Content uploaded by Federico Perali
Author content
All content in this area was uploaded by Federico Perali on Mar 31, 2015
Content may be subject to copyright.
64% Majority Rule in Ducal Venice: Voting for the Doge
Author(s): Jay S. Coggins and C. Federico Perali
Source:
Public Choice,
Vol. 97, No. 4 (1998), pp. 709-723
Published by: Springer
Stable URL: http://www.jstor.org/stable/30024456
Accessed: 01/10/2009 15:13
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless
you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you
may use content in the JSTOR archive only for your personal, non-commercial use.
Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
http://www.jstor.org/action/showPublisher?publisherCode=springer.
Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed
page of such transmission.
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of
content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms
of scholarship. For more information about JSTOR, please contact support@jstor.org.
Springer is collaborating with JSTOR to digitize, preserve and extend access to Public Choice.
http://www.jstor.org
Public Choice 97: 709-723, 1998.
@ 1998 Kluwer Academic Publishers. Printed in the Netherlands. 709
64%
Majority
rule in Ducal Venice:
Voting
for the Doge*
JAY
S. COGGINS' & C. FEDERICO PERALI2
'Department of Applied
Economics, University
of Minnesota,
St. Paul, MN 55108, U.S.A.;
21stituto
di Economia e Politica
Agraria, Via
Artigliere,
8, 1-37129 Verona,
Italy
Accepted
24 October 1996
Abstract. A recent
result of Caplin
and Nalebuff
(1988) demonstrates
that,
under certain con-
ditions on individual
preferences
and their distribution across
society, super-majority
rule
per-
forms
well as a social decision rule. If the required super-majority
is chosen appropriately,
the
rule yields a unique
winner and voting cycles cannot occur. The voting procedure
for electing
a Doge in medieval
Venice,
developed
in 1268, employed
a super-majority
requirement agree-
ing with the Caplin
and Nalebuff formula.
We present
a brief history
of the Venetian
political
institutions,
show how the rule was employed,
and argue
that
it contributed to the remarkable
centuries-long political
stability
of Venice.
[The Venetian
government] preserved
itself for hundreds
of years in the
same form
and without sedition or civil discord. This was not because the
Venetians held no hatred or enmity as in other
cities, ... or because
there
were no ambitious and ill-regulated
minds that would generate
disorder
if they could. Rather,
it was because the orders of government
were such
that these elements were kept under control
(Guicciardini,
1973: 186).
1. Introduction
During
its golden age, Venice was among
the world's
premier
cities, boasting
a population
of some 160,000 in the year 1300. Her citizens were innova-
tors in commerce,
in armaments,
in architecture and the arts,
in the creation
of ocean-going vessels and in their navigation.
As merchants and artisans,
manufacturers and
craftsmen,
marauders
and statesmen,
they had few peers.
From the sixth century
to the end of the eighteenth,
Venice was a separate
state,
entirely independent
after
810. At a time when most political commu-
nities across the globe experienced
the rise of monarchies,
Venice retained
her republican
city-state institutions and continued as a potent diplomatic
and commercial force from
England
to Russia.
* We wish to thank
Jim Andreoni,
David Canon, Ian Coxhead, Bob Haveman,
and Andy
Reschovsky
for providing helpful
comments
on an earlier version.
710
How was Venice able to preserve
herself for over 12 centuries,
her status
as a financial
center and, especially in the last three centuries,
as an artis-
tic center intact and for lengthy
periods
unchallenged?
The secret
appears
to
lie to a considerable
degree
in the political institutions
by which Venice was
governed.
From
about 1000 onward,
there
appeared
a steady
flow of innova-
tions in the political processes by which public decisions were reached and
executed. The element of chance, as we shall see, played a central
role in
political life. Even more
important,
though,
was the menu of nomination and
voting schemes used by the leading families to elect officers
to posts all the
way from minor
administrative
councils to the pre-eminant political
office of
the city, the dogeship
(or dukeship)
of Venice.
The Venetians were innovators. It is hard to imagine that they were ever
further ahead of their
time than
when
they
devised the elaborate
voting
scheme
to choose a new Doge - the head of state who served a life term
-upon the
death
of the old. The scheme is of intrinsic
interest
for the way it foiled fac-
tionalism among the aristocratic class that participated
in government.
The
Venetians'
profundity
appears
to have run even deeper.
In designing the bal-
loting rules for filling the paramount
office of the land,
they anticipated
with
pin-point accuracy, by 720 years, a recent formal result on super-majority
rule due to Caplin
and Nalebuff
(1988).
Some two centuries
ago Condorcet
noted that simple majority
rule is ill-
behaved as a social decision rule. It is possible in the simplest situations
that no alternative can defeat all others in pair-wise voting, in which case
the rule produces no solution at all. Chaotic voting cycles are also possi-
ble, in the sense that
any alternative can be selected as the final outcome of
a carefully chosen agenda (McKelvey, 1979). Black (1948) suggested that
a super-majority
rule, in which an alternative defeats the status
quo only if
strictly
more than half of the voters
prefer
it, might
remedy
these difficulties.
Caplin
and Nalebuff
(1988) verify Black's insight,
establishing
conditions
on
individual
preferences
and on their distribution across society under which
super-majority
rule possesses some crucial
desirable
properties.
They derive
a precise super-majority
requirement
- which approaches
64% as the dimen-
sionality
of the issue space grows large
- guaranteeing
existence of a unique
winner
which is stable
in that no voting cycles are
possible.
The elaborate
process
by which the Venetian
Doge was elected culminated
in a vote requiring
a super-majority
that matches the Caplin and Nalebuff
(1988) requirement
as precisely as was possible for the choice setting that
was used. Our
purposes
are to present
the electoral
institution for choosing
the Doge, to argue
that the scheme itself contributed to the relative and
lasting
stability
of Venice as a political entity,
and to bring
to readers an awareness
of the remarkable
prescience
of its inventors.1
711
2. Politics
in the Venetian
Republic
Venice stands on a collection of islands lying in a saltwater
lagoon at the
northern
tip of the Adriatic Sea. Canals divide the city, and boats are the
Venetians' only mode of transit. The present-day
visitor can approach
by
sea or by a lone bridge
connecting
to the mainland. Much of the beauty and
charm that
attract visitors inhere
in the water that
engulfs the city. The geo-
graphical
setting doubtless
helps to explain
Venice's
longevity as a republic,
for it made defending
her relatively easy.
More important
in explaining the stability and durability
of the Repub-
lic were Venice's myriad political institutions,
including the provisions for
electing officials to public
office that animate
our
paper.
Developed
primarily
from 1000 through 1300, their foremost and deliberate aim was to foil the
factional battles that
during
the same period
often rent mainland monarchies
asunder. The Venetian
government
was an oligarchy.
Suffrage
never reached
the general population,
but was limited to a class of male elites or nobles
whose status was due either to birth
or, generally,
to commercial success.2
In theory,
important political decisions were also to be guided by the will
of the population
or arengo. The early Doges, each serving a term for life,
were absolute monarchs who often sought
to create
dynastic
power by pass-
ing the title on to a son. This impulse
went against
the tradition of "popular"
government
that had undergirded
independence
from the beginning.
In 1032
the Orseolo
dynasty
was overthrown
and a new Doge was elected along with
two ducal counsellors whose duty
was to squelch
any attempt by the Doge to
create
another
dynasty.
Thus was set in motion a series of collective decisions to control the pow-
er of the Doge and spread
public decision-making
widely among the ruling
elite. Major
constitutional reforms under
Doge Sebastiano
Ziani,
in 1172 and
1173, strengthened
the system of checks and
balances. The number of ducal
counsellors was increased from
2 to 6. A new council of 480 leading
citizens
- the Great Council
- was established. Its members were elected for only one
year,
and
among
its duties
was the selection of all of the chief public
officials.
It was also charged
with naming
a committee of 11 who were given the task
of electing the new Doge, ensuring
that he would be unable to choose his
own successor.
In 1185 the number
of ducal electors was increased
from 11 to 40. The
old system of nominating
the 11 from the Great Council was supplanted by
a nominating
committee of 4, who elected the 40 electors. In 1229 a Doge
election resulted
in a tie vote between Marino Dandolo and Giacomo Tiepo-
lo. The two men cast lots for the dogeship,
and
Tiepolo, who had
earlier won
acclaim as a diplomat
and statesman,
now also won the draw.
(In order to
avoid another tie the number of electors was increased to 41 soon afterward.)
712
Though
he had
gained by it Doge Tiepolo evidently
found the random selec-
tion distasteful,
and
during
his tenure he devised his celebrated set of statutes
(statuti)
aimed at striking
a balance between the power
of his own office and
the power of his advisors to restrict him. These statutes became the code
of Venetian law. In the ensuing years Tiepolo's code was modified, until in
1268 it reached a state that changed
very little, and only gradually,
for five
centuries.
Tiepolo's rules spelled out the procedure
for electing the Doge. They also
created a collection of advisory
bodies and councils and laid out their func-
tions and the procedures
for filling them. One purpose
of this scheme was
to promote
the stability
of the governance
structure.3 The largest
body was
the Great
Council, which included
"all
the most important people who were
available
in Venice and a sprinkling
of others"
(Lane, 1973: 96). In 1297 the
eligibility rules for the Great Council were revised to exclude all except
those
from the oldest families and to fix the list of eligible citizens. One result of
this serrata or closure was that
membership
rose over the
next
few decades as
more citizens hurried to establish their
eligibility.4
Another was that,
under-
standably,
the excluded
majority
were distraught
over the new arrangement,
but their
distress led to rather less unrest than might
be expected (Norwich,
1982: 184). Above the Great
Council,
but elected
by and
drawing
their
power
from it, were the Council of Forty
and the Senate.
Directly above these two
bodies in authority
was the six-member
Ducal Council. The three Heads of
the Council of Forty,
together
with the members of the Ducal Council and
the Doge himself, made up the Signoria, which was ultimately responsible
for conducting
the business of the government.
In later centuries this arrangement grew increasingly complex as new advi-
sory and administrative councils were created
for a variety
of purposes.
Two
elements of the scheme remained constant. One is that with a single extra-
ordinary exception all officials above the level of the Great Council served
very short terms
- generally
one year or less. The other is that nominations
for and elections to office were carried out using an amalgam
of lotteries and
actual
voting. Some candidates
were nominated
by the Signoria and others
by committees chosen by lot from the Great Council. The court of the Doge
included a boy or young man, the ballottino,
who cared for the small balls
(ballotta)
and urns that
were used as lottery
instruments.5 In some elections
he was responsible
for drawing
the ballotta on behalf of the nobles. Most
elections then took place in the Great Council. The practice
of election by
lottery was not uncommon
in the period, but only in Venice was a scheme
devised to exploit the virtue of lotteries
- their
tendency
to restrain
corrup-
tion - while negating through
the use of election their
leading
drawback
- a
clearly inferior
person may be elevated to a post above his level of ability.
713
In general the highest posts were occupied by men with a long and distin-
guished
record of public
service, high personal
merit and
integrity
and
public
esteem.
A number of measures to control
factionalism,
corruption,
and graft
were
employed. Office holders
were not permitted
to succeed themselves, though
many spent their careers
moving from one office to another. No family was
permitted
more than one member on the Ducal Council or any significant
nominating
committee or administrative board.
A nominee's relatives were
prohibited
from
voting
in an
election involving
him. Campaigns
were
entirely
forbidden;
men were sought
by offices rather than the other
way round. Once
elected to an office a person was required
to serve, and a heavy fine was
levied against
those who declined.6
In the middle
part
of the thirteenth cen-
tury
a public
brawl between two families led to a prohibition
against display-
ing family emblems or escutcheons on buildings.
The use of lot for choosing
nominating
committees was also meant to contain
factionalism and corrup-
tion.
The unique
and
outstanding exception
to the custom of brief terms of office
was the dogeship.
Though
this office carried less authority
after
the reforms
of Doge S. Ziani than it once had, the power and prestige
of the Doge were
considerable.
Evidently
the Venetians considered
the stability
fostered
by a
lengthy
term
to outweigh
the dangers attending
it. The Ducal
Council limited
the Doge's authority,
but the delicate task of electing the chief executive of
the government
(which took place while the state was in a form of crisis, its
head
having just died) was of paramount
importance.
It therefore
presented
a case in which a false step could not be taken
without the severest prejudice
to the national
interests;
and under such
circumstances,
it was no matter of wonder,
that there
should be an anxiety
to secure the
exercise of a mature
and
impartial judgment
and to minimize
the liability
of the process
to corrupt practices
(Hazlitt, 1900: 398).
The exceedingly
complicated
and
thoroughly
choreographed process
for choos
ing a new Doge and handing power to him represents the Venetians'
crowning
achievement
in the art of electoral
politics.
3. Electing the Doge
On the day of the Doge's death, the political apparatus
of Venice was in a
rather
fragile state. The eldest of the Ducal Counsellors was automatically
appointed
the Vice-Doge, but any faction wishing to subvert the procedure
and claim the ducal throne illegitimately would be tempted
to choose this
714
moment.
The ceremonies
to be held and rituals to be followed occupied
up to
a month's
time, and
only after their
completion
could a successor be elected.
In this period,
for practical purposes
the government
ceased to function. Not
once in the 500 years during
which the doge electoral scheme was in use
(from 1268 to 1797) was an insurrection
attempted
at this critical
juncture.
On the morning following the Doge's death the members of the Great
Council at least 30 years of age convened in the Council Hall in the Ducal
Palace. (In the Appendix
we present
a direct translation of the instructions
that
were followed in electing a Doge.) Its first
task
was to elect members to
two committees.
One, including
five members,
was to revise the ducal oath
or
promissione
(a set of rules
of conduct
for the Doge).7 The other,
including
three
members,
was to put
in order the financial affairs
of the deceased
Doge.
Its second task was to select a new ballottino who would serve throughout
the new Doge's term.8
All that followed required
his services.
The Great
Council having gathered
in its chambers,
a count was made of
the members
present.
In a balloting
urn
at the front were placed a number of
balls, their
number
equalling
the number
of members.
All but 30 of the balls
were silver;
the remaining
30 were gold. Each member
approached
the urn,
and the ballottino drew
a ball for him. Members
drawing
silver balls left the
hall straightaway,
while members
drawing gold balls immediately
withdrew
to an inner chamber.
Their relatives were
required
to leave the hall, according
to the prohibition
against
more than one family member
serving
on a nomi-
nating
committee.
The 30 so chosen drew once again,
this time from an urn
containing
30 balls of which 9 were gold and the others
silver.
Those drawing
silver balls left the ball and
the 9 retired once again
to the inner
chamber and
nominated 40 members,
"with the freedom to choose nominees from within
and outside
the Council"
(Cessi, 1968: 253). Each
member
nominated
at this
stage (which could of course take some time) was required
to receive at least
7 votes.
Upon completion
of the list of 40, the Great Council was reconvened,
and
the 40 names
were called out. These 40 were reduced
by lot to 12, in the same
manner as before.
The 12 nominated
25, with each
required
to receive
at least
9 votes. The 25 were reduced
by lot to 9, and the 9 nominated
45, with each
required
to receive at least 7 votes. The 45 were reduced
by lot to 11, and
the 11 nominated
41 Ducal Electors,
with each required
to receive at least 9
votes. At each stage
of the procedure,
the Great Council
was reconvened,
and
each slate of nominees
was required
to include no more
than one member of
any family.
The 41 Ducal Electors were charged with electing the new Doge. This
they
did by first
retiring
to the inner
chambers,
taking
the balloting
turns urns
715
with them.
The ensuing
procedure
is described
by Norwich
(1982: 166-167)
as follows.
Each elector
wrote the name of his candidate on a paper
and
dropped
it in
the urn;
the slips were then removed and
read,
and a list drawn
up of all
the names
proposed,
regardless
of the number of nominations for each. A
single slip for each name
was now placed in another
urn,
and one drawn.
If the candidate
concerned
was present,
he retired
together
with any oth-
er elector who bore the same surname,
and the remainder
proceeded
to
discuss his suitability.
He was then called back
to answer
questions
or to
defend
himself against
any accusations.
A ballot followed. If he obtained
the
required twenty-five
votes, he was declared
Doge; otherwise a second
name was drawn,
and so on.
The lengthy
process
reached
its climax, then,
with the selection of the Ducal
Electors and their
ensuing
deliberations. After the new Doge was elected his
name
was announced
to the entire
Great
Council,
which was then
required
to
confirm him by simple majority
vote (Da Mosto, 1960). After this his name
was proclaimed
to the city, whose citizens thereupon
indulged their fabled
love of pageantry
and
public
celebration.
4. 65%-majority rule and the Doge
With the central elements of the voting scheme
in place we are now prepared
to turn
to its formal properties.
A modicum of notation
shall prove useful.
Suppose that a group
of voters faces the task of choosing collectively a sin-
gle most-preferred
element of some alternative
set X, which is assumed
to lie
in 7Zn.
(The n dimensions of X might capture
the important
characteristics of
alternatives.)
Each voter
has a well-behaved
preference
ordering
over X. Fol-
lowing Caplin
and Nalebuff
(1988) let a social decision problem
be denoted
C, consisting of X, the voters, and their
preferences
over X. More than 200
years ago, Condorcet
discovered the curiosity that majority
rule performs
badly as a social decision rule, for even in a simple example it is possible
that
no majority
rule winner exists. Arrow
(1963) showed
that the problem
is
much more difficult
than was thought
previously:
in general
it is impossible
to devise any rule
that
compiles individual
preferences
into a collective pref-
erence ordering
without
violating at least one of a seemingly innocent
set of
conditions. Even when preferences
are required
to satisfy the rather
strong
Euclidean
assumption,
Plott (1967) and Kramer
(1973) showed that if n >
2 a majority-rule
winner almost never exists. McKelvey (1979) later showed
that a sequence
of pairwise
votes can lead to an outcome
anywhere
in X. That
is, voting cycles are
potentially
chaotic.
716
Table 1. Super-majority
values for
selected n
n m*(Cn) n m*(Cn)
1 0.5000 8 0.6103
2 0.5556 10 0.6145
3 0.5781 15 0.6202
4 0.5904 20 0.6231
5 0.5981 ... ...
6 0.6034 00 0.6321
Drawing
on another
insight
of Condorcet
(1976), and also of Black (1948)
- that
alternatives
commanding
a large majority
are
in some sense better than
other
majority
winners with a smaller
winning
margin
- Caplin
and Nalebuff
(1988), hereafter
C-N, recently produced
a more
promising
result
on majori-
ty rule.
They devised a precise way to calculate the degree
of super-majority
needed to ensure that the rule always produces
a unique
winner and that no
voting cycles are possible. Let 6 denote the required super-majority.
C-N
demonstrated that if preferences
are Euclidean and if the set of ideal points
is nonatomic on a set S C R", with a concave distribution of ideal points
on
S, then a rule
requiring
a majority
6 equalling
m* (C) = 1-(n/(n+1))n
is well-
behaved in their sense.9
The key to the C-N result
is that
in general
one must
require
a winning margin
strictly greater
than one half in order to guaran-
tee the existence of a unique winner and to rule out voting cycles. Table 1
presents
the required
super-majority
corresponding
to a few values of n.
Caplin and Nalebuff also show that when 6 < m*(C) there is in general
no 6-majority
rule winner and chaotic voting cycles in McKelvey's (1979)
sense are possible. When 6 > m*(C), voting cycles cannot occur but there
are many possible 6-majority
rule winners.
The first difficulty is of course
always serious.
When the aim in a given situation is to choose a unique
most-
preferred
alternative the second difficulty
may also be troublesome,
for the
outcome
ultimately
selected is indeterminate.
Let us now cast the Doge electoral
problem,
as nearly
as possible, in this
framework.
Consider
the set of outcomes (or candidates)
X to be the set of
all members
for the Great
Council, from which the Doge must be selected.
Suppose
that to each member
j can be associated a vector of characteristics
xj
E Rn. For
example,
characteristics
that seemed to play a role in the minds of
electors included a candidate's
age, his wealth,
his public
service
experience,
a notion of his "wisdom" or overall
cognitive
fitness,
and
possibly a measure
of his public acclaim in the entire Council. The dimension of the outcome
717
Table 2. Summary
of the Ducal electoral
procedure
Number of Required
Stage members Action taken super-majority
1 30 Chosen
by lot from the Great Council
2 9 Chosen
by lot from the 30
3 40 Nominated
by the 9 7/9 = 77.8%
4 12 Chosen
by lot from the 40
5 25 Nominated
by the 12 9/12 = 75.0%
6 9 Chosen
by lot from the 25
7 45 Nominated
by the 9 7/9 = 77.8%
8 11 Chosen
by lot from the 45
9 41 Nominated
by the 1 9/11 = 81.8%
10 1 Elected Doge by the 41 25/41 = 61.0%
space, n, is determined
by the number of such characteristics that electors
held in their minds while voting. It is impossible to know this number
pre-
cisely, but it seems likely that it was not less than
4 or 5.10
The C-N result
holds for a finite alternative
set X (which our problem
definitely has), but
they require
the set of voters to be large.
For the Doge problem
the number
of potential
voters
usually
numbered somewhat
between 1000 and
2000, and
the actual number of electors at any given stage
was much smaller than
this.
The two strands of our
story may now be woven together.
In short,
it seems
that the sequence of votes in the electoral
procedure
for the dogeship neat-
ly matches C-N's super-majority requirement.
In total five committees took
part
in elections. (A summary
of the stages of the procedure,
along with the
majority
requirements
at each stage, appears
in Table
2.) Let us leave aside
for now the final election and
consider the first
four,
which were nominating
elections. In Table 2 these are called stages 3, 5, 7, and
9; the required
super-
majorities
are
63 = 7/9, 65 = 3/4, 67 = 7/9, and
69 = 9/11, respectively.
In each
of the four
cases, regardless
of n, we have 6k > m*(C).
C-N assure
us, then,
that there are many super-majority
rule winners. But this is exactly what is
called for. The nominating
committees do not seek a single best alternative.
Rather
they wish to choose, respectively,
40, 25, 45, and 41 "winners". The
required
super-majorities
with 3 > m*(C) can be expected to produce
just
what is needed.11
The required
super-majority grows
further in stage
9. The number of poten-
tial winners
likewise becomes
large.
However,
it seems
probable
that the elec-
tors would all have understood that as the procedure
drew
closer to its finale
each individual
decision more
directly
affected
the final outcome.
Only a sub-
set of the
theoretically eligible candidates
- those with the greatest
stature and
718
wisdom and,
perhaps,
the oldest - would have been given serious
considera-
tion late in the process.
(An elderly Doge was likely to die sooner
rather than
later,
granting
other
aspirants
another
chance at the office.) Family rivalries
would not seem to reverse
this tendency,
for each elector would want a rel-
ative chosen for the next stage, and no family would want a weak member
chosen over a strong
member.
In short,
it is likely that the members
of the
Great Council who were given serious
consideration
in the late rounds would
have been similar
to each other
in some of the key individual
characteristics,
as C-N (Caplin
and
Nalebuff, 1988: 805) also suggest.
Now we come to the supreme
moment
of the proceedings:
the election in
stage 10 of the Doge himself. In this stage
the 41 Ducal Electors
must
choose
a single winner. A 6 rule as close as possible to m*(C)
- but no smaller
- is
what
C-N tell us is needed.
What
did the Venetians
require?
In the final
stage
they specified
25
610o
= - = 0.6098.
41
If it is true,
as we have
argued,
that
n > 4, given the 41-member Ducal Coun-
cil, 25/41 is the only ratio that satisfies the C-N rule. Twenty-four (giving
the ratio 24/41 = 0.5854) would be too small, leaving open the possibility of
continual
cycling and
no majority
winner.
Twenty-six (giving the ratio 26/41
= 0.6341) is too large,
exceeding even the value m*(Cso)
= 0.6285, and
thus
leading to an indeterminacy
in the outcome. In the formal sense of Caplin
and Nalebuff
the final
an all-important
election in the ducal
electoral scheme
was
just right.
To conclude this section we offer a last bit of interpretation
of the final
election. In their result, Caplin and Nalebuff (1988) note that if the appro-
priate super-majority requirement
is in place then there is no alternative that
can defeat the status
quo. Moreover,
only one status
quo can have this prop-
erty. When voting, the 41 faced a slightly different
problem.
Their choice
was between the named
candidate
and a lottery
of proposals,
with probabil-
ity distributed
uniformly
over the other names still in the urn.
This decision
problem
presents
certain
features
that we intend
to pursue formally
in future
work. But the connection to m*(C) can be seen if we consider the ex post
properties
of the procedure.
Once a Doge has been chosen, if the electors'
individual
preferences
and
the distribution
of these preferences
adhere to the
Caplin-Nalebuff
model then the winner
can be thought
of as the status
quo,
and with 6 = 25/41 we can be sure that no other alternative
could defeat
him
with this super-majority.
Though
the winner
was not a status
quo before the
election
began,
it would seem reasonable
that
the process
would locate a path
leading
to him. There should be only one such winner,
and even if more
than
719
one candidate could conceivably survive
the process and become a winner,
the first one so chosen will succeed
by the 25/41 rule against
all challengers.
5. Conclusions
At first
glance the complicated process for electing the Doge of Venice may
seem cumbersome and
unexceptional.
Was
all of the trouble
really necessary,
or useful? We believe that it was surely
useful, and very likely necessary
for
ensuring
the continued
stability
of the political order.
In historical
context,
the Venetians'
prescience seems to be rather
striking,
for they predated
the
early work of Condorcet
by more than five centuries.
Even more striking
is
the fact that
they actually
devised a scheme
employing Caplin
and Nalebuff's
requirement
(as precisely as could be done with a group
of 41 voters) more
than seven centuries before it was discovered and demonstrated
formally.
If there are any empirical lessons to be drawn from these events in the
centuries-distant
past, they must reside in the historical fact that the gover-
nance structure and the political process of Venice were exceedingly stable
for their time. Indeed,
in all of history,
where
durability
is concerned no set of
political
institutions has ever surpassed
the Venetian record.
Why was Venice
so stable
during
a time when all about
her governments
were collapsing
and
changing
hands
at a torrid
pace?
The entire constitutional
arrangement,
with
its checks and balances,
is no doubt the leading reason
(see note 2). Anoth-
er, which should
not be understated,
was her geographic
location.12
But we
should like to think the stability was also due at least in part
to the voting
process
for the dogeship,
with its built-in
stability
properties.
That something
exceptional
was being played out each time a new Doge
was elected
does not seem to have been self-evident
to everyone.
Muir
(1981:
279) avers that the scheme was only a "naive attempt
to keep one faction
from
dominating
the electoral
committees". To be sure,
one could agree
with
Norwich (1982: 166) that it "strikes
the modern mind as ridiculous".
But
naive?
We
prefer
to believe that it is the single best indicator of the Venetians'
foresight
and collective instinct
for political affairs.
Notes
1. The only paper
of which we are aware that looks at the formal
properties
of the Doge
voting scheme is by Lines (1986). Lines suggested
that the final vote in the Doge scheme
satisfied the properties
of approval
voting. The present
paper appears
to be the first to
connect the Venetians to Caplin
and Nalebuff
(1988).
2. Venetian
women were granted
no role whatsoever in the governance
of their city. In the
early years it was possible to enter the ruling class by achieving sufficient
social status.
720
Cessi (1968: 270) states that
"The
governing political
class was at first elevated to nobility
by its function rather than
by birth".
3. "[T]hose institutions
in which, ultimately,
the political power resided were subject to
exquisitely
calculated
systems of checks and balances that made their misuse always dif-
ficult and
usually impossible"
(Norwich, 1982:
280).
4. The original
Great
Council, in 1172, contained 480 members.
In 1296 membership
had
fallen to 210, but this number
grew to 1017 in 1311 and to 1212 in 1340 (Norwich, 1982:
184). By 1500 the number was more than 2000. After 1297 membership
was permanent
and
hereditary.
5. Ballotta,
the Italian
word for a small ball, is the source of the English
term ballot.
6. Certain
diplomatic posts were expensive, for the costs of travel and maintaining
a for-
eign office were born by the official himself. Unlike many of the local offices, these
were shunned if at all possible. In 1185 Doge Sebastiano
Ziani instituted the prohibi-
tion against declining an office. Being Doge was also expensive, for he was not paid for
his services and was also expected to fund the office out of his own purse.
Furthermore,
he was required
to disassociate
himself from all of his commercial interests. Some did
not wish to serve as Doge. Upon being notified,
in 1368, that he had been selected for the
honor,
Andrea Contarini refused. He soon changed
his mind,
under threat of having
all of
his possessions confiscated.
7. The institution
of the
promissione
was an important
check on the power
of the Doge. In a
sort
of Bayesian
learning process it was revised
based on the previous
Doge's experience
to further restrict his authority
(Cessi, 1968).
8. The procedure
for selecting a ballottino was designed
to be as random as possible. One of
the Ducal Councellors and one of the Heads of the Council of Forty
walked through
the
West door of the basilica and chose the first
boy aged 15 or less to walk by. Usually the
chosen boy's age was between 8 and 10;
his youth
and
innocence were meant to symbolize
the purity
of the process.
9. C-N's Theorem 3 establishes
that their
super-majority
rule
can be extended to large
finite
populations
with ideal points drawn
from a concave density on S. Their Proposition
7
shows that their results also hold in the case of a finite
alternative set X. In a later
paper,
Caplin
and Nalebuff
(1991) extend their 1988 result
by requiring only that
the distribution
of ideal points be log-concave. Though the later paper tightens slightly the bound on
required super-majorities,
for our purposes nothing changes materially
if we employ the
later
rule.
10. We must emphasize
the importance
of this point: if n < 3, the Doge election does not
match
m*
(C). However,
we believe firmly
that it is safe to suppose that n > 3, and that
the historical accounts
support
our supposition.
When
Sebastiano
Ziani was elected Doge
in 1173, he was praised
for being "highly intelligent,
energetic despite his seventy years,
and possessed of wide administrative
experience. He was also enormously
rich" (Nor-
wich, 1982: 110). In 1365 Marco Corner
was elected Doge, but only after he delivered
an impassioned speech defending
himself against
several
formal
objections:
"He
was too
old, being well over eighty; he was too poor, and would be unable
properly
to meet the
expenses and maintain the dignities of his office; he was too closely associated
with for-
eign powers for his loyalty to be beyond suspicion;
finally,
he was married
to a plebeian
wife, whose numerous
family would be bound to meddle
in the affairs of state"
(Norwich,
238-239). Maranini
(1931: 274) mentions the following negative requirements
for Doge:
He should have "a
not too proud
disposition
and a not too willing temper;
a political
char-
acter
not too powerful;
and a mature
age in order to reduce
the riskiness of an election for
life".
11. Though
the required
margins
seem to agree broadly
with their
result, it should be noted
that
the
C-N result does not
explain why the Venetians introduced
the
preliminary
electoral
stages. It would appear
that
the urge
to suppress corruption
and factionalism
provides
the
explanation.
721
12. Speaking
of Venice in the early 15th
century,
Norwich (1982: 280) writes, "For the best
part
of a thousand
years already,
those two or three miles of shallow
water
separating
them
from the mainland had not only protected
them from invaders but had
effectively isolated
them from Italian
political life; ... kept them untouched
by feudalism and the endless
territorial
squabbles
that it brought
in its wake; and enabled them to fix their attention,
except in moments of crisis, resolutely
eastward ... ".
References
Arrow,
K. (1963). Social choice and individual values. Second edition. New Haven: Yale
University
Press.
Black, D. (1948). The elasticity of committee decisions with an altering size of majority.
Econometrica 16: 262-272.
Caplin,
A. and
Nalebuff,
B. (1988). On 64%-majority
rule.
Econometrica
56: 787-814.
Caplin,
A. and Nalebuff, B. (1991). Aggregation
and social choice: A mean voter theorem.
Econometrica
59: 1-23.
Cessi, R. (1968). Storia della Repubblica
di Venezia.
Second edition. Milan: Casa Editrice
Giuseppe Principato.
Condorcet,
M. de (1976). Essay on the application
of mathematics
to the theory
of decision
making.
In K. Baker
(Ed.), Condorcet: Selected
writings.
Indianapolis:
Bobbs-Merrill.
Da Mosto, A. (1960). I Dogi di Venezia
nella vita Pubblica e Privata. Milan: Aldo Martello
Editore.
Guicciardini,
F. (1973). Democracy
of the Venetians. In G. Maranini
(Ed.), La Repubblica.
Florence: Vallecchi Editore.
Hazlitt,
W.C.
(1900). The Venetian
Republic:
Its rise, its growth,
and its
fall, Vol. I. London:
Adam
and Charles Black.
Kramer,
G.H. (1973). On a class of equilibrium
conditions
for majority
rule. Econometrica
41: 285-297.
Lane,
F.C.
(1973). Venice: A Maritime
Republic.
Baltimore: Johns
Hopkins University
Press.
Lines, M. (1986). Approval voting and strategy analysis: A Venetian
example. Theory
and
Decision 20: 155-172.
Maranini,
G. (1931). [Reprinted
1994].
La Costituzione
di Venezia,
Vol.
II.
Florence: La Nuova
Italia Editrice.
McKelvey,
R.D. (1979). General conditions for global intransitivities in formal
voting
models.
Econometrica 47: 1085-1112.
Muir,
E. (1981). Civil ritual in Renaissance Venice. Princeton:
Princeton
University
Press.
Norwich, J.J. (1982). [First
Vintage Books edition, 1989]. A history of Venice. New York:
Knopf.
Plott, C. (1967). A notion of equilibrium
and its possibility under majority
rule. American
Economic Review 57: 787-806.
722
Appendix
Modo dell'Elezione
del Serenissimo
Principe
di Venezia
(Mode of Election of the Most Serene
Prince
of Venice)
"After
the Doge's death,
the Counsellors
and the Heads of the Forties,
rep-
resenting
the City Government,
go to live in the Ducal Palace and gather
the Great
Council. The five correctors of the Doge's Oath,
of the Orders
of
Palace, and finally three inquisitors
of the dead Doge's actions are elected.
After having done this within three or four days, and made the Funerals,
the Great
Council, formed only by those who exceed thirty Years of age,
is gathered.
The above mentioned Oath
is read and confirmed.
After having
counted
the members of the Council,
as many
Balls as there are Gentlemen
in
the Council,
are
placed
in a Hat. Of these Balls, thirty
are
Gold, all the others
are
Silver.
Then,
one young Counsellor and one Head of the Forties
go to the
Church
of St. Mark
where
they find a young boy, named the Ballottino,
and
conduct
him to the Council.
All the Nobles of the Council are
requested
to approach
the Hat. For each
of them, the young boy places his hand inside the Hat. If he draws a Gold
Ball, the one for whom he picked
it is elected.
Meanwhile,
as each one elected
is made
public,
his Father, Sons, Brothers,
Uncles, and
all the other members
of the family leave the Council. If the young boy picks a Silver Ball that
Noble must leave the Council as well. Those who received the thirty
Gold
Balls, selected though
from different
Families, in number
of one per Family,
who are not linked by any sort of Kinship or blood relation, or otherwise
(as one says) are taken out of the Hat, are called the first thirties. The rest
of the Council must leave. Then, thirty
Balls, nine of which are Golden and
the others Silver, are deposited in the Hat. The young boy draws one Ball
for each of the first thirties.
Those who receive the nine Gold Balls remain
electors, and the others are
dismissed. These nine, in isolation,
elect 40 with
seven out of the nine Balls, in such a way that,
after
having
tossed the cards
of first,
second, etc., the first
4 must elect 5 each, and the other 5 must elect
only 4 so that
they elect a total
of 40. Then, the Great
Council is gathered.
The above-mentioned 40 are made public and the others leave. Then 40
Balls are placed in the Hat. Of these, 12 are Golden. Those who receive
the Gold Balls become electors; the others leave. These 12 elect 25 with
nine Balls, in such a way that the first
elects three,
and the others elect two
each, for a total of 25. Upon completion
of this election, the Great
Council
is gathered.
The 25 are made public and the others
leave. Then 25 Balls are
deposited in the Hat. Of these, nine are Golden. Those who receive them
become electors; the others are dismissed. These nine elect 5 with 7 Balls
in such a way that each elects 5 for a total of 45. Then the Great Council
723
is gathered.
The 45 elected are
made public;
the others are dismissed. Then
45 Balls are placed in the Hat. Of these, 11 are Golden. Those who receive
the 11 Balls are the electors and the others
leave. These eleven are those who
elect the Forty-ones
with nine Balls in the following way.
After
having
tossed
the cards
as above,
the first
eight elect four each while the last three
elect only
three
each, for a total of just Forty-one. Upon completion
of this election, the
Great
Council, including
those who are not thirty
Years old yet, is gathered
and confirms them. Now, after
having
created the Forty-ones,
listened to the
Holy Spirit
Mass and
given
the oath,
they
isolate
themselves,
and
with Scarlet
Balls signed by a Yellow Cross, elect the Doge with 25 Balls".
