Democratic Deficit and the Majority Principle
Hannu Nurmi ∗
Department of Political Science and Contemporary History
University of Turku
Finland
Abstract
The concept of democratic deficit refers to the discrepancy between
the decision outcomes of the representative institutions and the opinions of the electorate. Whenever these two coincide, the democratic
deficit vanishes.
We shall first deal with the simplest settings that involve only two
decision alternatives and two levels of decision making. It will be seen
that here we may encounter the democratic deficit in its plainest form:
the clear majority of voters preferring alternative a to alternative b,
while a vast majority of representatives having the opposite preference
even though every representative correctly votes according to the opinion of the majority of his/her electors. The culprit responsible for the
democratic deficit is the majority rule, simple or qualified.
With three or more alternatives the will of the people can become
inherently ambiguous, i.e. procedure-dependent. It turns out that a
major culprit is again the majority principle. The avoidance of democratic deficit in representative systems without sacrificing the majority
principle seems impossible, pace those deeming the majority principle
as a necessary ingredient of democratic governance.
Do the new advances in electoral system design provide ways to
ameliorate democratic deficit? With appropriate (cryptographic) methods that guarantee ballot secrecy, correct counting of ballots, random
sampling of voters and speedy processing of ballots, we could gradually replace representative systems with direct forms of participation.
We shall discuss these innovations and argue that the problems related
to the agenda control make these innovations of rather limited importance in democratic governance. At the same time it is likely that
the role of direct participation – possibly augmented with deliberative
processes – will increase in the future largely as a result of the electoral
innovations.
∗
The author wishes to acknowledge Andranik Tangian’s many useful comments on an
earlier version.
1
1
Introduction
Abraham Lincoln’s well-known definition of democracy as the government
of the people, by the people and for the people contains the basic goals
customarily associated with democracy. The first part, ‘of the people’, does
not require further commentary since it merely delineates the subjects of
government. The second and third parts are less obvious. Does the second
goal, ‘by the people’, mean that only direct forms of government will be
democratic or can indirect, representative forms also be included? Does ‘for
the people’, in turn, mean that only Pareto optimal political (i.e. those that
can be achieved without diminishing anyone’s welfare from the level of the
status quo) outcomes are justifiable? Upon strict literal reading no present
day democracy works according to the latter two desiderata; all systems
involve a significant, even dominant, degree of representative governance.
Moreover, very often the benefits accruing to a group or stratum of the
society are achieved at the loss of other strata or groups. This does not, of
course, in any way diminish the value of Lincoln’s definition as a normative
goal.
Very often the ‘by the people’ is translated into ‘by a majority of the
people’ and somewhat less often ‘for the people’ into ‘for a majority of the
people’. The reason for these translations is typically practical: there is
no unanimity or even near unanimity about policies or candidates in the
electorate. Hence, the requirement of consensus regarding the courses of
action collectively pursued would leave us completely empty-handed. Thus,
by diminishing the number of voters whose consent is required for collective
decisions one has better chances of getting motions passed in legislatures
and persons elected to public offices. An inevitable consequence is that in
most cases there will be voters whose opinions do not coincide with the
victorious policy options or candidates. Therefore, a democratic deficit is
simply a consequence of the lack of consensus among voters. What majority
seems to guarantee, however, is that in dichotomous choice situations the
deficit always victimizes strictly less than a half of the electorate. If higher
than majority thresholds, qualified majorities, were in use, the proportion
of frustrated voters could be larger. This would be the case if the status quo
is regarded worse than a given policy option by a larger than majority but
smaller than the required qualified majority of voters.
In this paper we shall dwell on the relationships between the majority
rule and democratic deficit. Our approach is purely theoretical, but at the
same time applied. To wit, we shall look at the implications of several wellknown results of social choice theory in an effort to trace their consequences
for the design of democratic decision making institutions, especially voting
systems. Surely, democratic deficit can also pertain to situations involving
no voting at all. Instead, other ways of achieving collectively binding decision are resorted to, e.g. bargaining among interest organizations. These
2
are beyond the scope of the present paper. In what follows we shall first
look at the main justifications of the majority rule. Thereafter, we discuss
a couple of majority voting paradoxes that may be encountered in dichotomous settings. We then move on to more general k-option choice situations
and see that the majority principle becomes inherently ambiguous there.
This ambiguity seriously undermines efforts to use the majority preferences
as tokens of the will of the people. In particular, the majority should not be
considered as an actor like in ‘by the people’ nor an object like in ‘for the
people’. We shall then consider the role of some modern innovations in reducing the democratic deficit. Our focus is on some versions of e-voting and
deliberative mechanisms. While a completely satisfactory e-voting mechanism is yet to be found (Galois 2015), some shortcomings of the existing
systems may be improved in several respects (e.g. verifiability of the ballot
assignments). From the democratic deficit viewpoint more promising are
attempts to combine deliberative mechanisms with agenda-formation in referenda. The work of List et al. suggests that deliberation may bring about
preference domain restrictions that are conducive to stable voting outcomes
(List et al. 2013). Hence, some types of preference aggregation paradoxes
may be avoidable through deliberative agenda-formation.
2
Why majority rule?
When a group of people has to make a choice between two options, say,
to join a trade treaty or not, it seems natural to give each voter one vote
– ‘yes’ or ‘no’ – and count the ballots. Whichever alternative gets more
votes is then declared the winner. Should each alternative get the same
number of votes, then the outcome is a tie. This setting describes the simple
majority rule. More than half a century ago Kenneth May gave an axiomatic
characterization of the majority rule (May 1952). To remind ourselves about
this result, we first define the majority rule in precise terms. There are two
alternatives – x and y – and n voters. We assume that each voter i’s opinion
Di concerning x and y is one and only one of the following: ‘x is strictly
better than y’, ‘x and y are equally good’ or ‘y is strictly better than x’.
These opinions are denoted by Di = 1, 0, −1, respectively. The collective
decision D can have each of these values as well. A group decision function
is then
D = f (D1 , D2 , . . . , Dn )
(1)
Now, denote by N (1) the number of 1’s in the decision function (i.e. the
number of individuals strictly preferring x to y). Similarly, let N (0) and
N (−1) be the number of 0’s and −1’s, respectively, in the decision function.
The simple majority rule can now be defined as follows:
3
Definition 1 Simple majority rule is a decision function that has the values
D = 1, 0 or −1 according to whether N (1) − N (−1) > 0, = 0 or < 0.
May’s characterization involves the following properties:
1. Decisiveness: the domain of f consists of the Cartesian product D1 ×
D2 × . . . × Dn . In other words, the function yields a value for any
combination of individual preferences over x and y.
2. Anonymity: any permutation of the individuals leaves the value of D
unchanged. That is, only the number of 1’s, 0’s and −1’s, not how
they are attached to specific individuals, determines the value of f .
3. Neutrality: f (−D1 , −D2 , . . . , −Dn ) = −f (D1 , D2 , . . . , Dn ). In words,
if everyone changes his/her mind so that those strictly preferring x to
y now strictly prefer y to x and vice versa and, moreover, those who
are indifferent between x and y, remain indifferent, then the outcome
should change from 1 to −1, from −1 to 1 or remain unchanged if it
was a tie.
4. Positive responsiveness: only one voter’s change of mind is required
to break a tie. More formally, if D = f (D1 , D2 , . . . , Dn ) = 0 or 1 and
if a new profile is formed so that all individuals except i keep their
opinions unchanged and i changes his opinion from −1 to 0, from
−1 to 1 or from 0 to 1, then x is chosen under the new profile, i.e.
D0 = f (D10 , D20 , . . . , Dn0 ) = 1.
May’s characterization theorem states that a group decision function is
the simple majority decision if and only if it satisfies decisiveness, anonymity,
neutrality and positive responsiveness. Arguably these properties are quite
natural and plausible. The first property pertains to the general applicability of the function in guaranteeing that under all opinion distributions a
collective decision can be found. The second and third properties, in turn,
exclude discriminating decision function. The fourth property, finally, states
that additional support, ceteris paribus, never harms a candidate and that
ties can be broken by the change of mind of a single individual.
The theorem gives quite a strong theoretical reason for adopting the
simple majority rule. Similar, but more conjectural justifications have been
presented by Buchanan, Tullock and Rae (Buchanan and Tullock 1962; Rae
1969). The upshot of all these efforts is that in two-alternative settings the
simple majority rule seems quite plausible. As is well-known, difficulties arise
when more than two alternatives are being considered. Some of these will
be discussed later in this paper. Before that, however, it is worth pointing
out that anomalies can well arise already in the two-alternative settings.
4
voter
voter A
voter B
voter C
voter D
voter E
winner
welfare
X
X
Y
Y
Y
Y
policy area
foreign affairs
X
Y
X
Y
Y
Y
culture
Y
X
X
Y
Y
Y
the voter votes for
X
X
X
Y
Y
?
Table 1: Ostrogorski’s paradox
3
Majority paradoxes in two-alternative settings
Most political decisions involve comparisons of alternatives (candidates, policies) along several criteria. It is quite typical that one alternative is preferred
to another on one criterion, but the preference is inverted on another criterion. When voting for a presidential candidate, we may have a large number
of criteria in mind ranging from purely personal characteristics to stands on
various political issues. In these kinds of situations, the majority may result in an ambiguous outcome. The case in point is Ostrogorski’s paradox
introduced and elaborated by Daudt and Rae (Rae and Daudt 1976; Daudt
and Rae 1978). Table 1 presents a instance of the paradox.
There are two candidates, X and Y, running for presidency and five
voters, A - E, voting.1 Each voter evaluates candidates using three criteria,
say welfare policy, foreign policy and cultural policy. Table 1 indicates for
each voter which candidate is closer to the voter’s policy ideal. Thus e.g.
voter B thinks that X is closer to his/her (hereafter his) ideal position on
welfare and cultural policy, while Y is closer on foreign policy. Let us assume
that each voter deems each criterion of roughly equal importance and casts
his vote for whichever candidate is closer to his position on a majority of
criteria. The right-most column lists the candidates to be voted for by each
voter on the basis of this principle. We see that voters A, B and C would vote
for X since X is closer to their positions on a majority of criteria. Similarly
D and E vote for Y since they prefer Y on every criterion. The outcome
then is that X receives 3 and Y 2 votes. Hence X wins.
Looking at Table 1 from another angle, we see that on the welfare criterion a majority of voters deems Y closer than X. The same is true on the two
other policy areas. Hence, one could argue that the overall winner ought to
be Y as it is the majority winner on all three policy areas. Thus, if the vote
was taken as in a direct democracy – i.e. each policy area being voted upon
1
The number of voters representing each preference rankings can be multiplied with a
fixed constant without changing anything. Thus e.g. instead five we could consider five
million voters with voters A - E standing for one million voters each.
5
voter
voter 1
voter 2
voter 3
voter 4
voter 5
issue
issue 2
Y
X
Y
X
X
issue 1
Y
X
X
Y
Y
issue 3
X
X
Y
Y
Y
Table 2: Anscombe’s paradox
separately – the winner would be Y. This outcome would, however, leave a
majority of voters – viz. A, B and C – frustrated since their candidate in
the indirect election is X. As a consequence of the ambiguity, democratic
deficit will emerge: the issue by issue voting winner Y will be defeated by
the ‘representative’ voting winner X.
Anscombe’s paradox demonstrates a seemingly similar discrepancy between various methods of aggregating votes (Anscombe 1976). The paradox
can be summarized by stating that it is possible that a majority of voters will
be on the losing side in dichotomous voting on a majority of issues. Table 2
illustrates. There two alternatives X and Y are again being voted upon.
Like above, they may be presidential candidates. There are three relevant
issues on which the voters are able to locate the candidates vis-à-vis their
own ideal positions at least to the extent that they can say which candidate
is closer to their own ideal position. The closest candidates for each voter
on each issue are indicated in Table 2. A glance at the table reveals that
this is not an instance of Ostrogorski’s paradox: Y wins on a majority of
issues and by a majority of voters. Instead, we observe that voter 1 is on
the losing side on issues 2 and 3, voter 2 on issues 1 and 3 and voter 3 on
issues 1 and 2. Hence, three voters out of five is in a minority on a majority
(two issues out of three) of issues. Clearly now a majority of voters becomes
a victim of democratic deficit.
The setting of Table 2 invokes incentives for collusion among voters 13. By virtue of constituting a majority these voters may impose whichever
outcome they choose. On the other hand, none of them is likely to agree on
a joint voting strategy that would involve deviating from his true opinion
on two or more issues. However, by coordinating their votes to X, Y, X (i.e.
X on issue 1, Y on issue 2 and X on issue 3) they can bring about this
outcome. This would involve only one change in each of the three voters’
true opinions. Hence, it would make sense for them to coordinate in this
manner.
One could conjecture that qualified majority rules – i.e. rules that require
larger than simple majorities to change the status quo – could eliminate
Anscombe’s paradox and the possibility that the democratic deficit afflicts
6
opinion
yes
no
district 1
45000
55000
...
...
...
district 9
45000
55000
district 10
100000
0
total
505000
495000
Table 3: Referendum paradox
the majority of voters. It turns out, however, that this is not the case (Nurmi
and Saari 2010, Th 6): even if the qualified majority calls for majorities one
shy of unanimity, i.e. n − 1 out of n votes are required for a motion to pass,
it is possible that the majority of voters does not win on any issue.
Both Ostrogorski’s and Anscombe’s paradoxes are related to aggregation. A similar but conceptually distinct paradox that also involves just two
alternatives is called the referendum paradox (Nurmi 1998). It occurs when
the same issue is being voted upon directly by voters and indirectly by their
representatives and when these two votes result in different outcomes. The
wider the margin of victory in the two votes, the more dramatic instance of
the paradox we are dealing with. Table 3 gives an instance of the paradox.
A country of 1 million voters is partitioned into 10 districts of equal populations; each district has 100000 voters. Each district sends one representative
to the parliament. The issue to be voted upon is dichotomous, e.g. joining
or not joining a multilateral trade agreement. Table 3 presents a fictitious
distribution of ‘yes’ and ‘no’ voters in the districts. In the first nine districts
a majority of voters supports the ‘no’ option, while district 10 is unanimously behinds the ‘yes’ alternative. In a referendum the ‘yes’ alternative
wins. Now, suppose that the same issue is subjected to a vote in the parliament. Then 9 MP’s out of 10 have a plausible reason to vote ‘no’ as the
majority of their supporters prefer this alternative. Hence, a clear majority
opinion in the popular vote can – quite plausibly – be contradicted in the
parliament with a large margin. This reminds us of the famous dictum of
the current president of European Commission Jean-Claude Juncker: ‘we all
know what to do, but we don’t know how to get re-elected once we have done
it’ (Juncker 2007). If the opinion of the whole population is ‘what should
be done’, then the MP’s elected from the 9 first districts might have hard
time justifying a ‘yes’ vote the majority of their electors and might, thus,
fail to be re-elected. More importantly, the paradox shows that should the
decisive vote be the one taken in the parliament (as is the case in countries
with consultative referenda), the democratic deficit may afflict a majority
of population even though the margin of majority in the parliament for the
opposite outcome is quite overwhelming.
The referendum paradox shows that in ordinary legislation even large
margins in parliamentary support for legislative proposals cannot exclude
the possibility of the opposite proposals enjoying a large majority support
in the electorate at large. In fact, very little can be inferred about the latter
7
4 voters
A
C
B
3 voters
B
C
A
2 voters
C
B
A
Table 4: Ambiguous majority principle
support on the basis of parliamentary vote margins.
4
More than two alternatives: Condorcet’s principle
In the preceding we have focused on situations involving only two alternatives for the simple reason that it is in these situations that the the simple
majority decision has an unambiguous meaning. With the advent of a third
alternative, the majority decision becomes ambiguous. Consider the following example (Table 4). All three alternatives can be considered winners
under three different procedures each resorting to some majority-related
principle. Firstly, A is the plurality winner, i.e. it is ranked first by more
voters than any other alternative. Secondly, B is the plurality runoff winner since no alternative gets the support of at least half the electorate in a
one-person-one-vote- election. Hence a runoff between A and B – the two
largest vote-getters – is required. In this contest, B wins with 5 votes to 4.
Thirdly, C is the Condorcet winner, i.e. it defeats its two competitors with
a majority of votes in pairwise comparisons (C beats A with 5 votes to 4, C
beats B with 6 votes to 3).
So, the ambiguity between three majority-related principles is maximal
in this setting. Let us see what the arguments against the selection of
each alternative might look like. Firstly, one could object the choice of A by
pointing out that it considered the worst alternative by a majority of voters.
Secondly, against the choice of B one could argue that a majority of voters
prefers another alternative, C, to it. Thirdly, those opposing the choice of
C could point out that C is the favorite alternative of the smallest number
of voters. So, each choice can be objected to with at least a modicum
of plausibility. It is worth observing that all three rules collapse into the
same outcome in all profiles where one alternative is ranked first by more
than half of the electorate since obviously the plurality and plurality runoff
methods coincide as no second round contest is required. At the same time,
the candidate ranked first by most voters becomes the (strong) Condorcet
winner. Hence, no discrepancy between rules emerges.
Despite the discrepancy exhibited by Table 4 and similar settings, the
Condorcet winner is often considered a particularly plausible criterion of
8
4 voters
A
C
D
B
3 voters
B
C
A
D
2 voters
D
C
B
A
Table 5: Condorcet winner ranked first by nobody
winning. Hence, the methods that result in a Condorcet winner when one
exists – the Condorcet extensions – are often deemed superior to the other
main class of procedures, the positional methods (Felsenthal and Machover
1992; McLean 1991; Risse 2001). And indeed, the Condorcet winner criterion is clearly majoritarian in spirit. Additional advantages have been
discovered by Campbell and Kelly (Campbell and Kelly 2015). Using their
terminology, let us call the method that always chooses the Condorcet winner the Condorcet rule. An important result of Campbell and Kelly states
that the Condorcet rule is the only anonymous, neutral and strategy-proof
rule in Condorcet domains (Campbell and Kelly 2003; Campbell and Kelly
2015; Merrill 2011). A rule is strategy-proof if and only if there is no situation where it is manipulable by an individual voter. A rule is manipulable
by voter i in the preference profile P = (P1 , . . . , Pn ) when by changing his
preference ranking from Pi to P ∗i , ceteris paribus, the ensuing outcome is
preferable by i to the original outcome. Thus, strategy-proof rules are not
manipulable by any individual under any profile. Note, however, that the
result is restricted to Condorcet domains, i.e. domains where a Condorcet
winner exists.2 Indeed, by a result of Gärdenfors, all Condorcet extensions
that are anonymous and neutral are manipulable (Gärdenfors 1976). The
result of Campbell and Kelly rests on a restriction of the domain of social
choice functions, viz. to the Condorcet domains.
Despite its prima facie plausibility it is not difficult to see that Condorcet
extensions may lead to severe problems related to the democratic deficit. To
wit, as Table 4 shows the Condorcet winner may be considered best by a
smaller group of voters than any other alternative. In fact, one may envision
settings where the Condorcet winner is not ranked first by a single voter.
Table 5 is an example of this kind of profile. Here C is the Condorcet winner,
but is ranked first by no voter. Thus, if the Condorcet winner is elected, the
democratic deficit afflicts every voter, not just a majority.
2
There are a couple of minor restrictions. Firstly, it does not hold when the number of
alternatives is 2 and the number of voters is even. Secondly, it is not known if the result
holds when the number of voters is a multiple of 4 and the number of alternatives is 3.
9
2 voters
D
C
B
A
2 voters
A
D
C
B
2 voters
B
A
D
C
1 voter
D
C
B
A
Table 6: Subset choices by Borda count
5
Is the Condorcet winner criterion worth holding
on to?
In the debate concerning the relative plausibility of Condorcet winner vs.
Borda winner, an often stated claim is that the Borda winner is crucially
dependent on the alternative set under consideration. More importantly, a
removal of an alternative may dramatically change the Borda ranking between the remaining alternatives. Similarly, adding an alternative may essentially change the Borda ranking among the rest of the alternatives. These
findings were made by Fishburn in his early book on social choice theory
(Fishburn 1973). Consider the 7-voter, 4-alternative profile of Table 6. The
alternatives might be the candidates in the athlete of the year contest where
prominent sport journalists vote on 4 main candidates by indicating their
ranking over these sportspersons.
Borda count results in the ranking D A B C. Before the results
are made known, some evidence turns out suggesting that D is guilty of
using illegal performance-enhancing drugs. D is, therefore, found ineligible
in the contest at hand. Since nothing else has changed in the circumstances,
it is decided that the submitted rankings be used in determining the Borda
ranking over the remaining three candidates. Upon computing the new
scores it is found that the new ranking is C B A, i.e. a complete
reversal of collective preference over A, B and C. Fishburn’s result states
that if alternative x is the Borda winner in set X, there are such profiles that
x wins in only one proper subset of X. Clearly then widening or narrowing
the alternative set opens avenues for outcome control. Could one then find
some other positional procedure that provides more stable outcomes under
variations of the alternative set? Saari’s answer is a resounding: no (Saari
2001). Table 7 shows the extreme instability of the plurality procedure
(Saari 2001, 70).
In Table 7 the collective ranking in terms of the plurality votes is: A B C D. Strike now the last alternative D out and recompute the
plurality scores for the remaining three alternatives to get C B A,
which reverses the previous ranking among A, B and C. Let us now elimate
the lowest-ranked alternative A and recompute the plurality scores to get
10
3
A
C
D
B
6
A
D
B
C
3
B
C
D
A
voters
5 2
B C
D B
C D
A A
5
C
D
B
A
2
D
B
C
A
4
D
C
B
A
Table 7: Instability of plurality procedure
B C, which again reverses the the previous ranking over B and C.
These examples come nowhere near in describing the profound instability
possibilities underlying the positional procedures. These are captured in
Saari’s theorem (Saari 2001, 72).
Theorem 1 Saari 1984. Consider a setting with at least three candidates.
Then proceed as follows:
• rank the candidates in any desired way and choose procedure to be used
in this set of candidates,
• eliminate one candidate, place the remaining ones into any ranking
(independently of the preceding ranking) and choose again a positional
procedure to be applied to this set of candidates,
• continue in this way until just two candidates are left and rank these
two using the majority rule.
There exists a profile which produces exactly the outcomes described above
when the voters vote in each subset using the designated positional procedure.
These profiles are completely chaotic: the result in the superset of alternatives in no way enables one to predict the collective choices in the subsets.
There is no systematic connection between winning in subsets and in the
outcome rankings in the supersets – or subsets, for that matter.
In defense of the Condorcet extensions one could, however, maintain
that removing alternatives from consideration because of ineligibility does
not change Condorcet winners. If an alternative wins all the others in binary
contests by a majority of votes in a set of alternatives, surely it will also
win all the remaining ones if an ineligible alternative is removed. So, Condorcet extensions would seem to be immune to removing alternatives from
the alternative set, while this is clearly not always the case with positional
procedures. There are, however, modifications in the choice setting that
change the Condorcet winner in a implausible way – while not changing the
Borda winner. Consider the profile of Table 8.
11
7
A
B
C
4
B
C
A
voters
4 4
A C
C B
B A
4
B
A
C
Table 8: Condorcet instability
Ignoring the vertical line for a moment, we have a 23-voter profile over
three alternatives. There is a Condorcet winner, viz. B which is also the
Borda winner. Observe that the 12-voter sub-profile on the right-hand side
of the vertical line constitutes a Condorcet-paradox profile: A defeats C,
C defeats B and B defeats A, all with an 8 to 4 margin. Focusing on this
sub-profile only, there is no reason – based on the ranking information only
– to put one alternative ahead of another since each alternative is ranked
first, second and third equally many (4) times. A perfect tie, then, in this
sub-profile. Focus now on the left side sub-profile of 11 voters. There A is a
strong Condorcet winner, but B is the Borda winner. Now, if the 12-voter
sub-profile is a perfect tie, its addition to some profile should, intuitively.
make no difference to the outcome in the latter: if there was a winner,
it should not change by the addition of a perfectly tied sub-profile. And,
indeed, this is the case if the Borda count is applied; B wins both in the
11- and 23-voter profiles. For Condorcet extensions, on the other hand, the
addition of the tied sub-profile changes the Condorcet winner from A to B.
So, both Condorcet extensions and the Borda count are subject to instabilities as the result of various modifications in the choice settings. What
makes the former methods more questionable, however, is the existence of
several results showing the incompatibility of the Condorcet extensions with
some other social choice desiderata. Of particular interest in the democratic
deficit discussion are results showing that all Condorcet extensions are vulnerable to the no-show paradox (Moulin 1988). A no-show paradox occurs
when a group of voters with identical opinions is better off (in the sense
of their own preferences) by not voting at all than by voting according to
their preferences (Fishburn and Brams 1983). In determining whether the
paradox can occur one has to compare two profiles: (i) one where everyone
submits a ranking and the result is determined on the basis of this, and (ii)
one which is otherwise the same as in (i), but a group of identically minded
voters abstains. If the outcome in (ii) is ranked higher in the preference
of the abstainers than the outcome of (i), then an instance of the no-show
paradox has occurred. The no-show paradox comes in two versions: the
‘plain’ one, just defined, and the strong version. The latter occurs when the
outcome in (ii) consists of the alternative ranked first by the abstainers. In
12
1 voter
D
E
A
B
C
1 voter
E
A
C
B
D
1 voter
C
D
E
A
B
1 voter
D
E
B
C
A
1 voter
E
B
A
D
C
Table 9: Black’s method and the no-show paradox
other words, the result of abstaining is not only required to be preferable
to the one in (i), but the best one for the abstainers. Table 9 presents an
instance of the strong version under a specific Condorcet extension, Black’s
method. The method is a combination of two principles: (i) if a Condorcet
winner exists, it is elected, otherwise (ii) the Borda winner is chosen.
In Table 9 alternative D is the Condorcet winner and is, therefore, the
winner of Black’s method. Now, consider the same profile modified so that
the right-most voter abstains. This is now the profile (ii) in the above
definition. In this (ii) profile there is no Condorcet winner. Accordingly, the
Borda winner E is elected by Black’s method. A glance at Table 9 reveals
that E is the first ranked alternative of the abstaining voter. We therefore
have an instance the strong no-show paradox.
Obviously the strong no-show paradox is more dramatic failure of responsiveness of a voting system than the ‘plain’ version of the paradox.
It is therefore worth asking what kind of procedures are vulnerable to this
stronger version. Pérez gives an answer to this question (Pérez 2001): nearly
all Condorcet extensions are vulnerable to the strong no-show paradox. The
only commonly known exception is the max-min rule (Kramer 1977).
From the vantage point of minimizing democratic deficit, the positional
procedures would seem preferable to Condorcet extensions. At least situations resembling that depicted in Table 5 can be avoided by plurality-related
systems. This is, admittedly, not a conclusive argument in favour of positional systems, but in the restricted domain of minimizing democratic deficit
it should have some bearing. By adopting Condorcet extensions one runs
the risk of encountering no-show paradoxes and these undermine the very
rationality of ‘going to the people’, i.e. turning to the electorate for advice.
The Borda count, on the other hand, can be directly related to the minimization of democratic deficit (Nitzan 1981). Consider a profile of individual
preferences over a set of alternatives. Take now any alternative, say x, and
a voter, say i, into consideration and determine the number of pairwise preference switches that are needed to make x the first ranked by i. Obviously
this is the same as counting the number of alternatives ranked higher than
x by i. Considering all voters gives us the sum measure of how far from
13
the observed profile is one where everybody ranks x the first. Comparing
these sum measures of all alternatives suggests a reasonable way of electing
the winner, viz. the alternative which has the smallest sum. It has been
shown by Nitzan that is precisely the Borda winner. This gives us a pretty
strong case for using Borda count as a method: it minimizes the democratic
deficit when the latter is measured as the distance from consensus. Admittedly, this argument against Condorcet extensions rests to some extent on
the definition of the democratic deficit as the difference between collective
outcomes and the individual preference rankings. Should one adopt a different approach to describing voter opinions, the conclusion might also be
different.
We now turn to some ideas, approaches and techniques that have been
developed over the past few decades to overcome the difficulties that are
associated with democratic deficit. Is it likely that the theoretical and
methodological innovations will improve the performance of existing – primarily representative – democracies specifically by reducing the degree of
democratic deficit? Our focus will be on innovations in the two target areas:
deliberative mechanisms and secret balloting in computer networks.
6
Technical innovations and democratic deficit
The first forms of democratic decision making were very different from those
observed in contemporary political systems. Especially, the city states of
ancient Greece – notably Athens – made extensive use of direct democracy.
Moreover, executive offices were typically filled by lot rather than election
(Tangian 2014). Over time, however, representative, election-based systems
have become the predominant forms of the democratic decision making. In
these the population elects a set of representatives who then deal with the
issue of public policy, including constitutional development. Several reasons
for the emergence of representative systems can be envisioned: with the
increasing division of labor and the ensuing complexity of governance, the
amount of time and resources required for handling legislative issues as well
as the very act of balloting have made it impossible for large segments of the
population to engage in direct democracy on a weekly, let alone daily basis. With the advent of modern information processing and communication
technology, this practical impossibility is about to vanish. In other words,
in developed polities basically all citizens could in principle take part in the
making of decisions on a number of issues on a daily basis. Thus, one of the
classic reasons for representative decision making has lost some of its significance. Could one then envision a system where all adult citizens would
– with the aid of modern IC technology – directly participate in legislation
and public policy choice, in general? While no one is seriously proposing a
system of governance based solely on direct democracy, it seems clear that
14
such a utopian system would go along way in minimizing the democratic
deficit – under the important proviso that the system applied in aggregating the individual ballots is reasonable. This proviso has been discussed
above. What we focus on in this section is what kind of opportunities the
modern IC technology provides for reducing the democratic deficit and what
are the main thus far unsolved challenges.
6.1
Agenda control
Regardless of their type (consultative, binding, constitutionally mandatory,
etc) the referenda are the main avenue of direct democracy in modern societies (Setälä 1999). The extent of their use varies a great deal from one
country to another. It is fair to say that they are nowhere the predominant method of making public decisions, but at best auxiliary devices of
popular control over policies and other legislation. Of crucial importance in
referenda is the question that is subjected to a vote, i.e. the agenda. Unfortunately, there are no direct ways of assessing the impact of the phrasing
of referendum questions to the outcomes, but the rich experimental literature on framing effects on individual choice behavior suggests that this is an
issue of considerable importance (Kahneman and Tversky 1979; Quattrone
and Tversky 1988; Shafir et al 1989). The order of voting effects, on the
other hand, have been given considerable attention in the theoretical social
choice literature. The pioneering result in this field is McKelvey’s theorem
on intransitivities of majority preference relations in spatial models of voting
(McKelvey 1979). As will be recalled, it states that in the absence of a core
(a majority undominated alternative), the trajectory of pairwise comparison
winners can lead from any point in the policy space to any other point in it,
i.e. under myopic voting the majority outcome depends solely on the agenda
of pairwise contests. The result assumes that the voter preferences have a
continuous utility presentation in the policy space. The conditions under
which the spatial voting game core is empty have been studied by Banks,
Saari and Schofield (Banks 1995; Saari 1997; Schofield 2008). The main implication of McKelvey’s theorem is thoroughly negative: in the absence of a
Condorcet winner-like alternative, the outcomes of pairwise majority voting
are basically arbitrary. In particular, they may not even be ‘close to the preferred alternatives of the individuals. In other words, with myopic voting
a fully informed agenda-controller essentially determines the outcomes of
pairwise majority voting. And yet, at each stage of the process, the winning
alternative is majority-preferred to the losing one, i.e. a ‘democratic’ choice
in the majoritarian sense.
A customary objection raised against the use of referenda is that the
voters allegedly use the opportunity to voice their opinions on other matters than the referendum issue, e.g. their opinion about the government or
the head of state. While this may, indeed, be the case, the plausibility of
15
this objection is questionable. Firstly, the objection may equally well be
used to support referenda so that the voters could signal their opinions on
more matters and, therefore, need not take the opportunity to ‘punish’ their
government, but rather its policies. Secondly, it is always possible for the
voters to cast their votes having something else in mind than the referendum
issue. In tactical voting (or – in more technical parlance – manipulation)
this happens most of the time in voting by representatives in parliaments.
Tactical considerations most certainly enter into the debates (and voting)
in parliaments when the referendum issues are being dealt with. In this
phase approaches stemming from the deliberative democracy might be useful. After all, deliberative democracy is more about discussing the issues
than settling them once and for all (LeDuc 2015, 140). It would thus seem
that deliberative bodies would have a useful role to play in the preparations
preceding referenda.
Another perhaps more technical and conjectural role could be envisaged
to deliberative bodies in the process of translating popular opinions into collective decisions bypassing the parliaments: the restriction of the domain of
opinions. More than half a century ago Duncan Black introduced the notion
of single-peaked preferences (Black 1948) and showed that if the preferences
of voters can be represented by single-peaked utility functions, the pairwise
majority voting could not end in a cyclic majority preference relation. This
result has subsequently been specified and extended in many directions.
E.g. Shepsle and Weingast argued that the legislative committee system
can under some circumstances act as a mechanism whereby legislative outcomes emerge as structure-induced equilibria as a consequence of the process
whereby each committee handles the issues from a single-dimensional perspective (Shepsle and Weingast 1981). Perhaps deliberative bodies could
perform similar dimensionality reducing activities as legislative committees
thus making the decision alternatives more transparent and manageable.
Some evidence to this effect already exists (List et al. 2013). Perhaps they
could even transform some opinion distributions into the Condorcet domain
(cf. the discussion on Campbell and Kelly’s theorem above). In any event
all mechanisms that might curtail the possibilities of agenda manipulation
are also devices that make referenda meaningful. As such deliberative institutions are well worth pondering about.
6.2
Elections in computer networks
The almost universally declining voting turnouts have prompted ideas to
resort to ICT in governance, in general, and elections, in particular. Indeed,
some countries – notably Estonia – already resort to electronic voting in computer networks (see www.vvk.ee/voting-methods-in-estonia/engindex/reportsabout-internet-voting-in estonia). Advantages of this are several: the convenience of voters, the speedy determination of election results, the inter16
pretation of the voter’s intention expressed in balloting, the reduced costs in
administering the election locales, to name a few. At the same time, there
are several weaknesses: the possible exclusion or alienation of voters not
used to computers, possibilities of failures due to technical problems (cuts
in electricity supply, hardware failures), possibilities of large-scale electoral
fraud by hacking the voting system, the possibility of breaches in ballot secrecy. These caveats notwithstanding, it is reasonable to ask if ICT based
voting would ameliorate concerns of democratic deficit.
Obviously, internet voting makes the act of balloting a lot easier – at
least to the computer-savvy voters – than the traditional voting in designated locales at publicly announced times using the equipment at hand
there. By the same token, elections and referenda could, technically, be used
much more frequently than currently. Hence, the possibilities for resorting
to direct democracy would be improved. At the same time, however, new
problems arise. To wit, how to combine the results of frequently held referenda into a coherent and consistent policy? The aggregation paradoxes
dealt with above can also be viewed as paradoxes pertaining to amalgamation votes on separate issues into public policy. In representative systems
it is the task and duty of political parties to present coherent and consistent policy alternatives to voters to be voted upon. The introduction of
frequently held policy related referenda would seem to diminish the role of
parties as organizers of interests or as agents of interest aggregation, in the
preferred parlance of scholars of the structure-functionalist persuasion.
So, ICT voting is certainly not a panacea, but it can rectify some shortcomings of existing voting systems. Of particular interest is the possibility
for voters to ascertain that their vote has been correctly counted. With
modern public-key cryptography methods have been developed to make this
possible without sacrificing ballot-secrecy, one of the corner-stones of democracy (Chaum 2004; Nurmi,Salomaa and Santean 1991). Similarly, cancelling
and re-casting one’s ballot can be made possible with use of cryptographic
protocols. The main obstacle in the way of large-scale adoption of ICTreliant balloting methods is the fact that with internet voting the conditions
under which the ballots are cast cannot be supervised by the voting authorities. Hence, there is no way of ascertaining whether the ballots have been
cast under morally acceptable circumstances (and not, e.g. at gun-point).
The Estonian voting protocols mix traditional voting (paper balloting at supervised locales) with the internet one in the sense that a voter can always
cancel his electronic ballot, show up at an election locale and re-cast his
ballot. Thereby the incentives for buying votes or forcing voters to vote in
a certain way are expected to be eliminated.
So, the ICT-based approaches to voting can be of considerable benefit
should one wish to engage the electorates in frequent referenda. As such
they do not, however, provide any means to counteract one of the most
serious drawbacks of referenda, viz. agenda manipulation. It seems that
17
deliberative mechanisms have some potential in curtailing the possibilities
of agenda manipulation. The extent that deliberative democracy can be
implemented using ICT remains to be seen. Anyway, it is at the intersection
of modern ICT and deliberative mechanisms that the most important steps
in direct democracy are likely to be taken.
6.3
Elections by sampling
Frequent, large-scale opinion polls and surveys are nowadays a common practice in all developed democracies. As far as the election polling is concerned
the opinion polls are also becoming increasingly accurate tools to predict
the election results.3 So, why not use a random sample of voters instead
of the population of active voters as the proxy of ‘demos’ ? This would in
a way continue the ancient Greek tradition of selecting the rulers by lot, a
tradition that has largely been forgotten over the past two millennia.4 Some
recent work aims at reviving the lottery as a method of democratic governance and using a truly random sample of the electorate to determine the
election result (Chaum 2015). The main advantage of random sample voting
(RSV) is the dramatic reduction of costs of a single election. This enables
the arrangement of a large number of elections and/or referenda without
increasing the overall expenditure on democratic decision making. Several
other advantages are also attributed to RSV. To wit, they provide more
incentives to participation than the traditional mass voting. This is due to
the fact that the likelihood of an individual voter in determining the election outcome is much higher in a random sample than in the population at
large. Similarly, the fact that a random – possibly small – sample of voters
determines the outcome of balloting changes the circumstances of election
3
Two recent quite high-profile failures in accuracy should, however, be born in mind:
the result of the UK parliamentary election of 2015 and the Greek referendum on the
financial package offered by the ‘institutions’ in July of 2015. In the former case, most
pollsters predicted a nearly even contest between the Conservative and Labour parties,
while the Conservatives in fact defeated Labour hands down. In the latter, the ‘yes’ and
‘no’ sides were estimated to be of roughly equal strength with ‘yes’ the slightly more
likely outcome, but in fact ‘no’ gained more than 60% of the votes. The vice-president of
World Association of Public Opinion Research, Claire Durant, reports in the context of the
Scottish 2014 referendum that there seems to be a tendency that the polls systematically
underestimate the support of ‘no’ side due to the fact that persons who do not disclose
their opinion are predominantly ‘no’ supporters (Durant 2014). The present author is
grateful to Andranik Tangian for reference to Durant’s work.
4
The ancient methods of election and governance are described in detail in (Tangian
2014). In fact, Aristotle considered both lottery and election as democratic methods,
provided that the body consisting of all citizens appoint from the set of all citizens by
using either of these methods. When some citizens – i.e. a proper subset of all citizens –
appoint by lot or by election from the set of all citizens, then the method is oligarchic in
Aristotle’s terminology (Aristotle, 100a31). Obviously this terminology has not survived
to the present day. Note, however, that Aristotle was not a proponent of democracy, but
‘mixed’ forms of government.
18
campaigning and advertising. To the extent that differences in resources
allocated to these activities creates a bias in the results in mass elections,
the higher relative cost of a single vote can diminish this bias. RSV also
enables the voters to ascertain the integrity of the ballot counting system in
a mathematically proven and yet relatively easily understandable manner.
Buying votes is made much more costly per vote than in mass election since
the voters whose ballots will be counted is not known to the buyers. By the
same token the coercion of voters is made far more difficult than in mass
elections. These are the main advantages of the RSV when compared with
mass elections. For details, see (Chaum 2015).
To an extent RSV only extends the practice of opinion polls and surveys
to a new level, viz. the collectively binding decisions. The main hurdle in its
adoption will no doubt be the perceived legitimacy. Is the electorate willing
to accept as legitimate the outcomes determined on the basis of finding out
the opinion of a small subset of it? Are people willing to play a part in
elections where it is not certain that their vote will be taken into account in
determining the outcome? This remains to be seen. For the purposes of this
paper RSV has a lot of potential in reducing the democratic deficit. This
is mainly due the possibility of conducting a large number of elections that
reliably reflect the opinions of the electorate on a large number of issues.
At the same time, the consistency and coherence of policies chosen is not
guaranteed. Also the possibilities of agenda control remain.
7
Conclusion
Democratic deficit is a somewhat loosely defined concept, but in this paper it
refers to a discrepancy between collective decisions and individual opinions.
In the preceding we have argued that equating the will of the people with the
will of the majority of people aggravates the democratic deficit. As is known
from Condorcet’s paradox, majority may be endowed with a ‘will’ that is not
even structurally similar to the will of any individual in the group. Majority
rule is, nonetheless, a clearly definable and often used method for teasing out
the will of the people. We have seen that – in contrast to a common opinion
– it may lead to paradoxes already in two-alternative contexts. From the
viewpoint of democratic deficit minimization it is important to note that its
extension to multi-alternative settings, the Condorcet extension methods,
may end up with alternatives that maximize the democratic deficit in the
sense of producing choices that are most preferred by no one in the electorate.
This suggests that perhaps positional methods could be more useful in an
effort to minimize the democratic deficit of outcomes. The distance-based
definition of the Borda count suggests a solution to the deficit minimization
problem: select as the collective choice the alternative that can be made
unanimously first-ranked with a smallest number of individual preference
19
switches of adjacent alternatives. If the manipulability of the Borda count
is viewed unacceptable, one could suggest Kemeny’s rule which – given the
reported individual preference ranking – determines the closest unanimous
ranking obtainable from the reported rankings with the smallest number of
preference switches between adjacent alternatives. As the result of Campbell and Kelly shows, this would guarantee non-manipulability in Condorcet
domains. As a drawback this method is afflicted by all those undesirable
properties that characterize Condorcet extensions (including the vulnerability to the no-show paradox). So, our search for a unique democratic deficit
minimizing method turned out to be inconclusive.
We also touched upon issues that may affect democratic deficit from the
outside of voting procedures. We argued that deliberative mechanisms may
be helpful in phrasing the referendum questions and restricting the domains
of preference profiles. The internet voting techniques can also be useful
in expanding the possibilities of direct democracy which presumably is the
best way of finding out the will of the people. The problems of aggregating
separate referendum outcomes into consistent policies, however, loom large.
Random-sample voting is a new approach to democratic governance. Its
basic principles are well in line with the minimization of democratic deficit,
but it still faces hurdles related to legitimacy and consistency.
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