explanatory variables in the „Calculus
of Voting‟ as exogenous.
Conclusion
The introduction of CV remains a hotly debated topic within many developed democracies.
This essay establishes a rational choice approach to understanding the institution of CV. The
nature of CV – a sanction applied to individuals as a simple incentive to vote – lends itself
perfectly to rational choice. CV is a sure method of increasing voter turnout only if citizens
face significant sanctions and enforcement, and at the cost of those who cast a ballot being
on average more apathetic. Following Riker and Ordeshook (1968), a rational choice
explanation considers the citizen‟s duty and costs as exogenous and uncorrelated with
omitted variables such as income. While the possibility that partisan effects certainly exist,
the direction and magnitude of the effect could only be determined by complex external
factors such as the degree of socio-economic cleavages within party competition and the
existence of other informal methods of achieving turnout, such as social coercion. Overtime
it is likely that any potential partisan effects of introducing CV are disappearing.
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14. Table 1: Compulsory Voting in 2008 (Table 2.1 in Birch 2009: 36)
14