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The Psychological Impact of Electoral Laws:

Measuring Duverger's Elusive Factor

André Blais and R. K. Carty

British Journal of Political Science / Volume 21 / Issue 01 / January 1991, pp 79 - 93

DOI: 10.1017/S0007123400006037, Published online: 27 January 2009

Link to this article: http://journals.cambridge.org/abstract_S0007123400006037

How to cite this article:

André Blais and R. K. Carty (1991). The Psychological Impact of Electoral Laws:
Measuring Duverger's Elusive Factor. British Journal of Political Science, 21, pp 79-93
doi:10.1017/S0007123400006037

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B.J.Pol.S. 21,79-93
Printed in Great Britain

The Psychological Impact of Electoral Laws:

Measuring Duverger's Elusive Factor
A N D R £ BLAIS AND R. K. CARTY*

Duverger's law regarding the impact of electoral systems on party competition depends upon
two effects: the mechanical and the psychological. The former is well defined and well docu-
mented, whereas the latter has more often been a matter for theoretical speculation. In this
article we provide an operational definition of the psychological effect of electoral systems
and measure its impact across twenty democratic systems over more than a century. Our findings
suggest that it does exist, that it works as Duverger predicted and that its impact is about
the same magnitude as the mechanical effect.

Maurice Duverger's analysis of party systems and party system change is shaped
by his belief in 'a natural political dualism'. Societies naturally move towards
two-party systems by the two complementary processes of fusion and elimina-
tion. And the latter is 'itself the result of two factors working together: a mecha-
nical and a psychological factor'.1 Duverger's famous law ('the simple-
majority single-ballot system favours the two-party system') simply asserts that
the ways in which these processes and factors work are intrinsic features of
particular electoral regimes.
Although Duverger does not provide formal definitions of his now famous
mechanical and psychological factors, the meaning seems clear enough. He
describes them as the 'phenomena of polarization and under-representation'. 2
The mechanical effect refers to electoral systems' systematic underrepresen-
tation (in the share of legislative seats as compared to popular votes) of 'third'
parties. The psychological effect refers to the tendency for voters, realizing
that votes for minor parties are not effectively translated into seats, to rally
to what they consider the least unacceptable of the two major parties. The
distinction between these two effects is now widely accepted and Taagepera
and Shugart express a widespread consensus when they assert that 'Duverger's
mechanical and psychological effects are notions useful in explaining how some
electoral rules reduce the number of parties.' 3
The very terms 'mechanical' and 'psychological' suggest objective and subjec-
tive factors and it is therefore not surprising that the former seems to be well
understood and easily measured while the latter remains a rather fuzzy notion

* Department of Political Science, University of Montreal, and Department of Political Science,

University of British Columbia, respectively.
1
Maurice Duverger, Political Parties (London: Methuen, 1954), pp. 215, 224.
2
Duverger, Political Parties, p. 240.
3
R. Taagepera and M. S. Shugart, Seats and Votes: The Effects and Determinants of Electoral
Systems (New Haven, Conn.: Yale University Press, 1989), p. 65. For a review of the literature
see W. H. Riker, 'Duverger's Law Revisited', in B. Grofman and A. Lijphart, eds, Electoral Laws
and Their Political Consequences (New York: Agathon Press, 1986).
80 BLAIS AND CARTY

whose process or magnitude is not clearly understood. Thus in the preface

to their recent magisterial study of electoral systems Taagepera and Shugart
concede 'The psychological effect still remains elusive to a large extent.'4
This article is a search for Duverger's elusive psychological factor. We seek
first to define what it is and how it works, then to measure its magnitude,
andfinallyto assess its relative impact as compared to the mechanical effect.
The nature of the mechanical effect, which Rae demonstrated exists in all
electoral systems, is clear enough.5 According to Taagepera and Shugart it
'refers to the tendency of certain electoral rules to give a bonus to the larger
parties and penalize the smaller parties, giving them less than the seat shares
based on ideal PR ... [it] is mechanical in the sense that no human manipulation
or strategy is involved.'6 The mechanical effect pertains to the link between
votes and seats; it is observed by comparing shares of votes and shares of
seats.
The exact nature of the psychological effect is more difficult to specify.
Duverger writes about it in terms of its consequence; it leads to vote polariza-
tion. Taagepera and Shugart do not attempt to define it nor do they become
as precise in their references to it as they do with respect to the mechanical
effect. They write instead of a 'psychological attitude' which may lead supporters
voting for an underrepresented party (due to the workings of the mechanical
effect) to 'stop doing so because they feel it would be a waste of their vote'.
Such a characterization implies that the psychological impact affects the vote
itself. It 'reduces the number of votes for the small party'.7 With Duverger
they see the effect as a matter of vote distribution. And this provides us with
a clear distinction: the psychological factor affects the vote, the mechanical
factor affects the seats (given the vote).
That the psychological effect works by affecting the vote distribution might
lead one to conclude that it is exclusively a function of voter reactions and
strategy. Certainly this seems to be the message in a good deal of the literature.
Thus Duverger, Riker, and Taagepera and Shugart all refer to voters' decisions
and behaviour when they illustrate the process and effect of the psychological
factor. But clearly that cannot be the whole story. The distribution of votes
in an election depends on the interaction between voters and parties, and the
latter's strategy is as crucial as the former's. Political elites and party leaders
will anticipate the mechanical and therefore the psychological effects of electoral
systems as much as voters will. The Finnish PR case provides a clear example
of this for there 'parties do not run candidates in those districts where they
are very unlikely to win seats.'8 In a plurality system, where the mechanical
effect is most powerful, they should be less inclined to form new parties or

4
Taagepera and Shugart, Seats and Votes, p. xiv.
5
D. W. Rae, The Political Consequences of Electoral Laws (New Haven, Conn.: Yale University
Press, 1967).
6
Taagepera and Shugart, Seats and Votes, p. 65.
7
Taagepera and Shugart, Seats and Votes, p. 65.
8
Taagepera and Shugart, Seats and Votes, p. 120.
 The Psychological Impact of Electoral Laws 81

more inclined to merge old ones.9 As a consequence there should be fewer

parties contesting such elections. The psychological effect, therefore, should
encompass the anticipations of all political actors, elites as well as voters.

MEASURING THE PSYCHOLOGICAL EFFECT

A focus on voters has led some to search for the psychological effect of electoral
systems in the record of strategic voting in plurality elections.10 Spafford,
Lemieux and Cain all report that the Liberal vote in Britain is smaller in those
constituencies where there is a close race between the two major parties: given
a greater chance to influence the outcome more Liberals desert their party.
Blais et al. demonstrate that minor party voting in Quebec has been similarly
influenced by contextual strategic factors." On the other hand, Shively
reported negative findings in his analysis of a party's propensity to contest
a seat and its changing vote shares across consecutive British elections over
the 1892-1910 period.12 But, as Spafford pointed out, Shively does not properly
distinguish between situations in which sophisticated voting would or would
not be efficient.
In addition to aggregate level analysis, survey data has been brought to
bear on the issue. For Britain, Cain indicates that around 10 per cent of electors
vote for a party which is not their first preference and that the probability
of a strategic vote increases as the probability that the most preferred party
can win decreases.13 Black reports similar findings for Canada and Bensel
and Sanders estimate that around 10 per cent of Wallace's 1968 presidential
supporters in the United States voted strategically; they also show that the
probability of shifting was affected by the viability of Wallace within the state
where the voter resided.14
Thus studies based both on election results and survey responses provide

' This second process is the one Duverger calls 'fusion', arguing that it is one of two ways
(party elimination being the other) that bipartism is established. While he does not say as much,
Duverger seems to imply that (under the plurality formula) elite activity works through fusion,
voter-driven effects through elimination.
10
Riker, 'Duverger's Law Revisited', pp. 33-8.
" D. Spafford, 'Electoral Systems and Voters' Behavior: Comment and a Further Test', Compara-
tive Politics, 5 (1972), 129-34; P. Lemieux, 'The Liberal Party and British Political Change: 1955-
1974' (doctoral dissertation, Massachusetts Institute of Technology, 1977); B. E. Cain, 'Strategic
Voting in Britain', American Journal of Political Science, 22 (1978), 639-55; A. Blais, F. Renaud
and R. Desrosiers, 'L'effet en amont de la carte electorale: le cas de la region de Quebec a Pelection
federale de 1968', Canadian Journal of Political Science, 7 (1974), 648-72.
12
W. P. Shively, 'The Elusive Psychological Factor: A Test for the Impact of Electoral Systems
on Voters' Behavior', Comparative Politics, 3 (1970), 115-25.
13
Cain, 'Strategic Voting in Britain', pp. 646-54.
14
J. H. Black, 'The Multicandidate Calculus of Voting: Application to Canadian Federal Elec-
tions', American Journal of Political Science, 22 (1978), 609-38, and 'The Probability-choice Perspec-
tive in Voter Decision Making Models', Public Choice, 35 (1980), 565-74; R. F. Bensel and
M. E. Sanders, 'The Effect of Electoral Rules on Voting Behavior: The Electoral College and
Shift Voting', Public Choice, 34 (1979), 69-85.
82 BLAIS AND CARTY

strong evidence of strategic voting. As Riker concludes, 'the foregoing evidence

renders it undeniable that a large amount of sophisticated voting occurs -
mostly to the disadvantage of the third parties nationally - so that the force
of Duverger's psychological factor must be considerable.'15 Yet this approach
to the problem has three important limitations. Firstly, these findings do not
allow us to assess the relative importance of the psychological factor: 10 per
cent of the voters may vote strategically but that does not tell us what impact
they have on the total vote or the party system. Secondly, these analyses presume
that the psychological effect operates at the constituency level; they compare
electoral results or behaviour in constituencies of varying third-party strength.
But voters may be as (or even more) concerned with overall party strength
when they decide whether or not to vote strategically. Johnston el al. present
evidence that sophisticated voters take a party's competitive position at the
national as well as the constituency level into account; similarly, Bensel and
Sanders report that in US presidential elections vote shifting 'is heavily
influenced by perceptions of candidate viability at the national level'.16 Finally,
strategic voting studies merely look at voters' reactions whereas, as we argued
above, political elites may also anticipate the mechanical effects of the plurality
formula and either fuse existing parties or refrain from forming new ones.
Although Duverger's notion of the psychological factor, with its mix of voter
and elite anticipations of each other and how the mechanical factor will affect
them, appears more complex than a strategic voting calculus, he has a very
simple idea in mind. It is this that leads him to refer to the psychological
factor as 'the phenomena of polarization'. For him, the psychological- factor,
whatever the individual level processes that drive it, is largely an aggregate-level,
party-system phenomenon. It pertains to the distribution of vote shares among
competing parties.
Given this conception of the psychological factor, it follows that its direct
impact will be seen in fewer parties running, and third parties winning a smaller
vote share in plurality as compared to proportional representation systems;
party-system fractionalization at the national level should be greater in the
latter than in the former. The clearest and most straightforward test of the
psychological effect would therefore be one which compares the number of
parties and the extent of electoral fractionalization across different electoral
systems or examines change in those polities which have switched between
plurality and PR systems.17
There are two studies of vote distribution patterns in mixed electoral systems

15
Riker, 'Duverger's Law Revisited', p. 38.
16
R. Johnston, D. Elkins and D. Blake, 'Strategic Voting: Individual Reasoning and Collective
Consequences', paper presented at the annual meeting of the American Political Science Associa-
tion, Washington, DC, 1980; A. Blais, R. Johnston, H. Brady and J. Crete, 'The Dynamics of
Horserace Expectations in the 1988 Canadian Election', paper presented at the annual meeting
of the Canadian Political Science Association, Victoria, 1990; Bensel and Sanders, 'The Effect
of Electoral Rules', p. 82.
" The descriptive analysis Duverger provides depends a great deal on this latter approach.
 The Psychological Impact of Electoral Laws 83

that encourage our use of such an approach. Fisher examined West German
election results on both plurality and PR ballots; Shugart looked at the multi-
tiered Venezuelan elections.18 Both found evidence of the polarization that
Duverger argued was the essence of the psychological factor at work. But
as these two studies deal with mixed electoral systems they are not able to
consider the psychological impact on elites as opposed to voters, and the find-
ings can hardly be generalized in a straightforward fashion. They do, however,
confirm the implications of the work on strategic voting. There can be little
doubt that electoral systems exert a psychological effect. A careful comparative
analysis can unlock its magnitude.

THE RESEARCH DESIGN

We start with a simple assumption. The most basic and fruitful way to measure
the psychological impact of electoral regimes is to compare party systems and
voting patterns across various electoral systems. We are not concerned with
seat-vote relationships (the mechanical factor) but with the polarization of
the vote itself which reflects the psychological factor. There are two principal
aspects of Duverger's central hypothesis to be tested:
(1) Fewer parties contest elections in plurality systems. This reflects the psycho-
logical effect at the elite level.
(2) The vote is less fractionalized (i.e. more polarized) in a plurality system
as voters refrain from wasting their votes on minor parties.
In both cases plurality formula systems are compared and contrasted with
PR and majority systems. In the latter cases we use first ballot or preference
votes. Duverger clearly believes that the mechanical and psychological factors
'are not operative' in the case of majority systems and he argues that both
systems, in contrast to plurality ones, favour multi-partism in much the same
fashion.19 This is because voters need not be concerned with wasting their
first vote in a majority system. The second ballot, or lower preferences, takes
care of that problem. Like Duverger, we expect system fragmentation, be it
the number of parties or electoral fractionalization, to be as high in majority
as in PR systems.
For the purposes of detailed statistical comparison we constructed a large
data base with individual elections as the basic unit of analysis. The principal
source is the International Almanac of Electoral History updated (to 1985) by
its authors' supplements published in the European Journal of Political

" S. L. Fisher, 'The Wasted Vote Thesis: West German Evidence', Comparative Politics, 6
(1973), 295-9; M. Shugart, 'The Two Effects of District Magnitude: Venezuela as a Crucial Experi-
ment', European Journal of Political Research, 13(1985), 353-64.
" Duverger, Political Parties, pp. 239-45, is ambivalent about the second ballot and thinks
the factors at work on it 'are not entirely identical' with the influences generated by proportional
electoral regimes. He is not as interested in majority systems which he writes of as old, little
used and, by implication, less important.
84 BLAIS AND CARTY

Research.20 This has the advantage of providing enough cases to ensure suffi-
cient variation among both the dependent and independent variables to permit
a careful measurement and analysis of the psychological effect of electoral
systems. At the same time their universe of Western industrialized nations is
relatively homogeneous as compared to all the systems in which elections have
occurred.21
This provides us with a data set of 509 general elections held in twenty
countries over more than a century. About half the elections were held under
PR (52.8 per cent), while the other half were split between plurality (25.3 per
cent) and majority (21.8 per cent) formulae.
Our hypotheses require two dependent variables. The first is simply the
number of parties contesting the election (./Vi).22 The second is the extent of
electoral fractionalization. We will use as a first indicator of fractionalization
Laakso and Taagepera's 'effective number of electoral parties' (N2), which
equals MZp} when p( is the share of the vote obtained by the tth party.23
But this measure provides only one picture of voting patterns and to capture
Duverger's notion of polarization we also use the share of the vote obtained
by the leading party (Lv),24 by the second party (Sv), and by all other parties
(Tv) (hereafter called third parties) combined. These shares convey a clear sense
of the type of fractionalization that exists among voters.
The major independent variable is the electoral formula and it has three
categories: plurality, majority and proportional. Although we are primarily
concerned with the impact of the formula, that impact probably depends upon
the constituency structure. We know, for instance, that the relative effect of
PR on the degree of proportionality is dependent on district magnitude.25
Our constituency structure variable simply distinguishes between single-member
and multi-member districts. Although it would have been much more preferable
to treat the variable as a numerical one and to use the effective average district
magnitude, district magnitude data are not available for the complete data
set and so we have had to settle for this cruder indicator.26 All PR elections
20
T. T. Mackie and R. Rose, The International Almanac of Electoral History (London: Macmil-
lan, 1982).
21
Where bicameral legislatures exist only contests for the popular (lower) house are recorded.
22
The Mackie and Rose Almanac includes all parties that have at least once secured more
than 1 per cent of the vote in a national election.
23
M. Laakso and R. Taagepera, 'Effective Number of Parties: A Measure With Application
to West Europe', Comparative Political Studies, 12 (1979), 3-27.
24
The leading party is defined as the one with a plurality of the vote.
25
Rae, Political Consequences, pp. 114-25; R. Taagepera, 'Effect of District Magnitude and
Properties of Two-Seat Districts', in A. Lijphart and B. Grofman, eds, Choosing an Electoral
System: Issues and Alternatives (New York: Praeger, 1984), pp. 92-8, and 'Reformulating the
Cube Law for Proportional Representation Elections', American Political Science Review, 80 (1986),
489-504.
26
This data constraint is perhaps the major limitation of this study. But even Taagepera and
Shugart's Seats and Votes is missing data for various countries for particular periods and relies
on guesstimates for others. See their Table 12.2, pp. 138-9, where, for instance, data for Denmark,
1913-32 is missing, while question marks signal uncertainty about cases like Germany 1920-33.
 The Psychological Impact of Electoral Laws 85

are, of course, held in multi-member districts. We also have thirty-seven cases

of multi-member district majority elections (Belgium, 1847-98; and Switzerland,
1896-1917), and twenty-one multi-member district plurality elections. All of
the latter are from Japan and are also, therefore, characterized by a limited
vote ballot.27
Electoral fractionalization is likely to be influenced by factors other than
the electoral system, and more specifically by a number of institutional variables
that have an independent impact on the party system. Four such variables
are included in the analysis. The first is the size of the legislature. Following
Taagepera and Shugart's discussion of 'the cube root law of assembly sizes'
we expect that the greater the size of the legislature the greater the number
of parties.28 The second is the existence of universal suffrage. Historically,
universal adult male suffrage often coincided with the adoption of PR and
an increase in the number of parties to represent newly enfranchised interests.
That being so, universal suffrage may itself be associated with an increase
in the number of parties. The third is direct presidential elections. Such elections
are believed to provoke political duality by forcing the party system to polarize
into two camps. One natural consequence of that should be a lower fractionali-
zation of the electoral party system. The fourth is the presence of federal institu-
tions. Federalism exists where social diversity of the sort that can support
separate parties exists. Federal institutions provide a basis for a large number
of parties and may encourage party elites to maintain smaller regional parties
rather than fuse with others as Duverger expected the psychological effect
would require.29
One potential difficulty with our approach is that it uses elections held over
a long period of time, and across a wide range of systems. It is therefore import-
ant to control for time-period and/or country effects. This we do through the
construction of a set of dummy variables. Initially we focus on long periods,
distinguishing among pre-First World War, the interwar period and post-
Second World War elections, and then we move to consider shorter (decennial)
period effects. For place effects we first look at groupings of countries that
have been used in previous research: European, Scandinavian and English-
speaking countries.30 We then test for the existence of any country-specific
forces. In doing so we hope to control for those social, economic or cultural

27
For an analysis of Japan, see Steven R. Reed, 'Structure and Behaviour: Extending Duverger's
Law to the Japanese Case', British Journal of Political Science, 20 (1990) 335-56.
28
Taagepera and Shugart, Seats and Votes, pp. 173-83.
29
These propositions are derived from a broad literature, including Taagepera, 'Reformulating
the Cube Law'; A. M. Carstairs, A Short History of Electoral Systems in Western Europe (London:
Allen and Unwin, 1980); Riker, 'Duverger's Law Revisited'; and M. Duverger, 'Duverger's Law:
Forty Years Later', in Grofman and Lijphart, Electoral Laws.
30
G. B. Powell, Contemporary Democracies: Participation, Stability and Violence (Cambridge,
Mass.: Harvard University Press, 1972); R. Rose, 'Elections and Electoral Systems: Choices and
Alternatives', in V. Bogdanor and D. Butler, eds, Democracy and Elections: Electoral Systems
and Their Political Consequences (Cambridge: Cambridge University Press, 1983).
86 BLAIS AND CARTY

factors that are common to a group of countries or specific to any one of

them.

THE PSYCHOLOGICAL EFFECT

The first task is to consider the basic patterns of polarization, as measured
by our several dependent variable indicators. The typical election in the data
set is contested by seven political parties but the number of effective parties
at the national level is just four (Table 1). The leading party averages just

TABLE 1 Indicators of Electoral Fractionalization*

Standard
Mean Deviation
N{ Number of electoral parties 6.6 3.2
N2 Effective number of electoral parties 3.7 1.4
Lv Vote share: leading party (%) 41.1 10.0
Sv Vote share: second party (%) 29.5 9.6
Tv Vote share: third parties (%) 29.4 16.5

* AT =509.

over 40 per cent of the vote, the second party 30 per cent, leaving a final
30 per cent to all the other parties. As one would expect, given the logical
relationships among them, there are rather strong correlations among the five
variables, which increases our confidence that we are tapping various aspects
of the same phenomenon.
There is some apparent temporal variation in the party system fragmentation
(Table 2). Although there seems to be little difference between the interwar

T AB LE 2 Electoral Fractionalization by Periods

Up to 1919 1920-44 1945-85
4.8 7.2 7.4
3.3 3.9 3.8
45.2 38.5 39.7
31.5 28.1 28.9
23.3 33.3 31.2
(N) (150) (113) (246)

and postwar patterns, party systems appear to have been less fragmented before
the First World War. In particular, the number of parties actually contesting
elections was smaller, as was the support for third parties. Given the timing
of the adoption of universal suffrage in many European democracies this sug-
gests something of its impact on party systems and electoral competition.
 The Psychological Impact of Electoral Laws 87

This brings us to the electoral formulae themselves (Table 3). As predicted,

electoral fractionalization is lower in plurality systems. Typically there are three
more parties contesting an election in PR than in single-member plurality sys-
tems; the effective number of parties is 56 per cent higher. Third parties obtain
twice as many votes, a nineteen percentage point difference. The evidence of
the majority system is more ambivalent than Duverger thought. District magni-
tude clearly makes a difference. Single-member district majority systems behave
like PR, but electoral polarization is apparently greatest in multi-member major-
ity systems where third parties typically obtain less than 10 per cent of the
vote.

T A B LE 3 Electoral Fractionalization by Electoral Systems

Plurality Majority PR

Single- Multi- Single- Multi-

member member member member
4.6 5.3 7.0 2.9 7.8
N2 2.7 3.6 4.2 2.3 4.2
L, 45.9 44.8 38.7 53.9 37.7
sv 37.2 26.3 26.5 38.0 26.3
Tv 16.7 28.9 34.9 8.1 35.9
(N) (108) (21) (74) (37) (269)

At this point we need to ask whether these patterns are explicable by other
exogenous factors. That requires a multivariate anlaysis. We have regressions
for each of the five dependent variables. The regressions (Table 4) testify to
the existence of substantial country-specific effects in seven systems: Israel,
France, Germany before the Second World War, the Netherlands, Switzerland,
Finland and Denmark. This effectively excludes these systems from our esti-
mates of the relative balance of mechanical and psychological effects and thus
probably makes our measure of the psychological impact a conservative one.
Especially pronounced is the greater fractionalization with respect to every
indicator for pre-Second World War Germany, the greater number of parties
in Israel, the weakness of the leading party in France and the strength of
third parties in Switzerland.
Some of these country effects are almost certainly accounted for by institu-
tional factors we have not been able to measure. In particular the very high
fractionalization observed in Israel and the Netherlands no doubt stems from
the high district magnitudes in those two countries, which reinforces Taagepera
and Shugart's claim that district magnitude is the crucial factor in an electoral
88 BLAIS AND CARTY

TAB LE 4 The Determinants of Electoral Fractionalization

Variables /V, N2 Lv
4
i. T
Israel + 5.4 (8.4) + 1.4 (5.3) - 4 . 7 (2.2) -6.6 (3.1) + 11.3 (3.9)
France + 1.4 (2.3) + 1.7 (7.0) -16.5 (8.2) -2.7 (1.3) + 19.2 (6.9)
Germany
(pre-1914) + 7.5(14.9) + 3.3(16.0) -17.1(10.2) -15.4 (9.2) + 32.5(14.1)
Netherlands +4.4(10.0) +2.0(11.0) -13.8 (9.4) -4.7 (3-2) + 18.5 (9.1)
Switzerland + 3.4 (6.9) +2.1(10.5) -13.9(16.3) -16.1 (9.9) + 30.0(13.3)
Finland +0.7 (1.6) + 1.2 (7.1) - 9 . 6 (6.9) -6.2 (4.5) + 15.8 (8.3)
Denmark + 1.9 (5.0) +0.8 (5.1) - 5 . 5 (4.2) -6.9 (5.4) + 12.4 (7.0)
No universal
suffrage -2.0 (6.0) -0.5 (3.4) + 3.7 (3.4) + 5.8 (5.2) -9.5 (6.3)
Federalism -0.6 (2.2) -0.6 (5.4) + 1.9 (2.2) + 9.1(10.2) -11.0 (9.0)
Plurality -1.4 (5.5) -0.5 (5.0) +2.9 (3.5) + 3.6 (4.3) -6.5 (5.6)
Majority -1.0 (3.1) -0.1 (1.0) +2.7 (2.5) -3.9 (3.6) -1.2 (0.8)
Majority x
multi-member -2.0 (3.9) -1.2 (6.1) + 9.5 (5.7) + 11.3 (6.8) -20.8 (9.1)
Constant + 6.7(12.6) + 3.7(21.1) +41.6(37.0) +28.1(27.6) + 29.3(12.3)

R2 0.60 0.63 0.54 0.49 0.68

Note: N = 509. In Tables 4, 5 and 6 cell entries refer to the regression coefficients, the entries
in parenthesis to the t statistic. For instance, the equation for N\ (the number of parties running
in the election) indicates that compared to PR elections (the reference point) there
are 1.4 fewer parties running in plurality elections.

system. But that cannot be the whole story, for Table 4 indicates fractionaliza-
tion was even greater in pre-Second World War Germany, where the effective
district magnitude was actually lower.31
Two institutional variables - the existence of universal suffrage and federalism
- prove to be quite significant. The impact of universal suffrage appears to
be particularly important: it seems to have led to the creation of two new
parties, and to an increase in the third parties' vote by the order often percentage
points. This explains, as we anticipated, the differences observed (Table 2)
between pre-First World War and subsequent periods. On the other hand,
the finding that third parties' support is weaker in federal than in unitary
countries was quite unanticipated. It could be that major-party elites are more
sensitive to potential third-party concerns in federal systems and are conse-
quently more adept at practising brokerage politics, or perhaps that federal
institutions provide third-party elites with alternate, and more promising, elec-
toral arenas. Whatever the explanation, the workings of electoral regimes in
federal systems deserve closer attention.
Our principal concern, however, is with the differential impact of electoral
formulae. The regressions indicate that, everything else being equal and exclud-
31
For estimates, see Taagepera and Shugart, Seats and Votes, Table 12.2, p. 138. This may
also testify to the difficulty of producing reliable district magnitude data.
 The Psychological Impact of Electoral Laws 89

ing the seven deviant countries (amongst them those with some of the purest
PR systems), there are an average of 6.7 parties contesting PR system elections,
but only 5.3 in plurality ones. The effective number of parties is 0.5 lower
in the latter, a relative decrease of 14 per cent. Support for third parties, perhaps
the clearest indicator of polarization, is six and a half percentage points lower
in plurality systems, a relative decrease of 22 per cent.32 Given the conservative
bias of our measure, this is straightforward and strong evidence for a psychologi-
cal factor of the sort Duverger argued exists.
One might argue that this impact is not as dramatic as Duverger's analysis
suggests, and as the simple cross-tabulations (Table 3) imply. It is true that
there is no absolute polarization of the vote; the effect is best described as
incremental. Still, PR systems do have one more party and noticeably stimulate
the third parties' vote. The relative amplitude of the psychological factor mea-
sured by these two critical indicators is thus in the order of 20 per cent. More-
over, this is the overall net systemic impact, with specific constituency effects
likely to be higher. These results contradict Taagepera and Shugart's assertion
that the district-level 'is the only level at which a quantitative inquiry of this
[psychological] effect can be started',33 and supports those who argue that
strategic voting takes place at both constituency and national levels.
The results also demonstrate that the working of the majority formula is
profoundly shaped by district magnitude. As Duverger claimed, the single-
member district variant is hardly distinguishable from PR, except that the
number of parties is a little lower. The multi-member majority system, however,
produces strikingly different outcomes which are characterized by a very strong
polarization of the vote: the typical outcome is a system with just two effective
parties and with third parties' voters virtually disappearing. However, we con-
sider this latter result to be rather tentative, based as it is on a few (thirty-seven)
cases in two countries and a crude indicator of district magnitude.34
By comparison, the psychological factor seems unambiguous in plurality
systems, working exactly as predicted by Duverger. It does appear as if both
elites and voters anticipate the mechanical effect and behave accordingly. The
former seem more reluctant to form new parties, the latter more reluctant
to support third parties. Moreover, the greater support given to the major
parties is split between the leading and second parties, as Duverger expected.
The psychological effect of the plurality formula should not be interpreted
as favouring the leading party; it is biased against third parties. This is what
the wasted vote thesis implies for it argues that a proportion of potential third-
party voters rally to the least objectionable of the two major parties.
32
This estimate is difficult to compare with Rae's in The Political Consequences of Electoral
Laws given the different data bases and the numerous classification errors identified by A. Lijphart
in 'The Political Consequences of Electoral Laws, 1945-85', American Political Science Review,
84(1990).
33
Taagepera and Shugart, Seats and Votes, p. 214.
34
For a graphical presentation of an analysis which rests upon numerical estimates of district
magnitude, see Taagepera and Shugart, Seats and Votes, Figure 13.2, p. 144.
90 BLAIS AND CARTY

We have argued that the psychological effect has both an elite and a mass
dimension. Of the equations reported in Table 4, the first one (jVb the number
of parties in the system) can be taken as an indication of the elite component,
the other four measuring the total impact of the psychological factor. Of course,
elites may respond to anticipated psychological effects, especially in plurality
systems, by simply not sponsoring a candidate in individual electoral districts
where they do not expect to win. The Liberals in post-Second World War
Britain provide a classic example of this strategy. This makes AT, a rather con-
servative, minimum estimate of the proportion of the psychological effect that
can be attributed to elites as opposed to voters. But it also has the virtue
of focusing on the systemic as opposed to local dimension of the effect.
Using the number of parties (Nt) ensures that our interpretation of elite
behaviour will be informed by those heading the most marginal parties in the
system. This is precisely what we want, for it is these politicians, not those
heading the system's major parties, that Duverger implies will be most prone
to the pressures of the psychological effect.

TABLE 5 The Psychological Impact at the Level of the Electorate

Variables N2 u s. T,
N\ +0.2(13.1) - 1 . 1 (7.4) - 0 . 7 (4.7) + 1.7 (9.1)
Israel +0.3 (1.1) + 1.1 (0.4) - 2 . 9 (1.3) + 1.9 (0.7)
France + 1.4 (6.6) -15.0 (7.8) - 1 . 7 (0.9) + 16.7 (6.5)
Germany
(pre-1914) + 1.7 (8.2) -9.2 (4.8) -10.3 (5.2) + 19.5 (7.6)
Netherlands + 1.1 (6.2) -9.1 (5.9) -1.7 (1.1) + 10.8 (5.3)
Switzerland + 1.4 (7.7) -10.3 (6.3) -13.8 (8.2) +24.1(11.0)
Finland + 1.1 (7.2) -8.9 (6.8) -5.8 (4.3) + 14.6 (8.3)
Denmark +0.4 (2.9) -3.4 (2.7) -5.6 (4.3) + 9.0 (5.4)
No universal
suffrage -0.0 (0.4) + 1.6 (5.5) +4.4 (4.0) -6.0 (4.1)
Federalism -0.5 (4.9) + 1.3 (1.6) + 8.7 (9.9) -10.0 (8.8)
Plurality -0.2 (2.5) + 1.4 (1.7) +2.6 (3.1) -4.0 (3.7)
Majority +0.1 (0.7) + 1.6 (1.6) -4.6 (4.2) + 3.0 (2.1)
Majority x
multi-member -0.8 (4.6) + 7.4 (4.6) + 9.9 (6.0) -17.4 (8.1)
Constant +2.2(14.8) +48.6(37.5) + 32.7(26.8) + 18.7 (7.0)

R2 0.72 0.58 0.51 0.72

Note: N = 509. See also footnote to Table 4.

To sort out the mass component, it is necessary to examine the vote distribu-
tion controlling for the number of parties contesting the election. This is done
in Table 5. The results confirm that both the elite and mass components have
significant effects. With respect to fractionalization of the electoral party system
 The Psychological Impact of Electoral Laws 91

(N2), the mass dimension looks to be marginally less important than the elite
one: the partial mass effect of the plurality rule is 0.2 (Table 5) compared
to a global effect of 0.5 (Table 4). But if one looks at third-parties' support,
the critical indicator in a wasted vote interpretation of the factor, the largest
part of the total impact (6.5) is worked out at the voters' level (4.0). It also
appears to be voters' reactions rather than party leaders' strategies which
account for greater fractionalization with universal suffrage and greater polari-
zation in federal countries when plurality rather than PR formulae are used.
However, the general lesson is clear: both political elites and voters behave
strategically.
How big is Duverger's psychological factor? There are two ways to ascertain
its relative importance. Thefirstis to assess, as we have done here, the difference
it makes. Our data indicates that the third parties' vote is 22 per cent lower
in plurality electoral systems than under PR (Table 4). Given that of all the
single indicators this one comes closest to representing Duverger's conceptuali-
zation of the factor, we think it reasonable to conclude that the total psychologi-
cal impact is of the magnitude of 20 per cent. This is a substantial difference.
The second way to estimate the size of the psychological factor is to compare
it to the mechanical factor which is at work in all electoral regimes.

PSYCHOLOGICAL AND MECHANICAL EFFECTS COMPARED

An electoral system's mechanical factor is the impact it has on the seat/vote
ratio. In particular, it refers to an omnipresent bias in favour of major parties
and against minor parties. The plurality rule has a significantly greater bias
than has PR. It follows that with the same share of votes major parties will
win more seats (and minor parties fewer seats) in plurality as compared to
PR elections. The mechanical impact can be operationalized as the additional
share of seats major parties win under a plurality formula, given their share
of the vote. At the systemic level it can be measured by the smaller effective
number of legislative parties, given the effective number of electoral parties.
Table 6 documents the mechanical effect. It demonstrates that, for a given
share of the vote, the leading party wins four percentage points more seats,
while third parties receive three percentage points fewer seats, under a plurality
electoral regime as compared to PR. This should be compared with the psycho-
logical effect's impact of three and six points respectively (Table 4).
Much the same pattern can be seen in the number of effective parties in
the system. With the effective number of electoral parties held constant, the
mechanical impact of a plurality rule reduces the number of effective legislative
parties by three-tenths of a percentage point (Table 6), whereas the psychologi-
cal impact on the effective number of electoral parties is to reduce the number
by five-tenths of a point. Thus our indicators all lead to the same conclusion:
the impact of Duverger's psychological effect is of the same magnitude as the
mechanical factor.
92 BLAIS AND CARTY

T AB LE 6 The Determinants of the Mechanical Bias

Variables L, Ss T,
Electoral fractionalization +0.5(5.9) + 1.1(6.9) -1.0(6.5) +0.7(14.5)
Electoral fractionalization2 +0.0(5.8) +0.0(0.0) +0.0(0.1) +0.0 (7.1)
Norway -0.3(3.3) +4.0(2.8) -1.2(1.0) - 2 . 1 (2.3)
New Zealand -0.2(2.1) + 2.7(2.1) + 1.3(1.1) - 4 . 4 (5.2)
Plurality -0.3(6.0) +4.1(5.2) -3.6(5.0) - 3 . 0 (5.5)
Majority -0.2(3.0) -0.6(0.6) -0.8(1.1) +0.6 (1.0)
Majority x multi-member -0.2(2.0) + 5.2(3.8) -6.9(5.8) - 3 . 3 (3.5)
Constant + 1.0(5.6) -3.2(0.9) + 0.4(0.2) + 2.2 (2.9)
R2 0.92 0.79 0.73 0.94

Note: N = 509. See also footnote to Table 4. N^ = effective number of legislative parties; Ls = leading
party seat share (%); Ss = second party seat share (%); Ts = third parties' seat share (%).

CONCLUSIONS
Duverger's arguments about the impact of electoral regimes on party compe-
tition have dominated the literature despite a rather vague understanding of
his psychological factor. The reverse is true of his other factor, the mechanical
one. We argue that the former consists of the anticipations, by both elites
and voters, of the workings of the mechanical factor and both groups' conse-
quent behaviour. The mechanical factor pertains to seat/vote relationships and
the impact of the psychological factor is reflected in the distribution of votes.
Conceptualizing Duverger's psychological factor in this way allows us to
look for clear evidence of its existence by comparing the distribution of votes
across different electoral systems. The data show that plurality systems do
foster polarization. Our analysis has also permitted the first empirical estimates
of two dynamic elements to the psychological factor - the behaviour of elites
and of voters. Both exist although the latter appears to be somewhat stronger.
The data also allowed us to substantiate the presence of the psychological
factor by isolating it from, and comparing it to, the mechanical factor. The
estimates indicate they are of about the same size.
Indeed, these findings may underrepresent somewhat the actual magnitude
of the psychological effect. Our analytic technique assumes that PR has no
psychological effect but in fact even PR systems have a modest mechanical
factor bias and there is no inherent reason why that should not be anticipated
by elites and voters. Our findings solely indicate the additional psychological
effect associated with a plurality electoral system. Moreover, we have only
measured the psychological impact on the overall national system and, as we
know, strategic voting of a similar sort also takes place at the constituency
level.
Now that we have been able to confirm empirically Duverger's analysis of
the presence and impact of the psychological impact of the electoral system
on electoral competition it is essential that explanations of the vote integrate
 The Psychological Impact of Electoral Laws 93

strategic voting into their models. More generally, this analysis supports recent
research documenting and measuring the importance of electoral institutions
on political and competitive behaviour. In this it strengthens the case for institu-
tional interpretations of political life and activity.