“Weighed, not counted”: territorial (mis)representation in Italian metropolitan council elections

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Introduction
After a lengthy stage of development (see below), Italian Law no.56/2014 (commonly known as the "Delrio Law") established "metropolitan cities" as a new level of government, replacing and redefining functions previously performed by provincial governments in selected major urban areas.
One of their three key governing bodies is the metropolitan council, a representative assembly the members of which are elected via an indirect, second-level, proportional system in which the electorate (i.e., those having the right to vote) and the potential candidates comprise all sitting mayors and councillors from metropolitan city municipalities.The election mechanism applies a differential weighting scheme that reflects the population size of the municipalities in which voters serve as mayors or councillors.Using the outcomes of the metropolitan council elections held in the years 2021 and 2022 in eight metropolitan cities, this study highlights the variety of ways (many of which appear to be largely unintended by the Delrio Law) in which demographic weighting bestows significantly greater (and, arguably, unwarranted) power to larger cities' representatives, essentially disrupting the principles of territorial representation that the weighting scheme intended to embody.
The study also focuses on how the legal framework for metropolitan council elections generates institutional instability and identifies potential adjustments of the electoral system -especially "square-root" weighting -that could attenuate some of its negative consequences.
Section 2 provides an overview of the metropolitan councils' functions and the voting rules that govern their election, with a particular emphasis on demographic weighting schemes.Section 3 briefly outlines the strictly "political" outcomes of the 2021-22 metropolitan council elections.The election outcomes pertaining to territorial features is the focus of Section 4, which examines the relationship between population size, on the one hand, and, on the other, voter turnout, list composition, candidacies' success and voters' degree of influence.Issues involving institutional sustainability area are addressed in Section 5, which explores the intricate upshot of forfeitures and substitutions of metropolitan council seats.Section 6 illustrates a proposal for the attenuation of disproportionate territorial representation, via an implementation of demographic weighting based on the so-called "square-root method", and simulates the election outcomes that would have ensued from its adoption.Other proposals to improve the current MC election system are briefly discussed in Section 7. The last section develops some concluding remarks.

Metropolitan councils and their electoral system
In 2014, the Italian Parliament enacted Law no.56 (the so-called "Delrio Law", after Graziano Delrio, the minister of regional affairs who proposed it).Among its many measures, the law established 10 "metropolitan cities" ("metro cities", from now on) which replaced the provincial governments that hitherto had ruled over the same territories, thus finally implementing a level of local government introduced in a revision of the Italian constitution in 2001 and originally mandated by Law no.142/1990 (Baccetti 2014; Forte 2014; Busso and Galanti 2015; Bolgherini et al. 2016).
The enactment of the Delrio Law defined both metro cities and the remaining provinces as territorial administrative entities comprising "vast areas".The institutional simplification pursued by the reform was bolstered by the anticipated abolishment of the residual provinces, as envisaged within a general, wide-ranging proposal for revising the Italian Constitution; but that attempt faltered when voters rejected it during a referendum held in 2016 (Bull 2017; Fusaro 2017).
The law also defines procedures for the creation of additional metro cities, namely acknowledging the ability of "special statute" regions (which enjoy a certain degree of administrative autonomy) to create additional metro cities; 5 have been established in this way (although some have not yet become operational), all located in the insular regions of Sicily and Sardinia: Cagliari, Catania, Messina, Palermo, Sassari.
Metro cities perform vital functions involving socio-economic development goals, including: formulation of 3-year strategic plans; general territorial planning (communications, service networks, infrastructure); organization of coordinated management systems for public services; transportation mobility, road systems, urban planning compatibility and consistency; promotion and coordination of socio-economic development (support for innovative business and research); promotion and coordination of computerization and digitization systems; tasks previously performed by provinces in the sphere of school networks and buildings and environmental protection; other functions assigned to them by regional governments (art. 1, clauses 44 e 46).Metro cities perform their functions via three key organs.The metropolitan mayor is a post held de iure by the (elected) mayor of the metro city's capital (see below, Section 8, however, for a recent Constitutional Court ruling concerning the legitimacy of this provision).The metropolitan conference is an assembly, with advisory status, of all the mayors of the metro city's municipalities (comuni).
The metropolitan council ("MC", from now on) is an elected assembly performing general direction and control functions; the electoral system shaping its composition is the main focus of this article. 1e Delrio Law states that MC elections are to be held every five years, no later than 60 days after the inauguration of the capital city's municipal council.The electorate comprises all elected mayors and municipal council members of the metro city's municipalities (i.e., ordinary citizens do not participate in MC elections); thus, the MC is the end product of an indirect, second-level voting system. 2 Elections feature competing lists, each of which includes a number of candidates no fewer than half and no greater than the total number of contended MC seats; the latter are 14, 18 or 24, depending on the size of the metro city's population.All sitting councillors and mayors (with the obvious exception of the metropolitan mayor) are eligible to stand as candidates.
Individual voters cast a vote for one list and may express a single preference for one of the chosen list's candidates.Seats are proportionally distributed among the lists according to the d'Hondt method, but before this occurs voters' ballots undergo a differential weighting procedureindisputably the electoral system's most distinctive feature.Each ballot is assigned a weight that is determined by the size of the population in the municipality where the voter serves as mayor or councillor (see Section 4).
Other provisions of the Delrio Law also exert considerable influence on the composition of MCs.
If an elected metropolitan councillor ("MCer", from now on) for any reason whatsoever ceases to be a mayor/councillor in her municipality, she vacates her MC seat as well.In case of seat forfeiture, the former MCer is substituted by the unelected candidate (belonging to the same list) with the highest number of weighted preferences.
This electoral system engenders a bias -arguably an unwarrantedly large one -in favour of larger towns and especially the capital, as well as other dysfunctional (probably unintended) effects, for reasons that will be identified and explained in the following sections.
1 An example may help the reader understand: the metropolitan mayor of the metro city of Bologna is the mayor of the municipality of Bologna; the metropolitan conference of Bologna comprises 55 individuals, i.e., all the mayors of the 55 municipalities making up the metro city; the metropolitan council of Bologna has 18 elected members.The metropolitan mayor presides over both the metropolitan conference and the metropolitan council.
2 Some regional governments challenged the constitutionality of the indirect elections introduced by the Delrio Law, but the Constitutional Court upheld the law, highlighting the "total compatibility of a second-level electoral mechanism with the democratic principle" and arguing that the voting system in no way weakened the "representative and elective character of territorial government organs" (ruling no.50/2015).A few years later the Constitutional Court reaffirmed the legitimacy of indirect elections, deemed as appropriate for pursuing the goals of institutional simplification and costcutting with respect to direct elections (ruling no.168/2018).The Delrio Law does allow metro cities to amend their charters to introduce the direct election of the metropolitan mayor and the MC, but only within the context of a national law (yet to be enacted) and other exacting constraints (art. 1, clause 22).

2021-22 MC elections: political outcomes
Six MC elections were held in Italy during 2021: Reggio Calabria (January 24); Venice and Bologna (November 28); Turin, Milan and Rome (December 19).Another two elections occurred in 2022: Naples (March 13); Genova (November 6).It would be interesting to dwell on a description of the political profile and outcomes of these elections, but constraints on the length of this article require brevity.Let it suffice to say that the political "supply" consistently offered "centre-right" and "centreleft" options, but also varied appreciably from one MC to another.In Genova (18 seats), only two lists (one centre-left, one centre-right) were presented.Venice (18 seats), Rome (24), Turin (18) featured three lists (the third being the Five-Star Movement's).In Reggio Calabria (14) and Bologna (18), four lists competed: in the former, there were one centre-right list, two centre-left ones and an additional list associated with a former mayor of Naples, Luigi De Magistris, featuring candidates predominantly originating from a single town; the latter featured two centre-right lists, a centre-left one and a "civic" list involving the Five-Star Movement.Five lists competed in Milan (24): three centre-right, one centre-left and a "civic" list.Naples (24) was an outlier, with 11 lists, with at least three centre-left and as many centre-right lists, plus five others.
In each of these elections, a clear political majority emerged, with 6 MCs going to the centre-left and 2 to the centre-right (Table 1).Each majority perfectly mirrored the winning list/coalition/mayoral candidate in the prior municipal elections in the capital city. 3The centre-left ran multiple lists in 2 elections, which it won; the centre-right ran multiple lists in 3 elections and lost each of them.By and large, MC elections displayed a strongly bipolar dynamic, with the centre-right and the centre-left together achieving 90% of votes and 94% of seats, with modest results accruing to the Five-Star Movement and other "civic" lists.Naples is again an outlier: there 9 of 11 lists earned at least one seat, and the centre-right and the centre-left accounted for "only" 74.3% of the votes (and 19 of the 24 elective seats).

Territory-related outcomes
As previously mentioned, perhaps the most distinctive feature of MC elections is the weighting of ballots on the basis of demographic brackets.More specifically, all municipalities are classified into nine brackets, and vote weights are determined in such a way as to guarantee that the total number of potential votes expressed by a bracket roughly reflects the incidence of that bracket's population on the total population of the metro city.
In principle, in each metro city 100,000 weighted votes are allocated proportionally among the 9 brackets according to the relative incidence of the population of the municipalities belonging to each bracket (excluding any municipalities placed into receivership) on the overall population.For example, if the municipalities belonging to a given bracket account for 20% of the metro city's population, 20% of the weighted votes are allocated to that bracket.Within each bracket, the corresponding weighting coefficient is determined by the ratio between the number of weighted votes allocated to the bracket itself and its total number of voters, i.e., mayors and councillors.In other words, each voter "represents", roughly, the same number of residents.(Since each coefficient is rounded down to the closest integer, the overall number of potential weighted votes is, in practice, slightly lower than 100,000.)This weighting procedure is then adjusted in two ways: no single municipality (as a rule, the capital) can generate more than 45% of all potential weighted votes; no single demographic bracket can generate more than 35% of all potential weighted votes. 4ble 2 displays the weighting coefficients applied in the 8 elections examined here, as well as the number of voters and municipalities involved in each election.For example, in the metro city of Rome, voters from a very small municipality (i.e., with less than 3,000 inhabitants) cast ballots each having a weight of 23; the weight increases as one moves to the higher brackets and reaches 918 for ballots cast by the mayor and municipal councillors from the capital of Rome.In Rome, an individual voter from the capital enjoys a voting "firepower" that is 230 times greater than that of a voter from a very small town (see "Capital / A Ratio" row in Table 2).In other metro cities the imbalance is less extreme, but even in Reggio Calabria, Bologna and Genova, every capital city voter casts a ballot that is at least 40 times "heavier" than the one cast by a small-town voter.In other words, since votes and preferences are weighed rather than counted, the electoral efficacy of individual voters varies to a large extent, as a function of town size. 5To underscore the extent of this imbalance, consider the example of Milan: the lowest demographic bracket comprises 104 voters, that together can generate 520 weighted votes; a single voter from the capital generates, all by herself, 714 weighted votes.Voters are, presumably, fully aware of their electoral efficacy6 and behave correspondingly when they decide whether to participate in the MC election.As Figure 1 shows, voter turnout in each metro city tends to increase as one shifts from the lower to the higher demographic brackets: practically all voters from the upper four brackets (municipalities with at least 100,000 inhabitants) go to the polls, whereas participation rates drop significantly among electorates expressed by smaller towns.This pattern is particularly marked in the North. 7Naples is again an outlier: overall turnout was an extraordinary 96%.Note: In this chart (and in Table 3) the F, G, H and I brackets are collapsed into a single category, which contains just one municipality, namely the corresponding metro city's capital.The sole exception involves Naples, which, besides the capital (H bracket), also features Giugliano in Campania (F bracket).
Differential voter participation is, in all likelihood, an unintended (yet hardly unpredictable) effect of the electoral system.The same can be said about another consequence: whereas a bracket's electoral potential weight is strictly determined by the Delrio Law, its actual weight is also affected by voter turnout.In so far as voters perceive (dis)incentives to vote and act upon them, the weighted vote distribution further favours larger towns.The preceding comments focus on the electoral efficacy of voters and its relationship with the territorial dimension of town size.But the selection of candidates and their success in getting elected also need to be addressed.As previously mentioned, in MC elections the candidate pool and the electorate coincide (except for the metropolitan mayor's obvious exclusion from the former); therefore, the composition of the candidate pool is reflected in the "potential voters" column of Table 3 provided by the F-G-H-I brackets had a stronger than average probability of getting elected; this was especially true for Naples, Milan and Reggio Calabria.In general, candidates who were also capital city councillors expressed a superior electoral performance, with a likelihood of election 2-3 times greater with respect to other candidates (Turin and Genova, however, do not mirror this overall pattern).In most contexts, however, the bracket expressing the highest success rate (electees/candidates) was not the most populous one.
The influential impact of large city mayors and councillors, in other words, derives to a greater extent from their role as voters rather than from their being candidates.This emerges more clearly in  The Delrio Law (art. 1, clause 30) states that "the metropolitan council is elected with a direct, free and secret vote", thus echoing the Constitution (art.48): "votes shall be personal and equal, free and secret".The preceding analyses have provided ample evidence refuting the "equality" principle in MC elections (and, indeed, the Delrio Law does not cite equality).Yet, despite the significant advantages that the Delrio Law confers to voters from larger towns, the latter, and CCVs especially, are also subject to severe constraints -to wit, the "dark side" of being a powerful voter.But are CCVs' votes truly "free" and "secret"?In the 8 MC elections considered here, there are at least 5 instances of lists and 83 instances of candidates receiving exactly one vote/preference from a CCV.
Since ballots are differentially weighted and election outcomes are reported separately for each 8 The firepower of (most) CCVs is further augmented by another "latent" factor relating to the election system for municipal councils.The lists supporting the winning mayoral candidate enjoy a "majority premium" assigning them 60% of the seats in the municipal council if those lists earn at least 40% of the vote.The majority premium is applied to all municipal elections involving towns with at least 15,000 inhabitants, but in practice entails an additional disproportionate advantage, in terms of MC electoral efficacy, for the capital city's council majority CCVs.
One could also mention another "latent" factor, which however exerts practical effects that are much more marginal.Municipalities that undergo receivership (commissariamento) do not have any mayors or councillors that can run as candidates nor vote in MC elections, and such municipalities are by definition not capital cities: if a capital city were to undergo receivership, there would simply be no MC election to speak of.In the 8 MC elections examined in this article, a total of 21 municipalities (almost all in the South) were simply omitted (see Table 2).(Receivership, pursuant to dissolution of a municipal government, occurs when the latter violates the Constitution or the law or cannot function due to a variety of reasons, including the resignation or forfeiture of a majority of councillors, failure to approve the municipal budget, infiltration by organized crime, and threats to public order.)bracket, there are plenty of opportunities to identify and control individual voter behaviour, especially among CCVs and, with a bit more effort, other brackets comprising a small number of municipalities.
For example, in Reggio Calabria, the Territorio Metropolitano list, promoted by De Magistris, received just one vote from capital city voters, and just one capital city councillor was elected by Lista Civica La Strada, endorsed by De Magistris.There is no proof that the La Strada CCV voted for Territorio Metropolitano, but it does seem highly likely.In the same election, 8 candidates received exactly one preference.Similarly, in Turin, 12 candidates received exactly one preference from a CCV.Three of these candidates were presented by the Obiettivi Comuni list, i.e., the Five-Star Movement, which has precisely three members on the Turin city council.In the Naples MC election, Fratelli d'Italia and Territori in Azione each received one vote from CCVs, and just one councillor is expressed by each of the corresponding parties in the capital city's council.
Another 2 metropolitan lists received just one vote each from CCVs.Exactly one vote from a CCV was expressed for 7 candidates in Venice, 8 in Bologna, 17 in Milan and 11 in Rome.These are all situations in which, if the voting behaviour of CCVs was centrally coordinated, then it would have been easy for list promoters (and, indeed, in some cases, for anyone) to monitor and validate (non-)compliance.

Institutional (un)sustainability
This section explores MCs' institutional sustainability, i.e., their ability to reach the end of their five-year mandate with a low rate of turnover among their members and without permanent seat vacancies.This might seem, at first glance, a minor concern, but the MC election system entails structural threats to institutional sustainability.As previously mentioned, if an elected MCer ceases to be a mayor/councillor in his home municipality, his MC mandate is automatically subject to forfeiture and the vacated seat is assigned to the unelected candidate (from the same list) with the highest number of weighted votes.Of course, there are many reasons why mayors and councillors abandon their MC seats: voluntary resignation, getting elected or nominated to other posts, early dissolution of their municipal council, and -unfortunately -even death.But these are, obviously, exceptional and largely unforeseeable events, that can affect any elected assembly.However, there is also another mechanism leading to seat forfeiture that is, so to speak, "built in" to the election system.
An MC election is structurally and intimately linked to the capital city's municipal election: when the latter takes place, the former must follow (as a rule) within 60 days.However, some MCers come from municipalities that follow an election cycle that is not in synch with the capital's and are therefore subject to "guaranteed" forfeiture before the end of the MC's term.
For example, Rome's municipal elections, along with a few dozen other towns' belonging to the same metro city, were held in October 2021, and the MC election took place the following December.
Barring exceptional events such as those described above, any MCers originating from the municipality of Rome or the other towns that held elections at the same time can expect to serve a full five-year mandate.But most towns in the metro city of Rome held their elections earlier, and any MCer coming from those towns cannot count on being able to serve a full five-year MC term.The Delrio Law, in its only concession to institutional sustainability, does provide a loophole: if an MCer whose municipal mandate is ending is re-elected to the post of mayor or councillor, 9 she gets to keep her MC seat.
Table 5 outlines the potential forfeiture situation.In almost all of the MCs examined here, only a minority of candidates and electees can expect to serve out a full-term. 10In other words, the majority of elected MC members (95 out of 158, or 60%) are subject to "guaranteed" forfeiture before end of MC term and will need to vacate their seats if they are not immediately re-elected.One might think that this is not a particularly troubling circumstance, since there is a substitution procedure in place: initially unelected candidates fill vacated seats.However, the latter are also vulnerable to "guaranteed" forfeiture, and indeed they are at risk, with respect to initial MCers, to an even greater extent: 266 of the 357 unelected candidates (i.e., potential substitutes), or 75%, are due to complete their tenure in their home municipalities before the end of their MC's mandate. 11e number of potentially irreplaceable vacancies is hardly trivial: 48 out of 158 (30%), concentrated mostly in the MCs of Genova (12), Bologna (10), Rome and Turin (8 each).This problem is compounded by the fact that, of the 35 lists competing in the 8 MC elections examined here, 25 of them are "short", i.e., presented fewer candidates than the allowable maximum, which means that they have a greater likelihood of exhausting substitution possibilities.If the "guaranteed" forfeitures actually materialize, 13 lists out of 33 that earned seats will see their MC delegations shrink, and in 6 of the 8 MCs the initial ruling majority will evaporate (threatening the metro cities' governance capability).Of course, some of these "guaranteed" forfeitures will not actually occur, 9 Re-election ensuring one's continued MCer status can, counter-intuitively, occur in any municipality belonging to the metro city, even if the municipality is not the one that provided original access to the MC electorate and therefore even if re-election occurs in a different demographic bracket.
10 Venice features an apparently more stable situation, but this is due to the fact that its MC election (November 2021) was significantly delayed by the Covid-19 emergency; in fact, its municipal election was held in September 2020.Therefore, the current MC should last less than four years, and this allows some MCers coming from towns with elections not held simultaneously with Venice's to serve out a full (albeit shorter-than-usual) term.
11 Table 5 also reports the number of potential full-term substitutes receiving at least one preference: only 47 out of 357 (13%).In fact, 50% of non-elected candidates collected no preferences at all.Even if nobody expresses a preference for a given candidate, the latter remains eligible for substitution of forfeitures.Yet from a political standpoint, an individual who sits in an assembly after having received no support whatsoever in its election obviously raises an issue of political and representational legitimacy.As shown by Gasperoni and Caporale (2021), a handful of candidates garnering no preferences did end up occupying seats in MCs originally elected in 2016.
thanks to the re-election of sitting MCers in a municipal context, but experience shows (Gasperoni and Caporale 2021) that many will.In any case, it seems bizarre to entrust, as the Delrio Law does, MCs' institutional continuity to MCers' (uncertain and unpredictable) re-election to municipal councils.Moreover, as previously explained, such "guaranteed" forfeitures are not the only source of vacancies and institutional discontinuity.
One should keep in mind that MCers (including future ones, i.e., initially unelected candidates who will earn their seats due to others' forfeiture) who originate from the capital city are intrinsically not vulnerable to the type of forfeiture envisaged here: by definition, they will be able to keep their MC seats until the end of their MCs' five-year duration.This is arguably yet another privilege that the MC electoral system confers upon representatives of capital cities.The square-root method: a reasonable compromise?
The MC electoral system features many drawbacks, and therefore there are many ways in which it could be improved.The voting rules' most distinctive feature, as previously stated, is its indirect, second-level design relying on demographic weighting.This in part reflects Parliament's reasonable intention to avoid burdening the citizenry with yet another call to the polls, ensure governability, reserve a strong role for capital cities (and larger towns, in general) in metro city administration and, more generally, emphasize the centrality of territory.Nevertheless, demographic weighting and the extreme imbalance in weight coefficients dictated by the Delrio Law are a textbook example of how "certain individuals and territories often enjoy a higher degree of influence than their relative demographic weight of the polity would imply" (Beramendi et al. 2022, 1).Yet simply doing away with differential weighting would be a naïve solution (CCVs' incidence on the total vote would be reduced to a paltry 5% or less).Is there an intermediate approach?
Shortly after World War II and the founding of the United Nations, Lionel S. Penrose developed such an intermediate approach.Discussing decisions made by majority vote in committees and within a more general reflection on the "arithmetic of voting", Penrose argued that "the power of the individual vote is inversely proportional to the square root of the number of people in the committee" (1946, 55).He then explored the ways votes could be allocated in a "federal assembly of nations": "would it be for two nations of the sizes of China and Switzerland each have one vote?On the other hand, would it be any fairer if the greater one had 100 times as many votes as the lesser, as would result from allotting voting power or membership in the assembly on a strictly 'per capita' basis?The answer seems to be that the number of votes (or members) which each nation contributes to an assembly of spokesmen should be proportional to the number of people whose opinions each spokesman probably represents.The number of people represented by the spokesman of each electorate has been shown to be proportional to the square root of the number of people who can vote" (1946, 55).Largely forgotten and then re-discovered by Banzhaf (1965) and Coleman   (1971), the so-called "Penrose square-root method" fuelled a debate, a little more than 15 years ago, regarding voting rules within the European Union Council of Ministers (Życzkowski and   Słomczyński 2004; Słomczyński and Życzkowski 2006; Ratzer 2006).The square-root method has seen use in some international scientific associations (Słomczyński and Życzkowski 2006, 3-4) and a few local political contexts (The Economist 2021) but has been largely ignored in practice.
Weighting ballots proportionally not to population size but to its square root would continue to give an advantage to larger groups over smaller ones, but the extent of the imbalance would be attenuated.In order to ascertain the potential effects of the square-root method, simulations of the MC elections have been developed.More specifically, Table 6 shows what happens when the squareroot method is applied in two MC election scenarios: Turin, characterized by a comparatively high demographic incidence of smaller municipalities, and Rome, where conversely the capital city accounts for two-thirds of the metro city's population.The "Capital / A ratio" (already seen in Table 2) is a rough measure of territorial disparity and indicates how many potential voters in the A bracket need to be put together to counterbalance the electoral weight of a single CCV.In Turin, this measure is cut in half when the square-root method is implemented; in Rome it shrinks by two-thirds; in both cases CCVs continue to enjoy considerable firepower.On the assumption that turnout would not change, the incidence of brackets A, B and C on weighted actual votes increases (compared to the current situation) in both contexts, and the incidence of brackets E to I decreases.In any case, the square-root method would, by and large, curtail the electoral firepower accruing to voters from larger towns without seriously challenging the key role of capital cities within the electoral system's framework.Another interesting issue is whether the adoption of the square-root method would have any effect on the political outcomes of the MC elections.Again adopting the (unrealistic) assumption that voter turnout would remain the same and the (more realistic) assumption that the square-root method would not induce any voter to cast a ballot for a list that is different from the one actually chosen within the current system, Table 7 shows what would happen in terms of votes cast for the competing lists in each MC election.In 6 of the 8 elections, the majority would have a slightly smaller margin of victory (in terms of weighted votes), almost always by less than one percentage point.Rome is an exception: the majority would increase its margin of victory by more than 5 percentage points.In three elections (Bologna, Rome and Turin) there would be no change in the overall allocation of seats.In each of two elections (Venice and Naples), the Five-Star Movement would relinquish a seat to the centre-left; in both cases the majority would remain untouched (strangely enough, in Naples the centre-left would be weaker in terms of weighted votes but stronger in terms of seats).In Reggio Calabria, one seat would shift from one centre-left list to the other, without changing the majority/minority balance.In Rome, the centre-right would yield one seat to the centre-left, further strengthening the latter's majority.
The MC election in Milan would feature the most significant change: besides the transfer of one seat from one centre-right list to another (within the minority), the centre-left would surrender one seat to the "civic" list, thus endangering the stability of the centre-left majority (which would control only 12 of the 24 elective seats), which is already vulnerable (as previously argued) to potentially irreplaceable vacancies.One could argue that this simulated outcome faithfully reflects the fact that the centre-left did not earn the majority of the weighted votes.
In each voting arena, unsurprisingly, implementation of the square-root method would appreciably reduce the "capital / A ratio" (although the contraction would be marginal in Genova, where the ratio's value was already rather small); in four contexts, the ratio would decrease by at least 80%.
Although the changes envisaged here may not be particularly large, one can argue that the abovementioned turnout assumption is unrealistic: if the square-root method were implemented, more voters from smaller municipalities would have a greater incentive to vote and list promoters would have a greater incentive to encourage wider participation.12

Other tentative solutions
The population size of voters' home municipalities is the only facet of "territory" that is contemplated (via demographic weighting) by the MC electoral system.And this study has developed evidence-based arguments showing that this confers an overpowering influence upon the capital city component of the candidate pool and, especially, the electorate.Other dysfunctional features of the voting rules have also been identified.Are there sensible changes that could be introduced to address these issues?
Perhaps the most impactful reform would be to base territorial representation not (or not only) on municipalities' mere population size, but on criteria reflecting socio-economic conditions.A metro city's municipalities could be grouped into a small number of districts, each sharing socio-economic traits and expressing similar needs (mountain communities vs. seaside communities; rural vs. urban communities; prevalence of manufacturing vs. service vs. agricultural sectors; proximity to mobility opportunities, health services, schools; and on), regardless of their population size.Each district could have a certain number of pre-assigned MC seats, and their occupants could be voted for exclusively by mayors and councillors of municipalities belonging to the district.Such provincial zoning arrangements have already been largely identified and are used for various administrative purposes.
There are several other smaller-scale amendments, with correspondingly limited effects, that could be enacted.For example, rather than using resident population size to determine a municipality's bracket membership, one could use the size of its general electorate.This could shift some "weight" towards smaller towns, which tend to have a lower incidence of underage citizens, and away from larger ones.Moreover, population size includes residents who are foreigners, and their differential distribution among metro cities' municipalities could appreciably contribute to defining weight coefficients.To the extent that demographic weighting is maintained, the currently adopted correction thresholds (no municipality can express more than 45% of potential weighted votes, no bracket can express more than 35%) could be further lowered.Promoters of MC lists could be obliged to limit the number of candidates from capital cities or, more in general, higher demographic brackets, or, vice versa, include a minimum number of candidates from lower brackets.
In terms of institutional sustainability, the issues identified in the preceding section could be addressed in several ways.Firstly, and perhaps most simply, one simply eliminate the rule entailing the forfeiture of MC seats when their occupants leave their elected roles in municipal governments.This consideration raises the question: does an MCer's legitimacy derive primarily from her being elected in her original municipal context, or from being chosen in subsequent MC voting?If the second option seems reasonable, so does the elimination of the cited rule.Secondly, if such forfeitures continue to be maintained, the minimum list length could be raised, at least to the number of contended seats, to strengthen any given list's ability to supply substitutes.In other words, promoters of an MC list could be obliged to nominate at least 14/18/24 candidates, rather than half that number.Indeed, to avoid the danger of "exhausted lists" and irreplaceable vacancies, the minimum number of candidates could be even higher than the number of seats in play: there is no patent downside to lengthening minimum and maximum list sizes.Thirdly, candidates receiving no preferences whatsoever (or another non-zero minimum threshold) could be barred from access to MC seats.Although it could aggravate the "exhausted list" problem, this measure would also, possibly, motivate list promoters to encourage their electorates' to distribute their preferences among a wider number of candidates.

Discussion and concluding remarks
The legal framework governing any election can be interpreted as an institution exerting two primary effects on participation and voting: it provides opportunity structures and shapes information costs (Peters 2018) The patterns emerging from weighted ballots cast within each list strongly suggest that the expression of preferences in favour of individual candidates is, again, highly co-ordinated, especially among CCVs.For most lists, the distribution of preferences indicates a high level of awareness among "heavy" voters of the considerable power they wield: one need only examine turnout patterns, the quasi-obligation to attain CCV support in order to be elected, the fact that most candidates supported by CCVs receive at most two preferences from them, and the high incidence of "token" candidates (mostly women 13 ) with no preferences at all.MC elections, in other words, display suboptimal performance from the standpoint of general election quality criteria, such as provision of effective representation, accessible and meaningful elections, generation of stable and efficient governance, accountability, opposition oversight and voter anonymity.Many of the dysfunctional features of the MC electoral system had emerged in the previous elections (Gasperoni and Caporale 2021), and some of them could have been addressed (at least in the construction of the candidate lists) in the 2021-22 cycle -but they were not: the institutional and political learning curve has been remarkably flat.
The need to amend the metro city governance structure has nonetheless attained some visibility, due to a decision handed down by the Constitutional Court (ruling no.240/2021), which underlines the probable unconstitutionality of the Delrio Law's provision that "automatically" assigns the post of metropolitan mayor to the mayor of the metro city's capital.This measure entails a lack of representation and political responsibility towards citizens residing in towns that are not the capital 13 A critical issue not addressed in this article is gender representation.The Delrio Law requires each list to include no more than 60% of candidates of the same sex.Operational only since 2017 and clearly aimed at promoting the election of women in MCs, the measure has not been particularly successful: simply including women in candidate lists does not guarantee their election.Of the 33 lists competing in the 8 MC elections examined here, all (obviously) satisfied the requirement, but only 6 of them featured an equal number of men and women (or more women than men) among their candidates.Only 13% of female candidates (none in Reggio Calabria, just one in Naples) were elected.The majority of female candidates received no preferences at all, and over two-thirds of candidates receiving no preferences were women, suggesting that the inclusion of women among MC candidates is little more than an empty symbolic gesture (see Caporale  2017; Caporale and Gasperoni 2016).
(and who therefore have no say in the election of the capital's mayor).The Court, however, did not go as far as to express a formal judgment of constitutional illegitimacy and preferred to merely admonish Parliament and call for a suitable legislative intervention (De Donno 2022).
A variety of bills aiming to overhaul the Delrio Law have been presented in the current Italian Parliament, spurred into action mainly by the Constitutional Court's ruling and the need to address the uncertain status of the provincial level of government in light of the negative outcome of the 2016 constitutional referendum.The proposed laws offer an array of novel amendments to the current system.The most recurrent measure involves the direct election of the both the metropolitan mayor and the MC, a solution that substantively represents a return to the prior provincial election system (and could be motivated merely by the will to generate additional selective incentives to distribute among party activists); the direct election of the MC would undoubtedly mean foregoing some of indirect voting's indisputable advantages (less cumbersome procedures, lower expenditure, potentially more competent voters).Other proposals pertaining to election norms would extend the Delrio system for selecting provincial presidents (indirect election, demographic weighting) to metropolitan mayors and introduce the option of double gender preferences in MC elections.None of the potential amendments currently being discussed in Parliament directly addresses the problems identified in this article, nor pays any attention to the issue of demographic weighting, nor involves the possible remedies laid out in the previous two sections.
A compromise that does preserve both demographic weighting and the conferral of greater powers to larger towns is the "square-root method" explained in Section 6.The simulations developed there show that this alternative scheme would attenuate the current imbalance and introduce non-radical changes in the political outcomes.The positive changes could arguably be more marked if turnout were to be positively affected by square-root weighting.More generally, however, the square-root method and the bulk of parliamentary bills under discussion seem to subscribe acritically to a problematic, latent, yet crucial assumption of the Delrio Law: municipalities having roughly the same population size (and potentially nothing else in common) comprise a viable, interest-based community.It bears repeating: MC elections implement just one criterion (municipalities' population size) in their operational definition of territorial representation.
The 8 MCs that lie at the heart of this article have jurisdiction over a variety of important policy areas and host a population of over 15 million people (according to the 2011 census used for determining demographic weighting), who deserve better.

Figure 1 .
Figure 1.Voter turnout (valid votes for lists) by demographic bracket (percentage values) r & c-l) * Venice with shorter term (municipal elections in capital city no later than autumn 2025) ** Dissolution of initial majority in case of non-re-election.

Table 1 .
Political outcomes of the 2021-22 MC elections (majorities in bold)

Table 2 .
Ballot weighting coefficients and (theoretical) number of voters in the 2021-22 MC elections * Venice * Bologna * Milan * Rome ** Turin * Note: Corrective thresholds applied for demographic brackets > 35% * or single municipality > 45% ** .The dotted line separates the coefficients applied to the capital city from those applied to other municipalities.

Table 3 .
Territorial profile of the 2021-22 MC elections (% values, column totals within each metro city = 100), by demographic bracket (000s of residents) Table3sheds light on the make-up of each metro city's population, potential voters, potential weighted votes, actual voters, and actual weighted votes (as well as candidates and electees, which will be discussed later).If one considers Turin, for example, the two least populated brackets (A and B) account for 17.0% of potential weighted votes but only 11.5% of actual weighted votes (-5.5 percentage points), due to relatively low turnout among the electorate of those two brackets; conversely, the most populous brackets (E to I) account for 54.6% of potential weighted votes and 60.4% (+5.8 percentage points) of actual weighted votes, due to relatively high turnout achieved in those brackets.Similar (albeit smaller) shifts in favour of voters from larger towns can be observed in each of the other MC elections.
. If one compares the "potential voters" and "candidates" distributions in that table, it is clear that the being a mayor/councillor originating from a larger town (and especially one with at least 100,000 inhabitants) dramatically improves one's chances of being included in a candidate list; conversely, coming from a smaller town renders a candidacy relatively less likely.(Genova is a partial exception: the candidates' demographic distribution is not too dissimilar from the electorate's, and indeed the highest candidacy rate is recorded in the C bracket; Reggio Calabria also displays a comparatively high candidacy rate in the C bracket.)Running for a seat does not mean getting elected, of course: in the 8 MCs considered here, 515 candidates competed for 158 seats.In each MC election, candidates

Table 4
Overall, candidates receiving at least one preference from a CCV have a 76% chance (between 68 to 86% in the elections considered separately) of getting elected, versus a mere 8% chance (0 to 20%) if they have no CCV backing.Genova's MC is an extreme example: not even one candidate was elected without a CCV's support.
, which develops a typology of candidates on the basis of two criteria: election vs. non-election and reception/non-reception of at least one preference from a capital city voter (CCV).Although support from at least one CCV is neither a necessary nor a sufficient condition for election, it is exceedingly beneficial.

Table 4 .
Candidates by elected status and reception of support from capital city voters (CCVs) So, as the Delrio Law intended, the elected representatives of larger towns, and especially of capital cities, have a greater say in shaping the MC: the latter is presided over by the capital city's mayor; CCVs enjoy robust firepower at the polling station due to demographic weighting (and the relatively small number of CCVs).But, perhaps beyond the legislators' intentions, CCVs' electoral efficacy is additionally enhanced by differential voter turnout.CCVs also have a higher likelihood of being included in candidate lists and being elected.In any case, support from at least one CCV is almost a prerequisite for a candidate's election, highlighting CCVs' overwhelming clout.8

Table 5 .
Institutional sustainability in the MCs elected in 2021-22

Table 6 .
Implementation of the square-root method in two MC elections

Table 7 .
Political outcomes (list) of the implementation of the square-root method in the 2021-22 MC elections

Table 2 )
. Italian MC elections, and their use of demographic weighting, are an effective example of this interpretative approach.MC elections, as regulated by the Delrio Law, are conducted via an indirect, list-based system heavily shaped by demographic weighting.Larger towns, especially capitals, tend to be governed by established party organizations, giving them a clear advantage, right who -by design -account for a significant share of electoral firepower; it is predictably easier for established political actors to organize lists, recruit candidates and coach voters.(In order to be included in an MC election, a list must be formally supported by 5% of potential voters, i.e., in the metro cities examined here, by at least several dozen to almost 200 individuals.)Smaller councils need to coordinate a much larger number of voters, distributed among a much higher number of socially and geographically diverse towns, to attain a minimal of efficacy.It is not surprising that MC elections are accompanied by a low degree of public visibility; campaigns essentially consist of activities aiming to mobilize voters and provide them with behaviour guidance that takes place behind closed doors.
Centralized coordination of both list formation and, especially, voter behaviour is clearly incentivized by the MC electoral system.In all of the capital cities (and, indeed, in all towns with at least 100,000 residents), municipal councils comprise just a few dozen MC voters (see second half of