64% Majority Rule in Ducal Venice: Voting for the DogeAuthor(s): Jay S. Coggins and C. Federico PeraliSource: Public Choice, Vol. 97, No. 4 (1998), pp. 709-723Published by: SpringerStable URL: http://www.jstor.org/stable/30024456Accessed: 01/10/2009 15:13

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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.

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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

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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.)

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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.

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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

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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

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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.

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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

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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

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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

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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.

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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.

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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

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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

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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".